Recover the square spiral example code.
I hve no idea how this isn't in VCS. I checked hg and git. Is it in an old branch that I deleted before merging or something? I have backups from which to restore, but it would be nice to know how I effed it up in the first place, eh?
This commit is contained in:
Simon Forman
@@ -34,6 +34,31 @@ itself.
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.. _Concatinative: https://en.wikipedia.org/wiki/Concatenative_programming_language
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Example Code
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--------------------------------------------------
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Here is an example of Joy code::
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[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
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It might seem unreadable but with a little familiarity it becomes just as
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legible as any other notation. Some layout helps::
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[ [[abs] ii <=]
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[
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[<>] [pop !-] ||
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] &&
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]
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[[ !-] [[++]] [[--]] ifte dip]
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[[pop !-] [--] [++] ifte ]
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ifte
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This function accepts two integers on the stack and increments or
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decrements one of them such that the new pair of numbers is the next
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coordinate pair in a square spiral (like the kind used to construct an
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Ulam Spiral). For more information see :doc:`notebooks/Square_Spiral`
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Quick Start
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--------------------------------------------------
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+31
-31
@@ -76,7 +76,7 @@ E.g.:
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Implementation
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--------------
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.. code:: python
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.. code:: ipython2
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from functools import partial as curry
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from itertools import product
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@@ -86,7 +86,7 @@ Implementation
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The empty set and the set of just the empty string.
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.. code:: python
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.. code:: ipython2
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phi = frozenset() # ϕ
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y = frozenset({''}) # λ
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@@ -101,7 +101,7 @@ alphabet with two symbols (if you had to.)
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I chose the names ``O`` and ``l`` (uppercase “o” and lowercase “L”) to
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look like ``0`` and ``1`` (zero and one) respectively.
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.. code:: python
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.. code:: ipython2
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syms = O, l = frozenset({'0'}), frozenset({'1'})
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@@ -123,7 +123,7 @@ expression* is one of:
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Where ``R`` and ``S`` stand for *regular expressions*.
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.. code:: python
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.. code:: ipython2
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AND, CONS, KSTAR, NOT, OR = 'and cons * not or'.split() # Tags are just strings.
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@@ -133,7 +133,7 @@ only, these datastructures are immutable.
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String Representation of RE Datastructures
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.. code:: python
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.. code:: ipython2
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def stringy(re):
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'''
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@@ -175,11 +175,11 @@ Match anything. Often spelled “.”
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I = (0|1)*
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.. code:: python
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.. code:: ipython2
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I = (KSTAR, (OR, O, l))
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.. code:: python
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.. code:: ipython2
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print stringy(I)
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@@ -201,14 +201,14 @@ The example expression from Brzozowski:
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Note that it contains one of everything.
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.. code:: python
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.. code:: ipython2
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a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I))))
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b = (CONS, I, (CONS, O, l))
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c = (CONS, l, (KSTAR, l))
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it = (AND, a, (NOT, (OR, b, c)))
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.. code:: python
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.. code:: ipython2
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print stringy(it)
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@@ -223,7 +223,7 @@ Note that it contains one of everything.
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Let’s get that auxiliary predicate function ``δ`` out of the way.
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.. code:: python
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.. code:: ipython2
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def nully(R):
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'''
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@@ -263,7 +263,7 @@ This is the straightforward version with no “compaction”. It works fine,
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but does waaaay too much work because the expressions grow each
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derivation.
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.. code:: python
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.. code:: ipython2
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def D(symbol):
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@@ -308,7 +308,7 @@ derivation.
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Compaction Rules
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~~~~~~~~~~~~~~~~
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.. code:: python
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.. code:: ipython2
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def _compaction_rule(relation, one, zero, a, b):
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return (
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@@ -320,7 +320,7 @@ Compaction Rules
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An elegant symmetry.
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.. code:: python
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.. code:: ipython2
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# R ∧ I = I ∧ R = R
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# R ∧ ϕ = ϕ ∧ R = ϕ
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@@ -341,7 +341,7 @@ We can save re-processing by remembering results we have already
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computed. RE datastructures are immutable and the ``derv()`` functions
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are *pure* so this is fine.
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.. code:: python
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.. code:: ipython2
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class Memo(object):
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@@ -365,7 +365,7 @@ With “Compaction”
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This version uses the rules above to perform compaction. It keeps the
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expressions from growing too large.
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.. code:: python
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.. code:: ipython2
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def D_compaction(symbol):
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@@ -414,7 +414,7 @@ Let’s try it out…
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(FIXME: redo.)
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.. code:: python
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.. code:: ipython2
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o, z = D_compaction('0'), D_compaction('1')
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REs = set()
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@@ -533,10 +533,10 @@ machine transition table.
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Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”
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.. figure:: omg.svg
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:alt: State Machine Graph
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.. figure:: attachment:omg.svg
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:alt: omg.svg
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State Machine Graph
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omg.svg
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Start at ``a`` and follow the transition arrows according to their
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labels. Accepting states have a double outline. (Graphic generated with
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@@ -605,20 +605,20 @@ You can see the one-way nature of the ``g`` state and the ``hij`` “trap”
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in the way that the ``.111.`` on the left-hand side of the ``&``
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disappears once it has been matched.
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.. code:: python
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.. code:: ipython2
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from collections import defaultdict
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from pprint import pprint
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from string import ascii_lowercase
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.. code:: python
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.. code:: ipython2
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d0, d1 = D_compaction('0'), D_compaction('1')
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``explore()``
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~~~~~~~~~~~~~
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.. code:: python
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.. code:: ipython2
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def explore(re):
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@@ -645,7 +645,7 @@ disappears once it has been matched.
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return table, accepting
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.. code:: python
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.. code:: ipython2
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table, accepting = explore(it)
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table
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@@ -678,7 +678,7 @@ disappears once it has been matched.
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.. code:: python
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.. code:: ipython2
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accepting
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@@ -697,7 +697,7 @@ Generate Diagram
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Once we have the FSM table and the set of accepting states we can
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generate the diagram above.
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.. code:: python
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.. code:: ipython2
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_template = '''\
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digraph finite_state_machine {
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@@ -722,7 +722,7 @@ generate the diagram above.
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)
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)
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.. code:: python
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.. code:: ipython2
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print make_graph(table, accepting)
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@@ -776,7 +776,7 @@ Trampoline Function
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Python has no GOTO statement but we can fake it with a “trampoline”
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function.
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.. code:: python
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.. code:: ipython2
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def trampoline(input_, jump_from, accepting):
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I = iter(input_)
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@@ -793,7 +793,7 @@ Stream Functions
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Little helpers to process the iterator of our data (a “stream” of “1”
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and “0” characters, not bits.)
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.. code:: python
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.. code:: ipython2
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getch = lambda I: int(next(I))
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@@ -816,7 +816,7 @@ code. (You have to imagine that these are GOTO statements in C or
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branches in assembly and that the state names are branch destination
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labels.)
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.. code:: python
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.. code:: ipython2
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a = lambda I: c if getch(I) else b
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b = lambda I: _0(I) or d
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@@ -833,12 +833,12 @@ Note that the implementations of ``h`` and ``g`` are identical ergo
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``h = g`` and we could eliminate one in the code but ``h`` is an
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accepting state and ``g`` isn’t.
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.. code:: python
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.. code:: ipython2
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def acceptable(input_):
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return trampoline(input_, a, {h, i})
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.. code:: python
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.. code:: ipython2
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for n in range(2**5):
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s = bin(n)[2:]
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@@ -3,7 +3,7 @@ Using ``x`` to Generate Values
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Cf. jp-reprod.html
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.. code:: python
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.. code:: ipython2
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from notebook_preamble import J, V, define
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@@ -57,7 +57,7 @@ We can make a generator for the Natural numbers (0, 1, 2, …) by using
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Let’s try it:
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.. code:: python
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.. code:: ipython2
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V('[0 swap [dup ++] dip rest cons] x')
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@@ -81,7 +81,7 @@ Let’s try it:
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After one application of ``x`` the quoted program contains ``1`` and
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``0`` is below it on the stack.
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.. code:: python
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.. code:: ipython2
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J('[0 swap [dup ++] dip rest cons] x x x x x pop')
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@@ -94,11 +94,11 @@ After one application of ``x`` the quoted program contains ``1`` and
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``direco``
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----------
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.. code:: python
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.. code:: ipython2
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define('direco == dip rest cons')
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.. code:: python
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.. code:: ipython2
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V('[0 swap [dup ++] direco] x')
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@@ -149,13 +149,13 @@ Reading from the bottom up:
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G == [direco] cons [swap] swap concat cons
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G == [direco] cons [swap] swoncat cons
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.. code:: python
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.. code:: ipython2
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define('G == [direco] cons [swap] swoncat cons')
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Let’s try it out:
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.. code:: python
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.. code:: ipython2
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J('0 [dup ++] G')
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@@ -165,7 +165,7 @@ Let’s try it out:
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[0 swap [dup ++] direco]
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.. code:: python
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.. code:: ipython2
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J('0 [dup ++] G x x x pop')
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@@ -178,7 +178,7 @@ Let’s try it out:
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Powers of 2
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~~~~~~~~~~~
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.. code:: python
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.. code:: ipython2
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J('1 [dup 1 <<] G x x x x x x x x x pop')
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@@ -194,7 +194,7 @@ Powers of 2
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If we have one of these quoted programs we can drive it using ``times``
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with the ``x`` combinator.
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.. code:: python
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.. code:: ipython2
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J('23 [dup ++] G 5 [x] times')
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@@ -226,11 +226,11 @@ int:
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And pick them off by masking with 3 (binary 11) and then shifting the
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int right two bits.
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.. code:: python
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.. code:: ipython2
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define('PE1.1 == dup [3 &] dip 2 >>')
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.. code:: python
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.. code:: ipython2
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V('14811 PE1.1')
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@@ -252,7 +252,7 @@ int right two bits.
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If we plug ``14811`` and ``[PE1.1]`` into our generator form…
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.. code:: python
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.. code:: ipython2
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J('14811 [PE1.1] G')
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@@ -264,7 +264,7 @@ If we plug ``14811`` and ``[PE1.1]`` into our generator form…
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…we get a generator that works for seven cycles before it reaches zero:
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.. code:: python
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.. code:: ipython2
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J('[14811 swap [PE1.1] direco] 7 [x] times')
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@@ -280,11 +280,11 @@ Reset at Zero
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We need a function that checks if the int has reached zero and resets it
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if so.
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.. code:: python
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.. code:: ipython2
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define('PE1.1.check == dup [pop 14811] [] branch')
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.. code:: python
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.. code:: ipython2
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J('14811 [PE1.1.check PE1.1] G')
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@@ -294,7 +294,7 @@ if so.
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[14811 swap [PE1.1.check PE1.1] direco]
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.. code:: python
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.. code:: ipython2
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J('[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times')
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@@ -316,7 +316,7 @@ In the PE1 problem we are asked to sum all the multiples of three and
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five less than 1000. It’s worked out that we need to use all seven
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numbers sixty-six times and then four more.
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.. code:: python
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.. code:: ipython2
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J('7 66 * 4 +')
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@@ -328,7 +328,7 @@ numbers sixty-six times and then four more.
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If we drive our generator 466 times and sum the stack we get 999.
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.. code:: python
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.. code:: ipython2
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J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times')
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@@ -338,7 +338,7 @@ If we drive our generator 466 times and sum the stack we get 999.
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3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] direco]
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|
||||
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||||
.. code:: python
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||||
.. code:: ipython2
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||||
|
||||
J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum')
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@@ -351,13 +351,13 @@ If we drive our generator 466 times and sum the stack we get 999.
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Project Euler Problem One
|
||||
-------------------------
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||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('PE1.2 == + dup [+] dip')
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|
||||
Now we can add ``PE1.2`` to the quoted program given to ``G``.
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|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop')
|
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|
||||
@@ -445,15 +445,15 @@ Putting it all together:
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||||
F == + [popdd over] cons infra uncons
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fib_gen == [1 1 F]
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('fib == + [popdd over] cons infra uncons')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('fib_gen == [1 1 fib]')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('fib_gen 10 [x] times')
|
||||
|
||||
@@ -473,14 +473,14 @@ Now that we have a generator for the Fibonacci sequence, we need a
|
||||
function that adds a term in the sequence to a sum if it is even, and
|
||||
``pop``\ s it otherwise.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('PE2.1 == dup 2 % [+] [pop] branch')
|
||||
|
||||
And a predicate function that detects when the terms in the series
|
||||
“exceed four million”.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('>4M == 4000000 >')
|
||||
|
||||
@@ -488,11 +488,11 @@ Now it’s straightforward to define ``PE2`` as a recursive function that
|
||||
generates terms in the Fibonacci sequence until they exceed four million
|
||||
and sums the even ones.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('PE2')
|
||||
|
||||
@@ -535,7 +535,7 @@ So the Fibonacci sequence considered in terms of just parity would be:
|
||||
|
||||
Every third term is even.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1 0 fib] x x x') # To start the sequence with 1 1 2 3 instead of 1 2 3.
|
||||
|
||||
@@ -547,7 +547,7 @@ Every third term is even.
|
||||
|
||||
Drive the generator three times and ``popop`` the two odd terms.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1 0 fib] x x x [popop] dipd')
|
||||
|
||||
@@ -557,11 +557,11 @@ Drive the generator three times and ``popop`` the two odd terms.
|
||||
2 [3 2 fib]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('PE2.2 == x x x [popop] dipd')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1 0 fib] 10 [PE2.2] times')
|
||||
|
||||
@@ -574,7 +574,7 @@ Drive the generator three times and ``popop`` the two odd terms.
|
||||
Replace ``x`` with our new driver function ``PE2.2`` and start our
|
||||
``fib`` generator at ``1 0``.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec')
|
||||
|
||||
@@ -593,11 +593,11 @@ modifications to the default ``x``?
|
||||
An Interesting Variation
|
||||
------------------------
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('codireco == cons dip rest cons')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('[0 [dup ++] codireco] x')
|
||||
|
||||
@@ -620,11 +620,11 @@ An Interesting Variation
|
||||
0 [1 [dup ++] codireco] .
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('G == [codireco] cons cons')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('230 [dup ++] G 5 [x] times pop')
|
||||
|
||||
|
||||
@@ -7,7 +7,7 @@ to write a function that can compute the square root of a number.
|
||||
Cf. `"Why Functional Programming Matters" by John
|
||||
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
@@ -75,11 +75,11 @@ The generator can be written as:
|
||||
1 [23 over / + 2 /] [dup] swoncat make_generator
|
||||
1 [dup 23 over / + 2 /] make_generator
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 gsra')
|
||||
|
||||
@@ -92,7 +92,7 @@ The generator can be written as:
|
||||
Let's drive the generator a few time (with the ``x`` combinator) and
|
||||
square the approximation to see how well it works...
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 gsra 6 [x popd] times first sqr')
|
||||
|
||||
@@ -142,7 +142,7 @@ Predicate
|
||||
abs(a-b) ε <=
|
||||
(abs(a-b)<=ε)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_P [first - abs] dip <=')
|
||||
|
||||
@@ -156,7 +156,7 @@ Base-Case
|
||||
[b G] first
|
||||
b
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_B roll< popop first')
|
||||
|
||||
@@ -184,7 +184,7 @@ Pretty straightforward:
|
||||
|
||||
b [c G] ε within
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_R [popd x] dip')
|
||||
|
||||
@@ -199,14 +199,14 @@ The recursive function we have defined so far needs a slight preamble:
|
||||
[a G] x ε ...
|
||||
a [b G] ε ...
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
|
||||
define('sqrt gsra within')
|
||||
|
||||
Try it out...
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
J('36 sqrt')
|
||||
|
||||
@@ -216,7 +216,7 @@ Try it out...
|
||||
6.0
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 sqrt')
|
||||
|
||||
@@ -228,7 +228,7 @@ Try it out...
|
||||
|
||||
Check it.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
4.795831523312719**2
|
||||
|
||||
@@ -241,7 +241,7 @@ Check it.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython3
|
||||
|
||||
from math import sqrt
|
||||
|
||||
|
||||
@@ -36,7 +36,7 @@ implementation under the hood. (Where does the “type” come from? It has
|
||||
a contingent existence predicated on the disciplined use of these
|
||||
functions on otherwise undistinguished Joy datastructures.)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from notebook_preamble import D, J, V, define, DefinitionWrapper
|
||||
|
||||
@@ -87,11 +87,11 @@ Definition:
|
||||
|
||||
Tree-new == swap [[] []] cons cons
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('Tree-new == swap [[] []] cons cons')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('"v" "k" Tree-new')
|
||||
|
||||
@@ -163,11 +163,11 @@ comparison operator:
|
||||
P < == pop roll> pop first <
|
||||
P == pop roll> pop first
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('P == pop roll> pop first')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["old_key" 23 [] []] 17 "new_key" ["..."] P')
|
||||
|
||||
@@ -242,11 +242,11 @@ And so ``T`` is just:
|
||||
|
||||
T == cons cons [dipdd] cons infra
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('T == cons cons [dipdd] cons infra')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T')
|
||||
|
||||
@@ -266,7 +266,7 @@ This is very very similar to the above:
|
||||
[key_n value_n left right] value key [Tree-add] E
|
||||
[key_n value_n left right] value key [Tree-add] [P <] [Te] [Ee] ifte
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('E == [P <] [Te] [Ee] ifte')
|
||||
|
||||
@@ -278,11 +278,11 @@ instead of the right, so the only difference is that it must use
|
||||
|
||||
Te == cons cons [dipd] cons infra
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('Te == cons cons [dipd] cons infra')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te')
|
||||
|
||||
@@ -320,11 +320,11 @@ Example:
|
||||
key new_value [ left right] cons cons
|
||||
[key new_value left right]
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('Ee == pop swap roll< rest rest cons cons')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee')
|
||||
|
||||
@@ -355,14 +355,14 @@ Putting it all together:
|
||||
|
||||
Tree-add == [popop not] [[pop] dipd Tree-new] [] [R] genrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec')
|
||||
|
||||
Examples
|
||||
~~~~~~~~
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[] 23 "b" Tree-add') # Initial
|
||||
|
||||
@@ -372,7 +372,7 @@ Examples
|
||||
['b' 23 [] []]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["b" 23 [] []] 88 "c" Tree-add') # Greater than
|
||||
|
||||
@@ -382,7 +382,7 @@ Examples
|
||||
['b' 23 [] ['c' 88 [] []]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["b" 23 [] []] 88 "a" Tree-add') # Less than
|
||||
|
||||
@@ -392,7 +392,7 @@ Examples
|
||||
['b' 23 ['a' 88 [] []] []]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["b" 23 [] []] 88 "b" Tree-add') # Equal to
|
||||
|
||||
@@ -402,7 +402,7 @@ Examples
|
||||
['b' 88 [] []]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Series.
|
||||
|
||||
@@ -412,7 +412,7 @@ Examples
|
||||
['b' 23 ['a' 88 [] []] ['c' 44 [] []]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step')
|
||||
|
||||
@@ -444,7 +444,7 @@ values:
|
||||
------------------------- a < b
|
||||
L
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("1 0 ['G'] ['E'] ['L'] cmp")
|
||||
|
||||
@@ -454,7 +454,7 @@ values:
|
||||
'G'
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("1 1 ['G'] ['E'] ['L'] cmp")
|
||||
|
||||
@@ -464,7 +464,7 @@ values:
|
||||
'E'
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("0 1 ['G'] ['E'] ['L'] cmp")
|
||||
|
||||
@@ -514,7 +514,7 @@ Or just:
|
||||
|
||||
P == over [popop popop first] nullary
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('P == over [popop popop first] nullary')
|
||||
|
||||
@@ -541,11 +541,11 @@ to understand:
|
||||
|
||||
Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add') # Still works.
|
||||
|
||||
@@ -685,14 +685,14 @@ Working backward:
|
||||
|
||||
Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec')
|
||||
|
||||
Examples
|
||||
~~~~~~~~
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[] [foo] Tree-iter') # It doesn't matter what F is as it won't be used.
|
||||
|
||||
@@ -702,7 +702,7 @@ Examples
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter")
|
||||
|
||||
@@ -712,7 +712,7 @@ Examples
|
||||
'b' 'a' 'c'
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter")
|
||||
|
||||
@@ -731,7 +731,7 @@ to it will only occur once within it, and we can query it in
|
||||
`:math:`O(\log_2 N)` <https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2>`__
|
||||
time.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step')
|
||||
|
||||
@@ -741,11 +741,11 @@ time.
|
||||
[3 0 [2 0 [] []] [9 0 [5 0 [4 0 [] []] [8 0 [6 0 [] [7 0 [] []]] []]] []]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('to_set == [] swap [0 swap Tree-add] step')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[3 9 5 2 8 6 7 8 4] to_set')
|
||||
|
||||
@@ -758,11 +758,11 @@ time.
|
||||
And with that we can write a little program ``unique`` to remove
|
||||
duplicate items from a list.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('unique == [to_set [first] Tree-iter] cons run')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique') # Filter duplicate items.
|
||||
|
||||
@@ -872,7 +872,7 @@ Let’s do a little semantic factoring:
|
||||
|
||||
Now we can sort sequences.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
#define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec')
|
||||
|
||||
@@ -892,7 +892,7 @@ Now we can sort sequences.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order')
|
||||
|
||||
@@ -1070,7 +1070,7 @@ So:
|
||||
|
||||
Tree-get == [pop not] swap [] [P [T>] [E] [T<] cmp] genrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
# I don't want to deal with name conflicts with the above so I'm inlining everything here.
|
||||
# The original Joy system has "hide" which is a meta-command which allows you to use named
|
||||
@@ -1088,7 +1088,7 @@ So:
|
||||
] genrec
|
||||
''')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get')
|
||||
|
||||
@@ -1098,7 +1098,7 @@ So:
|
||||
'mike not in tree'
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('["gary" 23 [] []] "gary" [popop "err"] Tree-get')
|
||||
|
||||
@@ -1108,7 +1108,7 @@ So:
|
||||
23
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('''
|
||||
|
||||
@@ -1124,7 +1124,7 @@ So:
|
||||
2
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('''
|
||||
|
||||
@@ -1500,7 +1500,7 @@ Refactoring
|
||||
By the standards of the code I’ve written so far, this is a *huge* Joy
|
||||
program.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
DefinitionWrapper.add_definitions('''
|
||||
first_two == uncons uncons pop
|
||||
@@ -1519,7 +1519,7 @@ program.
|
||||
Tree-Delete == [pop not] [pop] [R0] [R1] genrec
|
||||
''', D)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete ")
|
||||
|
||||
@@ -1529,7 +1529,7 @@ program.
|
||||
['a' 23 [] ['b' 88 [] []]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete ")
|
||||
|
||||
@@ -1539,7 +1539,7 @@ program.
|
||||
['a' 23 [] ['c' 44 [] []]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete ")
|
||||
|
||||
@@ -1549,7 +1549,7 @@ program.
|
||||
['b' 88 [] ['c' 44 [] []]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete ")
|
||||
|
||||
@@ -1559,7 +1559,7 @@ program.
|
||||
['a' 23 [] ['b' 88 [] ['c' 44 [] []]]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step')
|
||||
|
||||
@@ -1569,7 +1569,7 @@ program.
|
||||
[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete ")
|
||||
|
||||
@@ -1579,7 +1579,7 @@ program.
|
||||
[4 0 [2 0 [1 0 [] []] []] [6 0 [5 0 [] []] [7 0 [] []]]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete ")
|
||||
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
@@ -81,13 +81,13 @@ the variables:
|
||||
The three arguments are to the left, so we can “chop off” everything to
|
||||
the right and say it’s the definition of the ``quadratic`` function:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
|
||||
|
||||
Let’s try it out:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('3 1 1 quadratic')
|
||||
|
||||
@@ -102,7 +102,7 @@ lines are the ``dip`` and ``dipd`` combinators building the main program
|
||||
by incorporating the values on the stack. Then that program runs and you
|
||||
get the results. This is pretty typical of Joy code.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('-5 1 4 quadratic')
|
||||
|
||||
|
||||
@@ -1,4 +1,4 @@
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from notebook_preamble import D, DefinitionWrapper, J, V, define
|
||||
|
||||
@@ -80,7 +80,7 @@ is a recursive function ``H :: A -> C`` that converts a value of type
|
||||
It may be helpful to see this function implemented in imperative Python
|
||||
code.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def hylomorphism(c, F, P, G):
|
||||
'''Return a hylomorphism function H.'''
|
||||
@@ -185,7 +185,7 @@ the left so we have a definition for ``hylomorphism``:
|
||||
|
||||
hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec')
|
||||
|
||||
@@ -203,13 +203,13 @@ To sum a range of integers from 0 to *n* - 1:
|
||||
- ``[G]`` is ``[-- dup]``
|
||||
- ``[F]`` is ``[+]``
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism')
|
||||
|
||||
Let’s try it:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('5 triangular_number')
|
||||
|
||||
@@ -219,7 +219,7 @@ Let’s try it:
|
||||
10
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[0 1 2 3 4 5 6] [triangular_number] map')
|
||||
|
||||
@@ -391,10 +391,8 @@ values.
|
||||
|
||||
A == [P] [] [G] [swons] hylomorphism
|
||||
|
||||
``range`` et. al.
|
||||
~~~~~~~~~~~~~~~~~
|
||||
|
||||
An example of an anamorphism is the ``range`` function which generates the list of integers from 0 to *n* - 1 given *n*.
|
||||
``range`` et. al. An example of an anamorphism is the ``range`` function which generates the list of integers from 0 to *n* - 1 given *n*.
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Each of the above variations can be used to make four slightly different
|
||||
``range`` functions.
|
||||
@@ -407,11 +405,11 @@ Each of the above variations can be used to make four slightly different
|
||||
H1 == [P] [pop c] [G] [dip F] genrec
|
||||
== [0 <=] [pop []] [-- dup] [dip swons] genrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('range == [0 <=] [] [-- dup] [swons] hylomorphism')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('5 range')
|
||||
|
||||
@@ -429,11 +427,11 @@ Each of the above variations can be used to make four slightly different
|
||||
H2 == c swap [P] [pop] [G [F] dip] primrec
|
||||
== [] swap [0 <=] [pop] [-- dup [swons] dip] primrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('5 range_reverse')
|
||||
|
||||
@@ -451,11 +449,11 @@ Each of the above variations can be used to make four slightly different
|
||||
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
|
||||
== [0 <=] [pop []] [[--] dupdip] [dip swons] genrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('5 ranger')
|
||||
|
||||
@@ -473,11 +471,11 @@ Each of the above variations can be used to make four slightly different
|
||||
H4 == c swap [P] [pop] [[F] dupdip G ] primrec
|
||||
== [] swap [0 <=] [pop] [[swons] dupdip --] primrec
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('5 ranger_reverse')
|
||||
|
||||
@@ -503,7 +501,7 @@ and makes some new value.
|
||||
|
||||
C == [not] c [uncons swap] [F] hylomorphism
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('swuncons == uncons swap') # Awkward name.
|
||||
|
||||
@@ -513,11 +511,11 @@ An example of a catamorphism is the sum function.
|
||||
|
||||
sum == [not] 0 [swuncons] [+] hylomorphism
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('sum == [not] 0 [swuncons] [+] hylomorphism')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[5 4 3 2 1] sum')
|
||||
|
||||
@@ -533,7 +531,7 @@ The ``step`` combinator
|
||||
The ``step`` combinator will usually be better to use than
|
||||
``catamorphism``.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[step] help')
|
||||
|
||||
@@ -562,11 +560,11 @@ The ``step`` combinator will usually be better to use than
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('sum == 0 swap [+] step')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[5 4 3 2 1] sum')
|
||||
|
||||
@@ -594,11 +592,11 @@ With:
|
||||
G == --
|
||||
P == 1 <=
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('5 factorial')
|
||||
|
||||
@@ -637,11 +635,11 @@ We would use:
|
||||
G == rest dup
|
||||
P == not
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1 2 3] tails')
|
||||
|
||||
|
||||
@@ -9,14 +9,14 @@ dictionary. However, there’s no function that does that. Adding a new
|
||||
function to the dictionary is a meta-interpreter action, you have to do
|
||||
it in Python, not Joy.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from notebook_preamble import D, J, V
|
||||
|
||||
A long trace
|
||||
------------
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('[23 18] average')
|
||||
|
||||
@@ -81,7 +81,7 @@ An efficient ``sum`` function is already in the library. But for
|
||||
``size`` we can use a “compiled” version hand-written in Python to speed
|
||||
up evaluation and make the trace more readable.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from joy.library import SimpleFunctionWrapper
|
||||
from joy.utils.stack import iter_stack
|
||||
@@ -99,7 +99,7 @@ up evaluation and make the trace more readable.
|
||||
Now we replace the old version in the dictionary with the new version,
|
||||
and re-evaluate the expression.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
D['size'] = size
|
||||
|
||||
@@ -108,7 +108,7 @@ A shorter trace
|
||||
|
||||
You can see that ``size`` now executes in a single step.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('[23 18] average')
|
||||
|
||||
|
||||
@@ -0,0 +1,421 @@
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
Square Spiral Example Joy Code
|
||||
==============================
|
||||
|
||||
Here is the example of Joy code from the ``README`` file:
|
||||
|
||||
::
|
||||
|
||||
[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
|
||||
|
||||
It might seem unreadable but with a little familiarity it becomes just
|
||||
as legible as any other notation. Some layout helps:
|
||||
|
||||
::
|
||||
|
||||
[ [[abs] ii <=]
|
||||
[
|
||||
[<>] [pop !-] ||
|
||||
] &&
|
||||
]
|
||||
[[ !-] [[++]] [[--]] ifte dip]
|
||||
[[pop !-] [--] [++] ifte ]
|
||||
ifte
|
||||
|
||||
This function accepts two integers on the stack and increments or
|
||||
decrements one of them such that the new pair of numbers is the next
|
||||
coordinate pair in a square spiral (like the kind used to construct an
|
||||
Ulam Spiral).
|
||||
|
||||
Original Form
|
||||
-------------
|
||||
|
||||
It's adapted from `the original code on
|
||||
StackOverflow <https://stackoverflow.com/questions/398299/looping-in-a-spiral/31864777#31864777>`__:
|
||||
|
||||
If all you're trying to do is generate the first N points in the
|
||||
spiral (without the original problem's constraint of masking to an N
|
||||
x M region), the code becomes very simple:
|
||||
|
||||
::
|
||||
|
||||
void spiral(const int N)
|
||||
{
|
||||
int x = 0;
|
||||
int y = 0;
|
||||
for(int i = 0; i < N; ++i)
|
||||
{
|
||||
cout << x << '\t' << y << '\n';
|
||||
if(abs(x) <= abs(y) && (x != y || x >= 0))
|
||||
x += ((y >= 0) ? 1 : -1);
|
||||
else
|
||||
y += ((x >= 0) ? -1 : 1);
|
||||
}
|
||||
}
|
||||
|
||||
Translation to Joy
|
||||
------------------
|
||||
|
||||
I'm going to make a function that take two ints (``x`` and ``y``) and
|
||||
generates the next pair, we'll turn it into a generator later using the
|
||||
``x`` combinator.
|
||||
|
||||
First Boolean Predicate
|
||||
~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
We need a function that computes ``abs(x) <= abs(y)``, we can use ``ii``
|
||||
to apply ``abs`` to both values and then compare them with ``<=``:
|
||||
|
||||
::
|
||||
|
||||
[abs] ii <=
|
||||
|
||||
I've defined two short-circuiting Boolean combinators ``&&`` and ``||``
|
||||
that each accept two quoted predicate programs, run the first, and
|
||||
conditionally run the second only if required (to compute the final
|
||||
Boolean value). They run their predicate arguments ``nullary``.
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
define('&& [nullary] cons [nullary [0]] dip branch')
|
||||
define('|| [nullary] cons [nullary] dip [1] branch')
|
||||
|
||||
Given those, we can define ``x != y || x >= 0`` as:
|
||||
|
||||
::
|
||||
|
||||
[<>] [pop 0 >=] ||
|
||||
|
||||
And ``(abs(x) <= abs(y) && (x != y || x >= 0))`` as:
|
||||
|
||||
::
|
||||
|
||||
[[abs] ii <=] [[<>] [pop 0 >=] ||] &&
|
||||
|
||||
It's a little rough, but, as I say, with a little familiarity it becomes
|
||||
legible.
|
||||
|
||||
The Increment / Decrement Branches
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Turning to the branches of the main ``if`` statement:
|
||||
|
||||
::
|
||||
|
||||
x += ((y >= 0) ? 1 : -1);
|
||||
|
||||
Rewrite as a hybrid (pseudo-code) ``ifte`` expression:
|
||||
|
||||
::
|
||||
|
||||
[y >= 0] [x += 1] [X -= 1] ifte
|
||||
|
||||
Change each C phrase to Joy code:
|
||||
|
||||
::
|
||||
|
||||
[0 >=] [[++] dip] [[--] dip] ifte
|
||||
|
||||
Factor out the dip from each branch:
|
||||
|
||||
::
|
||||
|
||||
[0 >=] [[++]] [[--]] ifte dip
|
||||
|
||||
Similar logic applies to the other branch:
|
||||
|
||||
::
|
||||
|
||||
y += ((x >= 0) ? -1 : 1);
|
||||
|
||||
[x >= 0] [y -= 1] [y += 1] ifte
|
||||
|
||||
[pop 0 >=] [--] [++] ifte
|
||||
|
||||
"Not Negative"
|
||||
~~~~~~~~~~~~~~
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
define('!- 0 >=')
|
||||
|
||||
Putting the Pieces Together
|
||||
---------------------------
|
||||
|
||||
We can assemble the three functions we just defined in quotes and give
|
||||
them them to the ``ifte`` combinator. With some arrangement to show off
|
||||
the symmetry of the two branches, we have:
|
||||
|
||||
::
|
||||
|
||||
[[[abs] ii <=] [[<>] [pop !-] ||] &&]
|
||||
[[ !-] [[++]] [[--]] ifte dip]
|
||||
[[pop !-] [--] [++] ifte ]
|
||||
ifte
|
||||
|
||||
As I was writing this up I realized that, since the ``&&`` combinator
|
||||
doesn't consume the stack (below its quoted args), I can unquote the
|
||||
predicate, swap the branches, and use the ``branch`` combinator instead
|
||||
of ``ifte``:
|
||||
|
||||
::
|
||||
|
||||
[[abs] ii <=] [[<>] [pop !-] ||] &&
|
||||
[[pop !-] [--] [++] ifte ]
|
||||
[[ !-] [[++]] [[--]] ifte dip]
|
||||
branch
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
define('spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte')
|
||||
|
||||
Let's try it out:
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
J('0 0 spiral_next')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
1 0
|
||||
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
J('1 0 spiral_next')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
1 -1
|
||||
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
J('1 -1 spiral_next')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
0 -1
|
||||
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
J('0 -1 spiral_next')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
-1 -1
|
||||
|
||||
|
||||
Turning it into a Generator with ``x``
|
||||
--------------------------------------
|
||||
|
||||
It can be used with the x combinator to make a kind of generator for
|
||||
spiral square coordinates.
|
||||
|
||||
We can use ``codireco`` to make a generator
|
||||
|
||||
::
|
||||
|
||||
codireco ::= cons dip rest cons
|
||||
|
||||
It will look like this:
|
||||
|
||||
::
|
||||
|
||||
[value [F] codireco]
|
||||
|
||||
Here's a trace of how it works:
|
||||
|
||||
::
|
||||
|
||||
[0 [dup ++] codireco] . x
|
||||
[0 [dup ++] codireco] . 0 [dup ++] codireco
|
||||
[0 [dup ++] codireco] 0 . [dup ++] codireco
|
||||
[0 [dup ++] codireco] 0 [dup ++] . codireco
|
||||
[0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
|
||||
[0 [dup ++] codireco] [0 dup ++] . dip rest cons
|
||||
. 0 dup ++ [0 [dup ++] codireco] rest cons
|
||||
0 . dup ++ [0 [dup ++] codireco] rest cons
|
||||
0 0 . ++ [0 [dup ++] codireco] rest cons
|
||||
0 1 . [0 [dup ++] codireco] rest cons
|
||||
0 1 [0 [dup ++] codireco] . rest cons
|
||||
0 1 [[dup ++] codireco] . cons
|
||||
0 [1 [dup ++] codireco] .
|
||||
|
||||
But first we have to change the ``spiral_next`` function to work on a
|
||||
quoted pair of integers, and leave a copy of the pair on the stack.
|
||||
From:
|
||||
|
||||
::
|
||||
|
||||
y x spiral_next
|
||||
---------------------
|
||||
y' x'
|
||||
|
||||
to:
|
||||
|
||||
::
|
||||
|
||||
[x y] [spiral_next] infra
|
||||
-------------------------------
|
||||
[x' y']
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 0] [spiral_next] infra')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[0 1]
|
||||
|
||||
|
||||
So our generator is:
|
||||
|
||||
::
|
||||
|
||||
[[x y] [dup [spiral_next] infra] codireco]
|
||||
|
||||
Or rather:
|
||||
|
||||
::
|
||||
|
||||
[[0 0] [dup [spiral_next] infra] codireco]
|
||||
|
||||
There is a function ``make_generator`` that will build the generator for
|
||||
us out of the value and stepper function:
|
||||
|
||||
::
|
||||
|
||||
[0 0] [dup [spiral_next] infra] make_generator
|
||||
----------------------------------------------------
|
||||
[[0 0] [dup [spiral_next] infra] codireco]
|
||||
|
||||
Here it is in action:
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 0] [dup [spiral_next] infra] make_generator x x x x pop')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[0 0] [0 1] [-1 1] [-1 0]
|
||||
|
||||
|
||||
Four ``x`` combinators, four pairs of coordinates.
|
||||
|
||||
Conclusion
|
||||
----------
|
||||
|
||||
So that's an example of Joy code. It's a straightforward translation of
|
||||
the original. It's a little long for a single definition, you might
|
||||
break it up like so:
|
||||
|
||||
::
|
||||
|
||||
_spn_P ::= [[abs] ii <=] [[<>] [pop !-] ||] &&
|
||||
|
||||
_spn_T ::= [ !-] [[++]] [[--]] ifte dip
|
||||
_spn_E ::= [pop !-] [--] [++] ifte
|
||||
|
||||
spiral_next ::= _spn_P [_spn_E] [_spn_T] branch
|
||||
|
||||
This way it's easy to see that the function is a branch with two
|
||||
quasi-symmetrical paths.
|
||||
|
||||
We then used this function to make a simple generator of coordinate
|
||||
pairs, where the next pair in the series can be generated at any time by
|
||||
using the ``x`` combinator on the generator (which is just a quoted
|
||||
expression containing a copy of the current pair and the "stepper
|
||||
function" to generate the next pair from that.)
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
define('_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&')
|
||||
define('_spn_T [!-] [[++]] [[--]] ifte dip')
|
||||
define('_spn_E [pop !-] [--] [++] ifte')
|
||||
define('spiral_next _spn_P [_spn_E] [_spn_T] branch')
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
V('23 18 spiral_next')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. 23 18 spiral_next
|
||||
23 . 18 spiral_next
|
||||
23 18 . spiral_next
|
||||
23 18 . _spn_P [_spn_E] [_spn_T] branch
|
||||
23 18 . [[abs] ii <=] [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] . [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . && [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . [nullary] cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[<>] [pop !-] ||] [nullary] . cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] . [nullary [0]] dip branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] [nullary [0]] . dip branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] . nullary [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] . [stack] dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [stack] . dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [stack] . dip infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . stack [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [18 23] . [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [18 23] [[abs] ii <=] . infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . [abs] ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] . ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] . [dip] dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] [dip] . dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] . dip [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 . abs 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 . 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] . i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . abs <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
False . [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
False [18 23] . swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [False] . first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 False . [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 False [0] . [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 False [0] [[[<>] [pop !-] ||] nullary] . branch [_spn_E] [_spn_T] branch
|
||||
23 18 . 0 [_spn_E] [_spn_T] branch
|
||||
23 18 0 . [_spn_E] [_spn_T] branch
|
||||
23 18 0 [_spn_E] . [_spn_T] branch
|
||||
23 18 0 [_spn_E] [_spn_T] . branch
|
||||
23 18 . _spn_E
|
||||
23 18 . [pop !-] [--] [++] ifte
|
||||
23 18 [pop !-] . [--] [++] ifte
|
||||
23 18 [pop !-] [--] . [++] ifte
|
||||
23 18 [pop !-] [--] [++] . ifte
|
||||
23 18 [pop !-] [--] [++] . [nullary not] dipd branch
|
||||
23 18 [pop !-] [--] [++] [nullary not] . dipd branch
|
||||
23 18 [pop !-] . nullary not [--] [++] branch
|
||||
23 18 [pop !-] . [stack] dinfrirst not [--] [++] branch
|
||||
23 18 [pop !-] [stack] . dinfrirst not [--] [++] branch
|
||||
23 18 [pop !-] [stack] . dip infra first not [--] [++] branch
|
||||
23 18 . stack [pop !-] infra first not [--] [++] branch
|
||||
23 18 [18 23] . [pop !-] infra first not [--] [++] branch
|
||||
23 18 [18 23] [pop !-] . infra first not [--] [++] branch
|
||||
23 18 . pop !- [18 23] swaack first not [--] [++] branch
|
||||
23 . !- [18 23] swaack first not [--] [++] branch
|
||||
23 . 0 >= [18 23] swaack first not [--] [++] branch
|
||||
23 0 . >= [18 23] swaack first not [--] [++] branch
|
||||
True . [18 23] swaack first not [--] [++] branch
|
||||
True [18 23] . swaack first not [--] [++] branch
|
||||
23 18 [True] . first not [--] [++] branch
|
||||
23 18 True . not [--] [++] branch
|
||||
23 18 False . [--] [++] branch
|
||||
23 18 False [--] . [++] branch
|
||||
23 18 False [--] [++] . branch
|
||||
23 18 . --
|
||||
23 17 .
|
||||
|
||||
@@ -148,11 +148,11 @@ Working backwards:
|
||||
Define ``treestep``
|
||||
-------------------
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from notebook_preamble import D, J, V, define, DefinitionWrapper
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
DefinitionWrapper.add_definitions('''
|
||||
|
||||
@@ -173,7 +173,7 @@ all nodes in a tree with this function:
|
||||
|
||||
sumtree == [pop 0] [] [sum +] treestep
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('sumtree == [pop 0] [] [sum +] treestep')
|
||||
|
||||
@@ -185,7 +185,7 @@ Running this function on an empty tree value gives zero:
|
||||
------------------------------------
|
||||
0
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[] sumtree') # Empty tree.
|
||||
|
||||
@@ -205,7 +205,7 @@ Running it on a non-empty node:
|
||||
n m +
|
||||
n+m
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23] sumtree') # No child trees.
|
||||
|
||||
@@ -215,7 +215,7 @@ Running it on a non-empty node:
|
||||
23
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23 []] sumtree') # Child tree, empty.
|
||||
|
||||
@@ -225,7 +225,7 @@ Running it on a non-empty node:
|
||||
23
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23 [2 [4]] [3]] sumtree') # Non-empty child trees.
|
||||
|
||||
@@ -235,7 +235,7 @@ Running it on a non-empty node:
|
||||
32
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23 [2 [8] [9]] [3] [4 []]] sumtree') # Etc...
|
||||
|
||||
@@ -245,7 +245,7 @@ Running it on a non-empty node:
|
||||
49
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep') # Alternate "spelling".
|
||||
|
||||
@@ -255,7 +255,7 @@ Running it on a non-empty node:
|
||||
49
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep') # Replace each node.
|
||||
|
||||
@@ -265,7 +265,7 @@ Running it on a non-empty node:
|
||||
[23 [23 [23] [23]] [23] [23 []]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep')
|
||||
|
||||
@@ -275,7 +275,7 @@ Running it on a non-empty node:
|
||||
[1 [1 [1] [1]] [1] [1 []]]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree')
|
||||
|
||||
@@ -285,7 +285,7 @@ Running it on a non-empty node:
|
||||
6
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function.
|
||||
|
||||
@@ -295,7 +295,7 @@ Running it on a non-empty node:
|
||||
6
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function.
|
||||
|
||||
@@ -339,7 +339,7 @@ Traversal
|
||||
|
||||
This doesn’t quite work:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep')
|
||||
|
||||
@@ -369,7 +369,7 @@ So:
|
||||
|
||||
[] [first] [flatten cons] treestep
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep')
|
||||
|
||||
@@ -401,7 +401,7 @@ So:
|
||||
|
||||
[] [i roll< swons concat] [first] treestep
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep')
|
||||
|
||||
@@ -429,7 +429,7 @@ Plugging in our BTree structure:
|
||||
|
||||
[key value] N [left right] [K] C
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind')
|
||||
|
||||
@@ -444,7 +444,7 @@ Plugging in our BTree structure:
|
||||
|
||||
Iteration through the nodes
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind')
|
||||
|
||||
@@ -456,7 +456,7 @@ Iteration through the nodes
|
||||
|
||||
Sum the nodes’ keys.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind')
|
||||
|
||||
@@ -468,7 +468,7 @@ Sum the nodes’ keys.
|
||||
|
||||
Rebuild the tree using ``map`` (imitating ``treestep``.)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind')
|
||||
|
||||
@@ -574,7 +574,7 @@ Putting it together
|
||||
|
||||
To me, that seems simpler than the ``genrec`` version.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
DefinitionWrapper.add_definitions('''
|
||||
|
||||
@@ -587,7 +587,7 @@ To me, that seems simpler than the ``genrec`` version.
|
||||
|
||||
''', D)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('''\
|
||||
|
||||
@@ -603,7 +603,7 @@ To me, that seems simpler than the ``genrec`` version.
|
||||
15
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('''\
|
||||
|
||||
|
||||
@@ -1,7 +1,7 @@
|
||||
Type Checking
|
||||
=============
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
import logging, sys
|
||||
|
||||
@@ -11,7 +11,7 @@ Type Checking
|
||||
level=logging.INFO,
|
||||
)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from joy.utils.types import (
|
||||
doc_from_stack_effect,
|
||||
@@ -22,7 +22,7 @@ Type Checking
|
||||
JoyTypeError,
|
||||
)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
D = FUNCTIONS.copy()
|
||||
del D['product']
|
||||
@@ -31,7 +31,7 @@ Type Checking
|
||||
An Example
|
||||
----------
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0]
|
||||
|
||||
@@ -46,7 +46,7 @@ An Example
|
||||
40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(fi, fo)
|
||||
|
||||
@@ -56,13 +56,13 @@ An Example
|
||||
([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1])
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from joy.parser import text_to_expression
|
||||
from joy.utils.stack import stack_to_string
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
e = text_to_expression('0 1 2 [3 4]') # reverse order
|
||||
print stack_to_string(e)
|
||||
@@ -73,7 +73,7 @@ An Example
|
||||
[3 4] 2 1 0
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
u = unify(e, fi)[0]
|
||||
u
|
||||
@@ -87,7 +87,7 @@ An Example
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
g = reify(u, (fi, fo))
|
||||
print doc_from_stack_effect(*g)
|
||||
@@ -101,11 +101,11 @@ An Example
|
||||
Unification Works “in Reverse”
|
||||
------------------------------
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
e = text_to_expression('[2 3]')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
u = unify(e, fo)[0] # output side, not input side
|
||||
u
|
||||
@@ -119,7 +119,7 @@ Unification Works “in Reverse”
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
g = reify(u, (fi, fo))
|
||||
print doc_from_stack_effect(*g)
|
||||
@@ -133,7 +133,7 @@ Unification Works “in Reverse”
|
||||
Failing a Check
|
||||
---------------
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
fi, fo = infer(dup, mul)[0]
|
||||
|
||||
@@ -146,7 +146,7 @@ Failing a Check
|
||||
31 (i1 -- i2) ∘
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
e = text_to_expression('"two"')
|
||||
print stack_to_string(e)
|
||||
@@ -157,7 +157,7 @@ Failing a Check
|
||||
'two'
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
try:
|
||||
unify(e, fi)
|
||||
|
||||
@@ -184,7 +184,7 @@ Compiling ``pop∘swap∘roll<``
|
||||
|
||||
The simplest way to “compile” this function would be something like:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def poswrd(s, e, d):
|
||||
return rolldown(*swap(*pop(s, e, d)))
|
||||
@@ -200,7 +200,7 @@ Looking ahead for a moment, from the stack effect comment:
|
||||
|
||||
We should be able to directly write out a Python function like:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def poswrd(stack):
|
||||
(_, (a, (b, (c, stack)))) = stack
|
||||
@@ -393,7 +393,7 @@ And there you have it, the stack effect for
|
||||
From this stack effect comment it should be possible to construct the
|
||||
following Python code:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def F(stack):
|
||||
(_, (d, (c, ((a, (b, S0)), stack)))) = stack
|
||||
@@ -408,7 +408,7 @@ Representing Stack Effect Comments in Python
|
||||
I’m going to use pairs of tuples of type descriptors, which will be
|
||||
integers or tuples of type descriptors:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
roll_dn = (1, 2, 3), (2, 3, 1)
|
||||
|
||||
@@ -419,7 +419,7 @@ integers or tuples of type descriptors:
|
||||
``compose()``
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def compose(f, g):
|
||||
|
||||
@@ -465,7 +465,7 @@ integers or tuples of type descriptors:
|
||||
``unify()``
|
||||
~~~~~~~~~~~
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def unify(u, v, s=None):
|
||||
if s is None:
|
||||
@@ -483,7 +483,7 @@ integers or tuples of type descriptors:
|
||||
``update()``
|
||||
~~~~~~~~~~~~
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def update(s, term):
|
||||
if not isinstance(term, tuple):
|
||||
@@ -493,7 +493,7 @@ integers or tuples of type descriptors:
|
||||
``relabel()``
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def relabel(left, right):
|
||||
return left, _1000(right)
|
||||
@@ -517,7 +517,7 @@ integers or tuples of type descriptors:
|
||||
``delabel()``
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def delabel(f):
|
||||
s = {u: i for i, u in enumerate(sorted(_unique(f)))}
|
||||
@@ -551,7 +551,7 @@ At last we put it all together in a function ``C()`` that accepts two
|
||||
stack effect comments and returns their composition (or raises and
|
||||
exception if they can’t be composed due to type conflicts.)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def C(f, g):
|
||||
f, g = relabel(f, g)
|
||||
@@ -560,7 +560,7 @@ exception if they can’t be composed due to type conflicts.)
|
||||
|
||||
Let’s try it out.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(pop, swap)
|
||||
|
||||
@@ -573,7 +573,7 @@ Let’s try it out.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(C(pop, swap), roll_dn)
|
||||
|
||||
@@ -586,7 +586,7 @@ Let’s try it out.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(swap, roll_dn)
|
||||
|
||||
@@ -599,7 +599,7 @@ Let’s try it out.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(pop, C(swap, roll_dn))
|
||||
|
||||
@@ -612,7 +612,7 @@ Let’s try it out.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
poswrd = reduce(C, (pop, swap, roll_dn))
|
||||
poswrd
|
||||
@@ -633,13 +633,13 @@ Here’s that trick to represent functions like ``rest`` and ``cons`` that
|
||||
manipulate stacks. We use a cons-list of tuples and give the tails their
|
||||
own numbers. Then everything above already works.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
rest = ((1, 2),), (2,)
|
||||
|
||||
cons = (1, 2), ((1, 2),)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(poswrd, rest)
|
||||
|
||||
@@ -671,7 +671,7 @@ The translation table, if you will, would be:
|
||||
0: 0,
|
||||
}
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
F = reduce(C, (pop, swap, roll_dn, rest, rest, cons, cons))
|
||||
|
||||
@@ -699,11 +699,11 @@ Dealing with ``cons`` and ``uncons``
|
||||
However, if we try to compose e.g. ``cons`` and ``uncons`` it won’t
|
||||
work:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
uncons = ((1, 2),), (1, 2)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
try:
|
||||
C(cons, uncons)
|
||||
@@ -723,7 +723,7 @@ The problem is that the ``unify()`` function as written doesn’t handle
|
||||
the case when both terms are tuples. We just have to add a clause to
|
||||
deal with this recursively:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def unify(u, v, s=None):
|
||||
if s is None:
|
||||
@@ -753,7 +753,7 @@ deal with this recursively:
|
||||
|
||||
return s
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(cons, uncons)
|
||||
|
||||
@@ -771,7 +771,7 @@ Part III: Compiling Yin Functions
|
||||
|
||||
Now consider the Python function we would like to derive:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def F_python(stack):
|
||||
(_, (d, (c, ((a, (b, S0)), stack)))) = stack
|
||||
@@ -779,7 +779,7 @@ Now consider the Python function we would like to derive:
|
||||
|
||||
And compare it to the input stack effect comment tuple we just computed:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
F[0]
|
||||
|
||||
@@ -816,7 +816,7 @@ Eh?
|
||||
|
||||
And the return tuple
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
F[1]
|
||||
|
||||
@@ -848,7 +848,7 @@ Python Identifiers
|
||||
We want to substitute Python identifiers for the integers. I’m going to
|
||||
repurpose ``joy.parser.Symbol`` class for this:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from collections import defaultdict
|
||||
from joy.parser import Symbol
|
||||
@@ -874,7 +874,7 @@ effect comment tuples to reasonable text format. There are some details
|
||||
in how this code works that related to stuff later in the notebook, so
|
||||
you should skip it for now and read it later if you’re interested.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def doc_from_stack_effect(inputs, outputs):
|
||||
return '(%s--%s)' % (
|
||||
@@ -914,7 +914,7 @@ Now we can write a compiler function to emit Python source code. (The
|
||||
underscore suffix distiguishes it from the built-in ``compile()``
|
||||
function.)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def compile_(name, f, doc=None):
|
||||
if doc is None:
|
||||
@@ -932,7 +932,7 @@ function.)
|
||||
|
||||
Here it is in action:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
source = compile_('F', F)
|
||||
|
||||
@@ -949,7 +949,7 @@ Here it is in action:
|
||||
|
||||
Compare:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def F_python(stack):
|
||||
(_, (d, (c, ((a, (b, S0)), stack)))) = stack
|
||||
@@ -957,7 +957,7 @@ Compare:
|
||||
|
||||
Next steps:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
L = {}
|
||||
|
||||
@@ -976,16 +976,16 @@ Next steps:
|
||||
|
||||
Let’s try it out:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from notebook_preamble import D, J, V
|
||||
from joy.library import SimpleFunctionWrapper
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
D['F'] = SimpleFunctionWrapper(L['F'])
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[4 5 ...] 2 3 1 F')
|
||||
|
||||
@@ -1012,7 +1012,7 @@ Compiling Library Functions
|
||||
We can use ``compile_()`` to generate many primitives in the library
|
||||
from their stack effect comments:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def defs():
|
||||
|
||||
@@ -1036,7 +1036,7 @@ from their stack effect comments:
|
||||
|
||||
return locals()
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for name, stack_effect_comment in sorted(defs().items()):
|
||||
print
|
||||
@@ -1205,7 +1205,7 @@ Python class hierarchy of Joy types and use the ``issubclass()`` method
|
||||
to establish domain ordering, as well as other handy behaviour that will
|
||||
make it fairly easy to reuse most of the code above.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
class AnyJoyType(object):
|
||||
|
||||
@@ -1251,14 +1251,14 @@ make it fairly easy to reuse most of the code above.
|
||||
|
||||
Mess with it a little:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from itertools import permutations
|
||||
|
||||
“Any” types can be specialized to numbers and stacks, but not vice
|
||||
versa:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for a, b in permutations((A[0], N[0], S[0]), 2):
|
||||
print a, '>=', b, '->', a >= b
|
||||
@@ -1278,7 +1278,7 @@ Our crude `Numerical
|
||||
Tower <https://en.wikipedia.org/wiki/Numerical_tower>`__ of *numbers* >
|
||||
*floats* > *integers* works as well (but we’re not going to use it yet):
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for a, b in permutations((A[0], N[0], FloatJoyType(0), IntJoyType(0)), 2):
|
||||
print a, '>=', b, '->', a >= b
|
||||
@@ -1303,13 +1303,13 @@ Tower <https://en.wikipedia.org/wiki/Numerical_tower>`__ of *numbers* >
|
||||
Typing ``sqr``
|
||||
~~~~~~~~~~~~~~
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
dup = (A[1],), (A[1], A[1])
|
||||
|
||||
mul = (N[1], N[2]), (N[3],)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
dup
|
||||
|
||||
@@ -1322,7 +1322,7 @@ Typing ``sqr``
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
mul
|
||||
|
||||
@@ -1340,7 +1340,7 @@ Modifying the Inferencer
|
||||
|
||||
Re-labeling still works fine:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
foo = relabel(dup, mul)
|
||||
|
||||
@@ -1361,7 +1361,7 @@ Re-labeling still works fine:
|
||||
The ``delabel()`` function needs an overhaul. It now has to keep track
|
||||
of how many labels of each domain it has “seen”.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from collections import Counter
|
||||
|
||||
@@ -1383,7 +1383,7 @@ of how many labels of each domain it has “seen”.
|
||||
|
||||
return tuple(delabel(inner, seen, c) for inner in f)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
delabel(foo)
|
||||
|
||||
@@ -1399,7 +1399,7 @@ of how many labels of each domain it has “seen”.
|
||||
``unify()`` version 3
|
||||
^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def unify(u, v, s=None):
|
||||
if s is None:
|
||||
@@ -1449,7 +1449,7 @@ of how many labels of each domain it has “seen”.
|
||||
|
||||
Rewrite the stack effect comments:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def defs():
|
||||
|
||||
@@ -1503,11 +1503,11 @@ Rewrite the stack effect comments:
|
||||
|
||||
return locals()
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
DEFS = defs()
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for name, stack_effect_comment in sorted(DEFS.items()):
|
||||
print name, '=', doc_from_stack_effect(*stack_effect_comment)
|
||||
@@ -1543,14 +1543,14 @@ Rewrite the stack effect comments:
|
||||
uncons = ([a1 .1.] -- a1 [.1.])
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
globals().update(DEFS)
|
||||
|
||||
Compose ``dup`` and ``mul``
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(dup, mul)
|
||||
|
||||
@@ -1565,7 +1565,7 @@ Compose ``dup`` and ``mul``
|
||||
|
||||
Revisit the ``F`` function, works fine.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
|
||||
F
|
||||
@@ -1579,7 +1579,7 @@ Revisit the ``F`` function, works fine.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*F)
|
||||
|
||||
@@ -1592,12 +1592,12 @@ Revisit the ``F`` function, works fine.
|
||||
Some otherwise inefficient functions are no longer to be feared. We can
|
||||
also get the effect of combinators in some limited cases.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def neato(*funcs):
|
||||
print doc_from_stack_effect(*reduce(C, funcs))
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
# e.g. [swap] dip
|
||||
neato(rollup, swap, rolldown)
|
||||
@@ -1608,7 +1608,7 @@ also get the effect of combinators in some limited cases.
|
||||
(a1 a2 a3 -- a2 a1 a3)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
# e.g. [popop] dipd
|
||||
neato(popdd, rolldown, pop)
|
||||
@@ -1619,7 +1619,7 @@ also get the effect of combinators in some limited cases.
|
||||
(a1 a2 a3 a4 -- a3 a4)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
# Reverse the order of the top three items.
|
||||
neato(rollup, swap)
|
||||
@@ -1636,7 +1636,7 @@ also get the effect of combinators in some limited cases.
|
||||
Because the type labels represent themselves as valid Python identifiers
|
||||
the ``compile_()`` function doesn’t need to generate them anymore:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def compile_(name, f, doc=None):
|
||||
inputs, outputs = f
|
||||
@@ -1652,7 +1652,7 @@ the ``compile_()`` function doesn’t need to generate them anymore:
|
||||
%s = stack
|
||||
return %s''' % (name, doc, i, o)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print compile_('F', F)
|
||||
|
||||
@@ -1668,7 +1668,7 @@ the ``compile_()`` function doesn’t need to generate them anymore:
|
||||
But it cannot magically create new functions that involve e.g. math and
|
||||
such. Note that this is *not* a ``sqr`` function implementation:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print compile_('sqr', C(dup, mul))
|
||||
|
||||
@@ -1696,7 +1696,7 @@ The functions that *can* be compiled are the ones that have only
|
||||
``AnyJoyType`` and ``StackJoyType`` labels in their stack effect
|
||||
comments. We can write a function to check that:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from itertools import imap
|
||||
|
||||
@@ -1704,7 +1704,7 @@ comments. We can write a function to check that:
|
||||
def compilable(f):
|
||||
return isinstance(f, tuple) and all(imap(compilable, f)) or stacky(f)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for name, stack_effect_comment in sorted(defs().items()):
|
||||
if compilable(stack_effect_comment):
|
||||
@@ -1828,7 +1828,7 @@ the “truthiness” of ``StackJoyType`` to false to let e.g.
|
||||
``joy.utils.stack.concat`` work with our stack effect comment cons-list
|
||||
tuples.)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def compose(f, g):
|
||||
(f_in, f_out), (g_in, g_out) = f, g
|
||||
@@ -1840,7 +1840,7 @@ tuples.)
|
||||
I don’t want to rewrite all the defs myself, so I’ll write a little
|
||||
conversion function instead. This is programmer’s laziness.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def sequence_to_stack(seq, stack=StackJoyType(23)):
|
||||
for item in seq: stack = item, stack
|
||||
@@ -1854,7 +1854,7 @@ conversion function instead. This is programmer’s laziness.
|
||||
NEW_DEFS['swaack'] = (S[1], S[0]), (S[0], S[1])
|
||||
globals().update(NEW_DEFS)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(stack, uncons)
|
||||
|
||||
@@ -1867,7 +1867,7 @@ conversion function instead. This is programmer’s laziness.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
reduce(C, (stack, uncons, uncons))
|
||||
|
||||
@@ -1887,7 +1887,7 @@ The display function should be changed too.
|
||||
|
||||
Clunky junk, but it will suffice for now.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def doc_from_stack_effect(inputs, outputs):
|
||||
switch = [False] # Do we need to display the '...' for the rest of the main stack?
|
||||
@@ -1935,7 +1935,7 @@ Clunky junk, but it will suffice for now.
|
||||
a.append(end)
|
||||
return '[%s]' % ' '.join(a)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for name, stack_effect_comment in sorted(NEW_DEFS.items()):
|
||||
print name, '=', doc_from_stack_effect(*stack_effect_comment)
|
||||
@@ -1973,7 +1973,7 @@ Clunky junk, but it will suffice for now.
|
||||
uncons = ([a1 .1.] -- a1 [.1.])
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print ; print doc_from_stack_effect(*stack)
|
||||
print ; print doc_from_stack_effect(*C(stack, uncons))
|
||||
@@ -1993,7 +1993,7 @@ Clunky junk, but it will suffice for now.
|
||||
(... a1 -- ... a1 [a1 ...])
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*C(ccons, stack))
|
||||
|
||||
@@ -2003,7 +2003,7 @@ Clunky junk, but it will suffice for now.
|
||||
(... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...])
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
Q = C(ccons, stack)
|
||||
|
||||
@@ -2024,7 +2024,7 @@ Clunky junk, but it will suffice for now.
|
||||
This makes the ``compile_()`` function pretty simple as the stack effect
|
||||
comments are now already in the form needed for the Python code:
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def compile_(name, f, doc=None):
|
||||
i, o = f
|
||||
@@ -2035,7 +2035,7 @@ comments are now already in the form needed for the Python code:
|
||||
%s = stack
|
||||
return %s''' % (name, doc, i, o)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print compile_('Q', Q)
|
||||
|
||||
@@ -2053,12 +2053,12 @@ comments are now already in the form needed for the Python code:
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
unstack = (S[1], S[0]), S[1]
|
||||
enstacken = S[0], (S[0], S[1])
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*unstack)
|
||||
|
||||
@@ -2068,7 +2068,7 @@ comments are now already in the form needed for the Python code:
|
||||
([.1.] --)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*enstacken)
|
||||
|
||||
@@ -2078,7 +2078,7 @@ comments are now already in the form needed for the Python code:
|
||||
(-- [.0.])
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*C(cons, unstack))
|
||||
|
||||
@@ -2088,7 +2088,7 @@ comments are now already in the form needed for the Python code:
|
||||
(a1 [.1.] -- a1)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*C(cons, enstacken))
|
||||
|
||||
@@ -2098,7 +2098,7 @@ comments are now already in the form needed for the Python code:
|
||||
(a1 [.1.] -- [[a1 .1.] .2.])
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
C(cons, unstack)
|
||||
|
||||
@@ -2117,7 +2117,7 @@ Part VI: Multiple Stack Effects
|
||||
|
||||
…
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
class IntJoyType(NumberJoyType): prefix = 'i'
|
||||
|
||||
@@ -2125,7 +2125,7 @@ Part VI: Multiple Stack Effects
|
||||
F = map(FloatJoyType, _R)
|
||||
I = map(IntJoyType, _R)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
muls = [
|
||||
((I[2], (I[1], S[0])), (I[3], S[0])),
|
||||
@@ -2134,7 +2134,7 @@ Part VI: Multiple Stack Effects
|
||||
((F[2], (F[1], S[0])), (F[3], S[0])),
|
||||
]
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for f in muls:
|
||||
print doc_from_stack_effect(*f)
|
||||
@@ -2148,7 +2148,7 @@ Part VI: Multiple Stack Effects
|
||||
(f1 f2 -- f3)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for f in muls:
|
||||
try:
|
||||
@@ -2164,7 +2164,7 @@ Part VI: Multiple Stack Effects
|
||||
(a1 -- a1 a1) (f1 f2 -- f3) (f1 -- f2)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from itertools import product
|
||||
|
||||
@@ -2180,7 +2180,7 @@ Part VI: Multiple Stack Effects
|
||||
def MC(F, G):
|
||||
return sorted(set(meta_compose(F, G)))
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for f in MC([dup], [mul]):
|
||||
print doc_from_stack_effect(*f)
|
||||
@@ -2191,7 +2191,7 @@ Part VI: Multiple Stack Effects
|
||||
(n1 -- n2)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for f in MC([dup], muls):
|
||||
print doc_from_stack_effect(*f)
|
||||
@@ -2264,7 +2264,7 @@ Giving us two unifiers:
|
||||
{c: a, d: b, .1.: .0.}
|
||||
{c: a, d: e, .1.: A* b .0.}
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
class KleeneStar(object):
|
||||
|
||||
@@ -2314,7 +2314,7 @@ Giving us two unifiers:
|
||||
|
||||
Can now return multiple results…
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def unify(u, v, s=None):
|
||||
if s is None:
|
||||
@@ -2386,7 +2386,7 @@ Can now return multiple results…
|
||||
def stacky(thing):
|
||||
return thing.__class__ in {AnyJoyType, StackJoyType}
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
a = (As[1], S[1])
|
||||
a
|
||||
@@ -2400,7 +2400,7 @@ Can now return multiple results…
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
b = (A[1], S[2])
|
||||
b
|
||||
@@ -2414,7 +2414,7 @@ Can now return multiple results…
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for result in unify(b, a):
|
||||
print result, '->', update(result, a), update(result, b)
|
||||
@@ -2426,7 +2426,7 @@ Can now return multiple results…
|
||||
{a1: a10001, s2: (a1*, s1)} -> (a1*, s1) (a10001, (a1*, s1))
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for result in unify(a, b):
|
||||
print result, '->', update(result, a), update(result, b)
|
||||
@@ -2446,7 +2446,7 @@ Can now return multiple results…
|
||||
|
||||
(a1*, s1) [a1*] (a2, (a1*, s1)) [a2 a1*]
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
sum_ = ((Ns[1], S[1]), S[0]), (N[0], S[0])
|
||||
|
||||
@@ -2458,7 +2458,7 @@ Can now return multiple results…
|
||||
([n1* .1.] -- n0)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
f = (N[1], (N[2], (N[3], S[1]))), S[0]
|
||||
|
||||
@@ -2470,7 +2470,7 @@ Can now return multiple results…
|
||||
(-- [n1 n2 n3 .1.])
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for result in unify(sum_[0], f):
|
||||
print result, '->', update(result, sum_[1])
|
||||
@@ -2489,7 +2489,7 @@ Can now return multiple results…
|
||||
|
||||
This function has to be modified to yield multiple results.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def compose(f, g):
|
||||
(f_in, f_out), (g_in, g_out) = f, g
|
||||
@@ -2501,7 +2501,7 @@ This function has to be modified to yield multiple results.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def meta_compose(F, G):
|
||||
for f, g in product(F, G):
|
||||
@@ -2517,7 +2517,7 @@ This function has to be modified to yield multiple results.
|
||||
for fg in compose(f, g):
|
||||
yield delabel(fg)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for f in MC([dup], muls):
|
||||
print doc_from_stack_effect(*f)
|
||||
@@ -2529,7 +2529,7 @@ This function has to be modified to yield multiple results.
|
||||
(i1 -- i2)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
|
||||
|
||||
@@ -2542,7 +2542,7 @@ This function has to be modified to yield multiple results.
|
||||
([n1* .1.] -- [n1* .1.] n1)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
|
||||
|
||||
@@ -2556,7 +2556,7 @@ This function has to be modified to yield multiple results.
|
||||
(n1 [n1* .1.] -- n2)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0]))
|
||||
print doc_from_stack_effect(*cons),
|
||||
@@ -2571,7 +2571,7 @@ This function has to be modified to yield multiple results.
|
||||
(a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n1 [n1* .1.] -- n2)
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
a = (A[4], (As[1], (A[3], S[1])))
|
||||
a
|
||||
@@ -2585,7 +2585,7 @@ This function has to be modified to yield multiple results.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
b = (A[1], (A[2], S[2]))
|
||||
b
|
||||
@@ -2599,7 +2599,7 @@ This function has to be modified to yield multiple results.
|
||||
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for result in unify(b, a):
|
||||
print result
|
||||
@@ -2611,7 +2611,7 @@ This function has to be modified to yield multiple results.
|
||||
{a1: a4, s2: (a1*, (a3, s1)), a2: a10003}
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
for result in unify(a, b):
|
||||
print result
|
||||
@@ -2681,7 +2681,7 @@ We need a type variable for Joy functions that can go in our expressions
|
||||
and be used by the hybrid inferencer/interpreter. They have to store a
|
||||
name and a list of stack effects.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
class FunctionJoyType(AnyJoyType):
|
||||
|
||||
@@ -2703,14 +2703,14 @@ Specialized for Simple Functions and Combinators
|
||||
For non-combinator functions the stack effects list contains stack
|
||||
effect comments (represented by pairs of cons-lists as described above.)
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
class SymbolJoyType(FunctionJoyType):
|
||||
prefix = 'F'
|
||||
|
||||
For combinators the list contains Python functions.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
class CombinatorJoyType(FunctionJoyType):
|
||||
|
||||
@@ -2731,7 +2731,7 @@ For combinators the list contains Python functions.
|
||||
For simple combinators that have only one effect (like ``dip``) you only
|
||||
need one function and it can be the combinator itself.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
import joy.library
|
||||
|
||||
@@ -2741,7 +2741,7 @@ For combinators that can have more than one effect (like ``branch``) you
|
||||
have to write functions that each implement the action of one of the
|
||||
effects.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def branch_true(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
@@ -2771,7 +2771,7 @@ updated along with the stack effects after doing unification or we risk
|
||||
losing useful information. This was a straightforward, if awkward,
|
||||
modification to the call structure of ``meta_compose()`` et. al.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
ID = S[0], S[0] # Identity function.
|
||||
|
||||
@@ -2833,7 +2833,7 @@ cruft to convert the definitions in ``DEFS`` to the new
|
||||
``SymbolJoyType`` objects, and some combinators. Here is an example of
|
||||
output from the current code :
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
1/0 # (Don't try to run this cell! It's not going to work. This is "read only" code heh..)
|
||||
|
||||
@@ -2956,7 +2956,7 @@ module. But if you’re interested in all that you should just use Prolog!
|
||||
|
||||
Anyhow, type *checking* is a few easy steps away.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
def _ge(self, other):
|
||||
return (issubclass(other.__class__, self.__class__)
|
||||
|
||||
@@ -10,7 +10,7 @@ Huet <https://www.st.cs.uni-saarland.de/edu/seminare/2005/advanced-fp/docs/huet-
|
||||
Given a datastructure on the stack we can navigate through it, modify
|
||||
it, and rebuild it using the “zipper” technique.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
@@ -23,7 +23,7 @@ strings, Symbols (strings that are names of functions) and sequences
|
||||
`trees <https://en.wikipedia.org/wiki/Tree_%28data_structure%29>`__ out
|
||||
of sequences.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1 [2 [3 4 25 6] 7] 8]')
|
||||
|
||||
@@ -54,14 +54,14 @@ show the trace so you can see how it works. If we were going to use
|
||||
these a lot it would make sense to write Python versions for efficiency,
|
||||
but see below.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('z-down == [] swap uncons swap')
|
||||
define('z-up == swons swap shunt')
|
||||
define('z-right == [swons] cons dip uncons swap')
|
||||
define('z-left == swons [uncons swap] dip swap')
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('[1 [2 [3 4 25 6] 7] 8] z-down')
|
||||
|
||||
@@ -77,7 +77,7 @@ but see below.
|
||||
[] [[2 [3 4 25 6] 7] 8] 1 .
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('[] [[2 [3 4 25 6] 7] 8] 1 z-right')
|
||||
|
||||
@@ -101,7 +101,7 @@ but see below.
|
||||
[1] [8] [2 [3 4 25 6] 7] .
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1] [8] [2 [3 4 25 6] 7] z-down')
|
||||
|
||||
@@ -111,7 +111,7 @@ but see below.
|
||||
[1] [8] [] [[3 4 25 6] 7] 2
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1] [8] [] [[3 4 25 6] 7] 2 z-right')
|
||||
|
||||
@@ -121,7 +121,7 @@ but see below.
|
||||
[1] [8] [2] [7] [3 4 25 6]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1] [8] [2] [7] [3 4 25 6] z-down')
|
||||
|
||||
@@ -131,7 +131,7 @@ but see below.
|
||||
[1] [8] [2] [7] [] [4 25 6] 3
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1] [8] [2] [7] [] [4 25 6] 3 z-right')
|
||||
|
||||
@@ -141,7 +141,7 @@ but see below.
|
||||
[1] [8] [2] [7] [3] [25 6] 4
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1] [8] [2] [7] [3] [25 6] 4 z-right')
|
||||
|
||||
@@ -151,7 +151,7 @@ but see below.
|
||||
[1] [8] [2] [7] [4 3] [6] 25
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1] [8] [2] [7] [4 3] [6] 25 sqr')
|
||||
|
||||
@@ -161,7 +161,7 @@ but see below.
|
||||
[1] [8] [2] [7] [4 3] [6] 625
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('[1] [8] [2] [7] [4 3] [6] 625 z-up')
|
||||
|
||||
@@ -184,7 +184,7 @@ but see below.
|
||||
[1] [8] [2] [7] [3 4 625 6] .
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1] [8] [2] [7] [3 4 625 6] z-up')
|
||||
|
||||
@@ -194,7 +194,7 @@ but see below.
|
||||
[1] [8] [2 [3 4 625 6] 7]
|
||||
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1] [8] [2 [3 4 625 6] 7] z-up')
|
||||
|
||||
@@ -210,7 +210,7 @@ but see below.
|
||||
In Joy we have the ``dip`` and ``infra`` combinators which can “target”
|
||||
or “address” any particular item in a Joy tree structure.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra')
|
||||
|
||||
@@ -270,13 +270,13 @@ been embedded in a nested series of quoted programs, e.g.:
|
||||
|
||||
The ``Z`` function isn’t hard to make.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
define('Z == [[] cons cons] step i')
|
||||
|
||||
Here it is in action in a simplified scenario.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
V('1 [2 3 4] Z')
|
||||
|
||||
@@ -314,7 +314,7 @@ Here it is in action in a simplified scenario.
|
||||
|
||||
And here it is doing the main thing.
|
||||
|
||||
.. code:: python
|
||||
.. code:: ipython2
|
||||
|
||||
J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z')
|
||||
|
||||
|
||||
@@ -16,6 +16,7 @@ These essays are adapted from Jupyter notebooks. I hope to have those hosted so
|
||||
Treestep
|
||||
Generator_Programs
|
||||
Newton-Raphson
|
||||
Square_Spiral
|
||||
Zipper
|
||||
Types
|
||||
TypeChecking
|
||||
|
||||
@@ -54,6 +54,29 @@ additional joy interpreter (the binary in the archive from La Trobe seems
|
||||
to run just fine on my modern Linux machine!) But I also hope that you
|
||||
can read and understand the Python code and play with the implementation
|
||||
itself.</p>
|
||||
<section id="example-code">
|
||||
<h2>Example Code<a class="headerlink" href="#example-code" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Here is an example of Joy code:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>It might seem unreadable but with a little familiarity it becomes just as
|
||||
legible as any other notation. Some layout helps:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[ [[abs] ii <=]
|
||||
[
|
||||
[<>] [pop !-] ||
|
||||
] &&
|
||||
]
|
||||
[[ !-] [[++]] [[--]] ifte dip]
|
||||
[[pop !-] [--] [++] ifte ]
|
||||
ifte
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>This function accepts two integers on the stack and increments or
|
||||
decrements one of them such that the new pair of numbers is the next
|
||||
coordinate pair in a square spiral (like the kind used to construct an
|
||||
Ulam Spiral). For more information see <a class="reference internal" href="notebooks/Square_Spiral.html"><span class="doc">Square Spiral Example Joy Code</span></a></p>
|
||||
</section>
|
||||
<section id="quick-start">
|
||||
<h2>Quick Start<a class="headerlink" href="#quick-start" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Install from <a class="reference external" href="https://pypi.org/project/Thun/">PyPI</a> in the usual way:</p>
|
||||
@@ -145,6 +168,7 @@ interesting aspects. It’s quite a treasure trove.</p>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Newton-Raphson.html">Newton’s method</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Square_Spiral.html">Square Spiral Example Joy Code</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Zipper.html">Traversing Datastructures with Zippers</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Types.html">The Blissful Elegance of Typing Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/TypeChecking.html">Type Checking</a></li>
|
||||
|
||||
@@ -96,14 +96,14 @@ R∘λ = λ∘R = R
|
||||
</section>
|
||||
<section id="implementation">
|
||||
<h2>Implementation<a class="headerlink" href="#implementation" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span> <span class="k">as</span> <span class="n">curry</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span> <span class="k">as</span> <span class="n">curry</span>
|
||||
<span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="and">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">ϕ</span></code> and <code class="docutils literal notranslate"><span class="pre">λ</span></code><a class="headerlink" href="#and" title="Permalink to this headline">¶</a></h3>
|
||||
<p>The empty set and the set of just the empty string.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">phi</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">()</span> <span class="c1"># ϕ</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">phi</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">()</span> <span class="c1"># ϕ</span>
|
||||
<span class="n">y</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">''</span><span class="p">})</span> <span class="c1"># λ</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -115,7 +115,7 @@ illustrate the algorithm and because you can represent any other
|
||||
alphabet with two symbols (if you had to.)</p>
|
||||
<p>I chose the names <code class="docutils literal notranslate"><span class="pre">O</span></code> and <code class="docutils literal notranslate"><span class="pre">l</span></code> (uppercase “o” and lowercase “L”) to
|
||||
look like <code class="docutils literal notranslate"><span class="pre">0</span></code> and <code class="docutils literal notranslate"><span class="pre">1</span></code> (zero and one) respectively.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">syms</span> <span class="o">=</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">'0'</span><span class="p">}),</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">'1'</span><span class="p">})</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">syms</span> <span class="o">=</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">'0'</span><span class="p">}),</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">'1'</span><span class="p">})</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
@@ -133,7 +133,7 @@ expression</em> is one of:</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Where <code class="docutils literal notranslate"><span class="pre">R</span></code> and <code class="docutils literal notranslate"><span class="pre">S</span></code> stand for <em>regular expressions</em>.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">KSTAR</span><span class="p">,</span> <span class="n">NOT</span><span class="p">,</span> <span class="n">OR</span> <span class="o">=</span> <span class="s1">'and cons * not or'</span><span class="o">.</span><span class="n">split</span><span class="p">()</span> <span class="c1"># Tags are just strings.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">AND</span><span class="p">,</span> <span class="n">CONS</span><span class="p">,</span> <span class="n">KSTAR</span><span class="p">,</span> <span class="n">NOT</span><span class="p">,</span> <span class="n">OR</span> <span class="o">=</span> <span class="s1">'and cons * not or'</span><span class="o">.</span><span class="n">split</span><span class="p">()</span> <span class="c1"># Tags are just strings.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Because they are formed of <code class="docutils literal notranslate"><span class="pre">frozenset</span></code>, <code class="docutils literal notranslate"><span class="pre">tuple</span></code> and <code class="docutils literal notranslate"><span class="pre">str</span></code> objects
|
||||
@@ -141,7 +141,7 @@ only, these datastructures are immutable.</p>
|
||||
</section>
|
||||
<section id="string-representation-of-re-datastructures">
|
||||
<h3>String Representation of RE Datastructures<a class="headerlink" href="#string-representation-of-re-datastructures" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stringy</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
|
||||
<span class="sd">'''</span>
|
||||
<span class="sd"> Return a nice string repr for a regular expression datastructure.</span>
|
||||
<span class="sd"> '''</span>
|
||||
@@ -180,10 +180,10 @@ only, these datastructures are immutable.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="o">|</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">I</span> <span class="o">=</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">I</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">.</span>
|
||||
@@ -198,13 +198,13 @@ only, these datastructures are immutable.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Note that it contains one of everything.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">I</span><span class="p">))))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">I</span><span class="p">))))</span>
|
||||
<span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">O</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
|
||||
<span class="n">c</span> <span class="o">=</span> <span class="p">(</span><span class="n">CONS</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="p">(</span><span class="n">KSTAR</span><span class="p">,</span> <span class="n">l</span><span class="p">))</span>
|
||||
<span class="n">it</span> <span class="o">=</span> <span class="p">(</span><span class="n">AND</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">NOT</span><span class="p">,</span> <span class="p">(</span><span class="n">OR</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">stringy</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">.</span><span class="mf">111.</span><span class="p">)</span> <span class="o">&</span> <span class="p">((</span><span class="o">.</span><span class="mi">01</span> <span class="o">|</span> <span class="mi">11</span><span class="o">*</span><span class="p">)</span><span class="s1">')</span>
|
||||
@@ -214,7 +214,7 @@ only, these datastructures are immutable.</p>
|
||||
<section id="nully">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">nully()</span></code><a class="headerlink" href="#nully" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Let’s get that auxiliary predicate function <code class="docutils literal notranslate"><span class="pre">δ</span></code> out of the way.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">nully</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">nully</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
|
||||
<span class="sd">'''</span>
|
||||
<span class="sd"> δ - Return λ if λ ⊆ R otherwise ϕ.</span>
|
||||
<span class="sd"> '''</span>
|
||||
@@ -252,7 +252,7 @@ only, these datastructures are immutable.</p>
|
||||
<p>This is the straightforward version with no “compaction”. It works fine,
|
||||
but does waaaay too much work because the expressions grow each
|
||||
derivation.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
|
||||
|
||||
@@ -296,7 +296,7 @@ derivation.</p>
|
||||
</section>
|
||||
<section id="compaction-rules">
|
||||
<h3>Compaction Rules<a class="headerlink" href="#compaction-rules" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_compaction_rule</span><span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_compaction_rule</span><span class="p">(</span><span class="n">relation</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="p">(</span>
|
||||
<span class="n">b</span> <span class="k">if</span> <span class="n">a</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span> <span class="c1"># R*1 = 1*R = R</span>
|
||||
<span class="n">a</span> <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="n">one</span> <span class="k">else</span>
|
||||
@@ -306,7 +306,7 @@ derivation.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>An elegant symmetry.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># R ∧ I = I ∧ R = R</span>
|
||||
<span class="c1"># R ∧ ϕ = ϕ ∧ R = ϕ</span>
|
||||
<span class="n">_and</span> <span class="o">=</span> <span class="n">curry</span><span class="p">(</span><span class="n">_compaction_rule</span><span class="p">,</span> <span class="n">AND</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">phi</span><span class="p">)</span>
|
||||
|
||||
@@ -325,7 +325,7 @@ derivation.</p>
|
||||
<p>We can save re-processing by remembering results we have already
|
||||
computed. RE datastructures are immutable and the <code class="docutils literal notranslate"><span class="pre">derv()</span></code> functions
|
||||
are <em>pure</em> so this is fine.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Memo</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Memo</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
||||
|
||||
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
|
||||
<span class="bp">self</span><span class="o">.</span><span class="n">f</span> <span class="o">=</span> <span class="n">f</span>
|
||||
@@ -347,7 +347,7 @@ are <em>pure</em> so this is fine.</p>
|
||||
<h3>With “Compaction”<a class="headerlink" href="#with-compaction" title="Permalink to this headline">¶</a></h3>
|
||||
<p>This version uses the rules above to perform compaction. It keeps the
|
||||
expressions from growing too large.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D_compaction</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D_compaction</span><span class="p">(</span><span class="n">symbol</span><span class="p">):</span>
|
||||
|
||||
<span class="nd">@Memo</span>
|
||||
<span class="k">def</span> <span class="nf">derv</span><span class="p">(</span><span class="n">R</span><span class="p">):</span>
|
||||
@@ -395,7 +395,7 @@ expressions from growing too large.</p>
|
||||
<section id="lets-try-it-out">
|
||||
<h2>Let’s try it out…<a class="headerlink" href="#lets-try-it-out" title="Permalink to this headline">¶</a></h2>
|
||||
<p>(FIXME: redo.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">o</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'0'</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'1'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">o</span><span class="p">,</span> <span class="n">z</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'0'</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'1'</span><span class="p">)</span>
|
||||
<span class="n">REs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
|
||||
<span class="n">N</span> <span class="o">=</span> <span class="mi">5</span>
|
||||
<span class="n">names</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">N</span> <span class="o">*</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)])))</span>
|
||||
@@ -500,8 +500,8 @@ machine transition table.</p>
|
||||
</div>
|
||||
<p>Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”</p>
|
||||
<figure class="align-default" id="id2">
|
||||
<img alt="State Machine Graph" src="../_images/omg.svg" /><figcaption>
|
||||
<p><span class="caption-text">State Machine Graph</span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p>
|
||||
<img alt="omg.svg" src="notebooks/attachment:omg.svg" /><figcaption>
|
||||
<p><span class="caption-text">omg.svg</span><a class="headerlink" href="#id2" title="Permalink to this image">¶</a></p>
|
||||
</figcaption>
|
||||
</figure>
|
||||
<p>Start at <code class="docutils literal notranslate"><span class="pre">a</span></code> and follow the transition arrows according to their
|
||||
@@ -555,18 +555,18 @@ a --1--> ∂1(a)
|
||||
<p>You can see the one-way nature of the <code class="docutils literal notranslate"><span class="pre">g</span></code> state and the <code class="docutils literal notranslate"><span class="pre">hij</span></code> “trap”
|
||||
in the way that the <code class="docutils literal notranslate"><span class="pre">.111.</span></code> on the left-hand side of the <code class="docutils literal notranslate"><span class="pre">&</span></code>
|
||||
disappears once it has been matched.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
|
||||
<span class="kn">from</span> <span class="nn">pprint</span> <span class="kn">import</span> <span class="n">pprint</span>
|
||||
<span class="kn">from</span> <span class="nn">string</span> <span class="kn">import</span> <span class="n">ascii_lowercase</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">d0</span><span class="p">,</span> <span class="n">d1</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'0'</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'1'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">d0</span><span class="p">,</span> <span class="n">d1</span> <span class="o">=</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'0'</span><span class="p">),</span> <span class="n">D_compaction</span><span class="p">(</span><span class="s1">'1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
<section id="explore">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">explore()</span></code><a class="headerlink" href="#explore" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">explore</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">explore</span><span class="p">(</span><span class="n">re</span><span class="p">):</span>
|
||||
|
||||
<span class="c1"># Don't have more than 26 states...</span>
|
||||
<span class="n">names</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">ascii_lowercase</span><span class="p">)</span><span class="o">.</span><span class="n">next</span><span class="p">)</span>
|
||||
@@ -592,7 +592,7 @@ disappears once it has been matched.</p>
|
||||
<span class="k">return</span> <span class="n">table</span><span class="p">,</span> <span class="n">accepting</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="n">explore</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span> <span class="o">=</span> <span class="n">explore</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>
|
||||
<span class="n">table</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -618,7 +618,7 @@ disappears once it has been matched.</p>
|
||||
<span class="p">(</span><span class="s1">'j'</span><span class="p">,</span> <span class="mi">1</span><span class="p">):</span> <span class="s1">'h'</span><span class="p">}</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">accepting</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">accepting</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="s1">'h'</span><span class="p">,</span> <span class="s1">'i'</span><span class="p">}</span>
|
||||
@@ -629,7 +629,7 @@ disappears once it has been matched.</p>
|
||||
<h3>Generate Diagram<a class="headerlink" href="#generate-diagram" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Once we have the FSM table and the set of accepting states we can
|
||||
generate the diagram above.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">_template</span> <span class="o">=</span> <span class="s1">'''</span><span class="se">\</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">_template</span> <span class="o">=</span> <span class="s1">'''</span><span class="se">\</span>
|
||||
<span class="s1">digraph finite_state_machine {</span>
|
||||
<span class="s1"> rankdir=LR;</span>
|
||||
<span class="s1"> size="8,5"</span>
|
||||
@@ -653,7 +653,7 @@ generate the diagram above.</p>
|
||||
<span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">make_graph</span><span class="p">(</span><span class="n">table</span><span class="p">,</span> <span class="n">accepting</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">digraph</span> <span class="n">finite_state_machine</span> <span class="p">{</span>
|
||||
@@ -699,7 +699,7 @@ hard-code the information in the table into a little patch of branches.</p>
|
||||
<h4>Trampoline Function<a class="headerlink" href="#trampoline-function" title="Permalink to this headline">¶</a></h4>
|
||||
<p>Python has no GOTO statement but we can fake it with a “trampoline”
|
||||
function.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">jump_from</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">jump_from</span><span class="p">,</span> <span class="n">accepting</span><span class="p">):</span>
|
||||
<span class="n">I</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">input_</span><span class="p">)</span>
|
||||
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="k">try</span><span class="p">:</span>
|
||||
@@ -714,7 +714,7 @@ function.</p>
|
||||
<h4>Stream Functions<a class="headerlink" href="#stream-functions" title="Permalink to this headline">¶</a></h4>
|
||||
<p>Little helpers to process the iterator of our data (a “stream” of “1”
|
||||
and “0” characters, not bits.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">getch</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="nb">int</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">getch</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="nb">int</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">I</span><span class="p">))</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">_1</span><span class="p">(</span><span class="n">I</span><span class="p">):</span>
|
||||
@@ -735,7 +735,7 @@ and “0” characters, not bits.)</p>
|
||||
code. (You have to imagine that these are GOTO statements in C or
|
||||
branches in assembly and that the state names are branch destination
|
||||
labels.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">c</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">c</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||
<span class="n">b</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">_0</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="ow">or</span> <span class="n">d</span>
|
||||
<span class="n">c</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">e</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||
<span class="n">d</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">I</span><span class="p">:</span> <span class="n">f</span> <span class="k">if</span> <span class="n">getch</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="k">else</span> <span class="n">b</span>
|
||||
@@ -750,11 +750,11 @@ labels.)</p>
|
||||
<p>Note that the implementations of <code class="docutils literal notranslate"><span class="pre">h</span></code> and <code class="docutils literal notranslate"><span class="pre">g</span></code> are identical ergo
|
||||
<code class="docutils literal notranslate"><span class="pre">h</span> <span class="pre">=</span> <span class="pre">g</span></code> and we could eliminate one in the code but <code class="docutils literal notranslate"><span class="pre">h</span></code> is an
|
||||
accepting state and <code class="docutils literal notranslate"><span class="pre">g</span></code> isn’t.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">acceptable</span><span class="p">(</span><span class="n">input_</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">acceptable</span><span class="p">(</span><span class="n">input_</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="n">trampoline</span><span class="p">(</span><span class="n">input_</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="p">{</span><span class="n">h</span><span class="p">,</span> <span class="n">i</span><span class="p">})</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">5</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="o">**</span><span class="mi">5</span><span class="p">):</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="nb">bin</span><span class="p">(</span><span class="n">n</span><span class="p">)[</span><span class="mi">2</span><span class="p">:]</span>
|
||||
<span class="nb">print</span> <span class="s1">'</span><span class="si">%05s</span><span class="s1">'</span> <span class="o">%</span> <span class="n">s</span><span class="p">,</span> <span class="n">acceptable</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
@@ -878,6 +878,7 @@ derivative-with-respect-to-N of some other state/RE:</p>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>
|
||||
|
||||
File diff suppressed because one or more lines are too long
@@ -40,7 +40,7 @@
|
||||
to write a function that can compute the square root of a number.</p>
|
||||
<p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
|
||||
Hughes</a></p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="a-generator-for-approximations">
|
||||
@@ -92,10 +92,10 @@ function we’re writing. If we let 1 be the initial approximation:</p>
|
||||
<span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
|
||||
@@ -103,7 +103,7 @@ function we’re writing. If we let 1 be the initial approximation:</p>
|
||||
</div>
|
||||
<p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and
|
||||
square the approximation to see how well it works…</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span>
|
||||
@@ -145,7 +145,7 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o"><=</span><span class="n">ε</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P [first - abs] dip <='</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P [first - abs] dip <='</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
@@ -157,7 +157,7 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B roll< popop first'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B roll< popop first'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
@@ -182,7 +182,7 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R [popd x] dip'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R [popd x] dip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
@@ -194,31 +194,31 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'sqrt gsra within'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Try it out…</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'36 sqrt'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'36 sqrt'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 sqrt'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 sqrt'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Check it.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
|
||||
|
||||
<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
@@ -63,7 +63,7 @@ the Sufficiently Smart Compiler can be modified to use an optimized
|
||||
implementation under the hood. (Where does the “type” come from? It has
|
||||
a contingent existence predicated on the disciplined use of these
|
||||
functions on otherwise undistinguished Joy datastructures.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="adding-nodes-to-the-tree">
|
||||
@@ -100,10 +100,10 @@ functions on otherwise undistinguished Joy datastructures.)</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">new</span> <span class="o">==</span> <span class="n">swap</span> <span class="p">[[]</span> <span class="p">[]]</span> <span class="n">cons</span> <span class="n">cons</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Tree-new == swap [[] []] cons cons'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Tree-new == swap [[] []] cons cons'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'"v" "k" Tree-new'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'"v" "k" Tree-new'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'k'</span> <span class="s1">'v'</span> <span class="p">[]</span> <span class="p">[]]</span>
|
||||
@@ -159,10 +159,10 @@ comparison operator:</p>
|
||||
<span class="n">P</span> <span class="o">==</span> <span class="n">pop</span> <span class="n">roll</span><span class="o">></span> <span class="n">pop</span> <span class="n">first</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'P == pop roll> pop first'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'P == pop roll> pop first'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["old_key" 23 [] []] 17 "new_key" ["..."] P'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["old_key" 23 [] []] 17 "new_key" ["..."] P'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'new_key'</span> <span class="s1">'old_key'</span>
|
||||
@@ -217,10 +217,10 @@ stack:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">T</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipdd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'T == cons cons [dipdd] cons infra'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'T == cons cons [dipdd] cons infra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'old_k'</span> <span class="s1">'old_value'</span> <span class="s1">'left'</span> <span class="s1">'Tree-add'</span> <span class="s1">'new_key'</span> <span class="s1">'new_value'</span> <span class="s1">'right'</span><span class="p">]</span>
|
||||
@@ -234,7 +234,7 @@ stack:</p>
|
||||
<span class="p">[</span><span class="n">key_n</span> <span class="n">value_n</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="n">value</span> <span class="n">key</span> <span class="p">[</span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span><span class="p">]</span> <span class="p">[</span><span class="n">P</span> <span class="o"><</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="n">ifte</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'E == [P <] [Te] [Ee] ifte'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'E == [P <] [Te] [Ee] ifte'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>In this case <code class="docutils literal notranslate"><span class="pre">Te</span></code> works that same as <code class="docutils literal notranslate"><span class="pre">T</span></code> but on the left child tree
|
||||
@@ -243,10 +243,10 @@ instead of the right, so the only difference is that it must use
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Te</span> <span class="o">==</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="n">dipd</span><span class="p">]</span> <span class="n">cons</span> <span class="n">infra</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Te == cons cons [dipd] cons infra'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Te == cons cons [dipd] cons infra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'old_k'</span> <span class="s1">'old_value'</span> <span class="s1">'Tree-add'</span> <span class="s1">'new_key'</span> <span class="s1">'new_value'</span> <span class="s1">'left'</span> <span class="s1">'right'</span><span class="p">]</span>
|
||||
@@ -274,10 +274,10 @@ instead of the right, so the only difference is that it must use
|
||||
<span class="p">[</span><span class="n">key</span> <span class="n">new_value</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Ee == pop swap roll< rest rest cons cons'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Ee == pop swap roll< rest rest cons cons'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'k'</span> <span class="s1">'new_value'</span> <span class="s1">'left'</span> <span class="s1">'right'</span><span class="p">]</span>
|
||||
@@ -302,43 +302,43 @@ instead of the right, so the only difference is that it must use
|
||||
<span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">R</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
<section id="examples">
|
||||
<h3>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] 23 "b" Tree-add'</span><span class="p">)</span> <span class="c1"># Initial</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] 23 "b" Tree-add'</span><span class="p">)</span> <span class="c1"># Initial</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'b'</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["b" 23 [] []] 88 "c" Tree-add'</span><span class="p">)</span> <span class="c1"># Greater than</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["b" 23 [] []] 88 "c" Tree-add'</span><span class="p">)</span> <span class="c1"># Greater than</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'b'</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">'c'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["b" 23 [] []] 88 "a" Tree-add'</span><span class="p">)</span> <span class="c1"># Less than</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["b" 23 [] []] 88 "a" Tree-add'</span><span class="p">)</span> <span class="c1"># Less than</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'b'</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">'a'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["b" 23 [] []] 88 "b" Tree-add'</span><span class="p">)</span> <span class="c1"># Equal to</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["b" 23 [] []] 88 "b" Tree-add'</span><span class="p">)</span> <span class="c1"># Equal to</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'b'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add'</span><span class="p">)</span> <span class="c1"># Series.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add'</span><span class="p">)</span> <span class="c1"># Series.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'b'</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">'a'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">'c'</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'b'</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">'a'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">'c'</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
|
||||
@@ -365,19 +365,19 @@ values:</p>
|
||||
<span class="n">L</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"1 0 ['G'] ['E'] ['L'] cmp"</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"1 0 ['G'] ['E'] ['L'] cmp"</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'G'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"1 1 ['G'] ['E'] ['L'] cmp"</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"1 1 ['G'] ['E'] ['L'] cmp"</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'E'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"0 1 ['G'] ['E'] ['L'] cmp"</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"0 1 ['G'] ['E'] ['L'] cmp"</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'L'</span>
|
||||
@@ -414,7 +414,7 @@ node key (by throwing everything else away):</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">P</span> <span class="o">==</span> <span class="n">over</span> <span class="p">[</span><span class="n">popop</span> <span class="n">popop</span> <span class="n">first</span><span class="p">]</span> <span class="n">nullary</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'P == over [popop popop first] nullary'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'P == over [popop popop first] nullary'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Using <code class="docutils literal notranslate"><span class="pre">cmp</span></code> to simplify <cite>our code above at
|
||||
@@ -434,10 +434,10 @@ to understand:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="n">add</span> <span class="o">==</span> <span class="p">[</span><span class="n">popop</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[[</span><span class="n">pop</span><span class="p">]</span> <span class="n">dipd</span> <span class="n">Tree</span><span class="o">-</span><span class="n">new</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">Ee</span><span class="p">]</span> <span class="p">[</span><span class="n">Te</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add'</span><span class="p">)</span> <span class="c1"># Still works.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add'</span><span class="p">)</span> <span class="c1"># Still works.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'b'</span> <span class="mi">23</span> <span class="p">[</span><span class="s1">'a'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="s1">'c'</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
|
||||
@@ -545,22 +545,22 @@ with an interesting situation:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span><span class="o">-</span><span class="nb">iter</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">roll</span><span class="o"><</span> <span class="p">[</span><span class="n">dupdip</span> <span class="n">rest</span> <span class="n">rest</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">step</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
<section id="id1">
|
||||
<h3>Examples<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] [foo] Tree-iter'</span><span class="p">)</span> <span class="c1"># It doesn't matter what F is as it won't be used.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] [foo] Tree-iter'</span><span class="p">)</span> <span class="c1"># It doesn't matter what F is as it won't be used.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter"</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter"</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'b'</span> <span class="s1">'a'</span> <span class="s1">'c'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter"</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter"</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span> <span class="mi">88</span> <span class="mi">44</span>
|
||||
@@ -575,16 +575,16 @@ to e.g. 0 and ignoring them. It’s set-like in that duplicate items added
|
||||
to it will only occur once within it, and we can query it in
|
||||
<cite>:math:`O(log_2 N)</cite> <<a class="reference external" href="https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2">https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2</a>>`__
|
||||
time.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'to_set == [] swap [0 swap Tree-add] step'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'to_set == [] swap [0 swap Tree-add] step'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 9 5 2 8 6 7 8 4] to_set'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 9 5 2 8 6 7 8 4] to_set'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
|
||||
@@ -592,10 +592,10 @@ time.</p>
|
||||
</div>
|
||||
<p>And with that we can write a little program <code class="docutils literal notranslate"><span class="pre">unique</span></code> to remove
|
||||
duplicate items from a list.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'unique == [to_set [first] Tree-iter] cons run'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'unique == [to_set [first] Tree-iter] cons run'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique'</span><span class="p">)</span> <span class="c1"># Filter duplicate items.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique'</span><span class="p">)</span> <span class="c1"># Filter duplicate items.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">7</span> <span class="mi">6</span> <span class="mi">8</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">9</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span>
|
||||
@@ -679,7 +679,7 @@ right side:</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Now we can sort sequences.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1">#define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec')</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1">#define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec')</span>
|
||||
|
||||
|
||||
<span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
@@ -695,7 +695,7 @@ right side:</p>
|
||||
<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span>
|
||||
@@ -835,7 +835,7 @@ because there’s no value to discard.</p>
|
||||
<span class="n">Tree</span><span class="o">-</span><span class="n">get</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="ow">not</span><span class="p">]</span> <span class="n">swap</span> <span class="p">[]</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">></span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="o"><</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># I don't want to deal with name conflicts with the above so I'm inlining everything here.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># I don't want to deal with name conflicts with the above so I'm inlining everything here.</span>
|
||||
<span class="c1"># The original Joy system has "hide" which is a meta-command which allows you to use named</span>
|
||||
<span class="c1"># definitions that are only in scope for a given definition. I don't want to implement</span>
|
||||
<span class="c1"># that (yet) so...</span>
|
||||
@@ -852,19 +852,19 @@ because there’s no value to discard.</p>
|
||||
<span class="s1">'''</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'mike not in tree'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["gary" 23 [] []] "gary" [popop "err"] Tree-get'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["gary" 23 [] []] "gary" [popop "err"] Tree-get'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1"> [] [[0 'a'] [1 'b'] [2 'c']] [i Tree-add] step</span>
|
||||
|
||||
@@ -876,7 +876,7 @@ because there’s no value to discard.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1"> [] [[0 'a'] [1 'b'] [2 'c']] [i Tree-add] step</span>
|
||||
|
||||
@@ -1175,7 +1175,7 @@ E == [
|
||||
</div>
|
||||
<p>By the standards of the code I’ve written so far, this is a <em>huge</em> Joy
|
||||
program.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<span class="s1">first_two == uncons uncons pop</span>
|
||||
<span class="s1">fourth == rest rest rest first</span>
|
||||
<span class="s1">?fourth == [] [fourth] [] ifte</span>
|
||||
@@ -1193,43 +1193,43 @@ program.</p>
|
||||
<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete "</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete "</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'a'</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">'b'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete "</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete "</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'a'</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">'c'</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete "</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete "</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'b'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">'c'</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete "</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete "</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'a'</span> <span class="mi">23</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">'b'</span> <span class="mi">88</span> <span class="p">[]</span> <span class="p">[</span><span class="s1">'c'</span> <span class="mi">44</span> <span class="p">[]</span> <span class="p">[]]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete "</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete "</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete "</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s2">"[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete "</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span> <span class="p">[]</span> <span class="p">[]]]]</span>
|
||||
|
||||
@@ -34,7 +34,7 @@
|
||||
|
||||
<div class="body" role="main">
|
||||
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="quadratic-formula">
|
||||
@@ -100,11 +100,11 @@ the variables:</p>
|
||||
</div>
|
||||
<p>The three arguments are to the left, so we can “chop off” everything to
|
||||
the right and say it’s the definition of the <code class="docutils literal notranslate"><span class="pre">quadratic</span></code> function:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Let’s try it out:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'3 1 1 quadratic'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'3 1 1 quadratic'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">-</span><span class="mf">2.618033988749895</span>
|
||||
@@ -114,7 +114,7 @@ the right and say it’s the definition of the <code class="docutils literal not
|
||||
lines are the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">dipd</span></code> combinators building the main program
|
||||
by incorporating the values on the stack. Then that program runs and you
|
||||
get the results. This is pretty typical of Joy code.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'-5 1 4 quadratic'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'-5 1 4 quadratic'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="o">-</span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">4</span> <span class="n">quadratic</span>
|
||||
|
||||
@@ -33,7 +33,7 @@
|
||||
|
||||
<div class="body" role="main">
|
||||
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="recursion-combinators">
|
||||
@@ -101,7 +101,7 @@ cons list”.</p></li>
|
||||
</ul>
|
||||
<p>It may be helpful to see this function implemented in imperative Python
|
||||
code.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hylomorphism</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hylomorphism</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
|
||||
<span class="sd">'''Return a hylomorphism function H.'''</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">H</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||
@@ -185,7 +185,7 @@ the left so we have a definition for <code class="docutils literal notranslate">
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hylomorphism</span> <span class="o">==</span> <span class="p">[</span><span class="n">unit</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">swoncat</span><span class="p">]</span> <span class="n">dipd</span> <span class="p">[</span><span class="n">dip</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="example-finding-triangular-numbers">
|
||||
@@ -200,17 +200,17 @@ of all positive integers less than that one. (In this case the types
|
||||
<li><p><code class="docutils literal notranslate"><span class="pre">[G]</span></code> is <code class="docutils literal notranslate"><span class="pre">[--</span> <span class="pre">dup]</span></code></p></li>
|
||||
<li><p><code class="docutils literal notranslate"><span class="pre">[F]</span></code> is <code class="docutils literal notranslate"><span class="pre">[+]</span></code></p></li>
|
||||
</ul>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Let’s try it:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 triangular_number'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 triangular_number'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 1 2 3 4 5 6] [triangular_number] map'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 1 2 3 4 5 6] [triangular_number] map'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">6</span> <span class="mi">10</span> <span class="mi">15</span><span class="p">]</span>
|
||||
@@ -362,9 +362,8 @@ values.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">hylomorphism</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="range-et-al">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al.<a class="headerlink" href="#range-et-al" title="Permalink to this headline">¶</a></h3>
|
||||
<p>An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</p>
|
||||
<section id="range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al. An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.<a class="headerlink" href="#range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Each of the above variations can be used to make four slightly different
|
||||
<code class="docutils literal notranslate"><span class="pre">range</span></code> functions.</p>
|
||||
<section id="range-with-h1">
|
||||
@@ -373,10 +372,10 @@ values.</p>
|
||||
<span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o"><=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'range == [0 <=] [] [-- dup] [swons] hylomorphism'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'range == [0 <=] [] [-- dup] [swons] hylomorphism'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 range'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 range'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">]</span>
|
||||
@@ -389,10 +388,10 @@ values.</p>
|
||||
<span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o"><=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">primrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 range_reverse'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 range_reverse'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span>
|
||||
@@ -405,10 +404,10 @@ values.</p>
|
||||
<span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o"><=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="p">[]]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]</span> <span class="n">dupdip</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 ranger'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 ranger'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span>
|
||||
@@ -421,10 +420,10 @@ values.</p>
|
||||
<span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">0</span> <span class="o"><=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">--</span><span class="p">]</span> <span class="n">primrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 ranger_reverse'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 ranger_reverse'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span><span class="p">]</span>
|
||||
@@ -445,17 +444,17 @@ and makes some new value.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">C</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="n">c</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">hylomorphism</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'swuncons == uncons swap'</span><span class="p">)</span> <span class="c1"># Awkward name.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'swuncons == uncons swap'</span><span class="p">)</span> <span class="c1"># Awkward name.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>An example of a catamorphism is the sum function.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">sum</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">swuncons</span><span class="p">]</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">hylomorphism</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'sum == [not] 0 [swuncons] [+] hylomorphism'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'sum == [not] 0 [swuncons] [+] hylomorphism'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[5 4 3 2 1] sum'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[5 4 3 2 1] sum'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
|
||||
@@ -465,7 +464,7 @@ and makes some new value.</p>
|
||||
<h3>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator<a class="headerlink" href="#the-step-combinator" title="Permalink to this headline">¶</a></h3>
|
||||
<p>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator will usually be better to use than
|
||||
<code class="docutils literal notranslate"><span class="pre">catamorphism</span></code>.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[step] help'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[step] help'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Run</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">program</span> <span class="n">on</span> <span class="n">each</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">a</span> <span class="n">sequence</span><span class="o">.</span>
|
||||
@@ -489,10 +488,10 @@ and makes some new value.</p>
|
||||
<span class="n">on</span> <span class="n">top</span> <span class="n">of</span> <span class="n">the</span> <span class="n">stack</span><span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'sum == 0 swap [+] step'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'sum == 0 swap [+] step'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[5 4 3 2 1] sum'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[5 4 3 2 1] sum'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
|
||||
@@ -513,10 +512,10 @@ and makes some new value.</p>
|
||||
<span class="n">P</span> <span class="o">==</span> <span class="mi">1</span> <span class="o"><=</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 factorial'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'5 factorial'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">120</span>
|
||||
@@ -545,10 +544,10 @@ pattern <code class="docutils literal notranslate"><span class="pre">H2</span></
|
||||
<span class="n">P</span> <span class="o">==</span> <span class="ow">not</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'tails == [] swap [not] [pop] [rest dup [swons] dip] primrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'tails == [] swap [not] [pop] [rest dup [swons] dip] primrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] tails'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] tails'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span><span class="p">]]</span>
|
||||
|
||||
@@ -42,12 +42,12 @@ we can implement e.g. a function that adds new functions to the
|
||||
dictionary. However, there’s no function that does that. Adding a new
|
||||
function to the dictionary is a meta-interpreter action, you have to do
|
||||
it in Python, not Joy.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="a-long-trace">
|
||||
<h2>A long trace<a class="headerlink" href="#a-long-trace" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[23 18] average'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[23 18] average'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
|
||||
@@ -105,7 +105,7 @@ it in Python, not Joy.</p>
|
||||
<p>An efficient <code class="docutils literal notranslate"><span class="pre">sum</span></code> function is already in the library. But for
|
||||
<code class="docutils literal notranslate"><span class="pre">size</span></code> we can use a “compiled” version hand-written in Python to speed
|
||||
up evaluation and make the trace more readable.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">iter_stack</span>
|
||||
|
||||
|
||||
@@ -121,14 +121,14 @@ up evaluation and make the trace more readable.</p>
|
||||
</div>
|
||||
<p>Now we replace the old version in the dictionary with the new version,
|
||||
and re-evaluate the expression.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">'size'</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">'size'</span><span class="p">]</span> <span class="o">=</span> <span class="n">size</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
<section id="a-shorter-trace">
|
||||
<h2>A shorter trace<a class="headerlink" href="#a-shorter-trace" title="Permalink to this headline">¶</a></h2>
|
||||
<p>You can see that <code class="docutils literal notranslate"><span class="pre">size</span></code> now executes in a single step.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[23 18] average'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[23 18] average'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
|
||||
|
||||
@@ -0,0 +1,463 @@
|
||||
|
||||
<!DOCTYPE html>
|
||||
|
||||
<html>
|
||||
<head>
|
||||
<meta charset="utf-8" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
|
||||
|
||||
<title>Square Spiral Example Joy Code — Thun 0.4.1 documentation</title>
|
||||
<link rel="stylesheet" type="text/css" href="../_static/pygments.css" />
|
||||
<link rel="stylesheet" type="text/css" href="../_static/alabaster.css" />
|
||||
<script data-url_root="../" id="documentation_options" src="../_static/documentation_options.js"></script>
|
||||
<script src="../_static/jquery.js"></script>
|
||||
<script src="../_static/underscore.js"></script>
|
||||
<script src="../_static/doctools.js"></script>
|
||||
<link rel="index" title="Index" href="../genindex.html" />
|
||||
<link rel="search" title="Search" href="../search.html" />
|
||||
<link rel="next" title="Traversing Datastructures with Zippers" href="Zipper.html" />
|
||||
<link rel="prev" title="Newton’s method" href="Newton-Raphson.html" />
|
||||
|
||||
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
|
||||
|
||||
|
||||
<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
|
||||
|
||||
</head><body>
|
||||
|
||||
|
||||
<div class="document">
|
||||
<div class="documentwrapper">
|
||||
<div class="bodywrapper">
|
||||
|
||||
|
||||
<div class="body" role="main">
|
||||
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="square-spiral-example-joy-code">
|
||||
<h1>Square Spiral Example Joy Code<a class="headerlink" href="#square-spiral-example-joy-code" title="Permalink to this headline">¶</a></h1>
|
||||
<p>Here is the example of Joy code from the <code class="docutils literal notranslate"><span class="pre">README</span></code> file:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[[[abs]ii <=][[<>][pop !-]||]&&][[!-][[++]][[--]]ifte dip][[pop !-][--][++]ifte]ifte
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>It might seem unreadable but with a little familiarity it becomes just
|
||||
as legible as any other notation. Some layout helps:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[ [[abs] ii <=]
|
||||
[
|
||||
[<>] [pop !-] ||
|
||||
] &&
|
||||
]
|
||||
[[ !-] [[++]] [[--]] ifte dip]
|
||||
[[pop !-] [--] [++] ifte ]
|
||||
ifte
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>This function accepts two integers on the stack and increments or
|
||||
decrements one of them such that the new pair of numbers is the next
|
||||
coordinate pair in a square spiral (like the kind used to construct an
|
||||
Ulam Spiral).</p>
|
||||
<section id="original-form">
|
||||
<h2>Original Form<a class="headerlink" href="#original-form" title="Permalink to this headline">¶</a></h2>
|
||||
<p>It’s adapted from <a class="reference external" href="https://stackoverflow.com/questions/398299/looping-in-a-spiral/31864777#31864777">the original code on
|
||||
StackOverflow</a>:</p>
|
||||
<blockquote>
|
||||
<div><p>If all you’re trying to do is generate the first N points in the
|
||||
spiral (without the original problem’s constraint of masking to an N
|
||||
x M region), the code becomes very simple:</p>
|
||||
</div></blockquote>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>void spiral(const int N)
|
||||
{
|
||||
int x = 0;
|
||||
int y = 0;
|
||||
for(int i = 0; i < N; ++i)
|
||||
{
|
||||
cout << x << '\t' << y << '\n';
|
||||
if(abs(x) <= abs(y) && (x != y || x >= 0))
|
||||
x += ((y >= 0) ? 1 : -1);
|
||||
else
|
||||
y += ((x >= 0) ? -1 : 1);
|
||||
}
|
||||
}
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
<section id="translation-to-joy">
|
||||
<h2>Translation to Joy<a class="headerlink" href="#translation-to-joy" title="Permalink to this headline">¶</a></h2>
|
||||
<p>I’m going to make a function that take two ints (<code class="docutils literal notranslate"><span class="pre">x</span></code> and <code class="docutils literal notranslate"><span class="pre">y</span></code>) and
|
||||
generates the next pair, we’ll turn it into a generator later using the
|
||||
<code class="docutils literal notranslate"><span class="pre">x</span></code> combinator.</p>
|
||||
<section id="first-boolean-predicate">
|
||||
<h3>First Boolean Predicate<a class="headerlink" href="#first-boolean-predicate" title="Permalink to this headline">¶</a></h3>
|
||||
<p>We need a function that computes <code class="docutils literal notranslate"><span class="pre">abs(x)</span> <span class="pre"><=</span> <span class="pre">abs(y)</span></code>, we can use <code class="docutils literal notranslate"><span class="pre">ii</span></code>
|
||||
to apply <code class="docutils literal notranslate"><span class="pre">abs</span></code> to both values and then compare them with <code class="docutils literal notranslate"><span class="pre"><=</span></code>:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="nb">abs</span><span class="p">]</span> <span class="n">ii</span> <span class="o"><=</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>I’ve defined two short-circuiting Boolean combinators <code class="docutils literal notranslate"><span class="pre">&&</span></code> and <code class="docutils literal notranslate"><span class="pre">||</span></code>
|
||||
that each accept two quoted predicate programs, run the first, and
|
||||
conditionally run the second only if required (to compute the final
|
||||
Boolean value). They run their predicate arguments <code class="docutils literal notranslate"><span class="pre">nullary</span></code>.</p>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'&& [nullary] cons [nullary [0]] dip branch'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'|| [nullary] cons [nullary] dip [1] branch'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Given those, we can define <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">!=</span> <span class="pre">y</span> <span class="pre">||</span> <span class="pre">x</span> <span class="pre">>=</span> <span class="pre">0</span></code> as:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="o"><></span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="o">||</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>And <code class="docutils literal notranslate"><span class="pre">(abs(x)</span> <span class="pre"><=</span> <span class="pre">abs(y)</span> <span class="pre">&&</span> <span class="pre">(x</span> <span class="pre">!=</span> <span class="pre">y</span> <span class="pre">||</span> <span class="pre">x</span> <span class="pre">>=</span> <span class="pre">0))</span></code> as:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="nb">abs</span><span class="p">]</span> <span class="n">ii</span> <span class="o"><=</span><span class="p">]</span> <span class="p">[[</span><span class="o"><></span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="o">||</span><span class="p">]</span> <span class="o">&&</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>It’s a little rough, but, as I say, with a little familiarity it becomes
|
||||
legible.</p>
|
||||
</section>
|
||||
<section id="the-increment-decrement-branches">
|
||||
<h3>The Increment / Decrement Branches<a class="headerlink" href="#the-increment-decrement-branches" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Turning to the branches of the main <code class="docutils literal notranslate"><span class="pre">if</span></code> statement:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>x += ((y >= 0) ? 1 : -1);
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Rewrite as a hybrid (pseudo-code) <code class="docutils literal notranslate"><span class="pre">ifte</span></code> expression:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">y</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">x</span> <span class="o">+=</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="n">X</span> <span class="o">-=</span> <span class="mi">1</span><span class="p">]</span> <span class="n">ifte</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Change each C phrase to Joy code:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="p">[[</span><span class="o">++</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">ifte</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Factor out the dip from each branch:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="p">[[</span><span class="o">++</span><span class="p">]]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]]</span> <span class="n">ifte</span> <span class="n">dip</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Similar logic applies to the other branch:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>y += ((x >= 0) ? -1 : 1);
|
||||
|
||||
[x >= 0] [y -= 1] [y += 1] ifte
|
||||
|
||||
[pop 0 >=] [--] [++] ifte
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
<section id="not-negative">
|
||||
<h3>“Not Negative”<a class="headerlink" href="#not-negative" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'!- 0 >='</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
<section id="putting-the-pieces-together">
|
||||
<h2>Putting the Pieces Together<a class="headerlink" href="#putting-the-pieces-together" title="Permalink to this headline">¶</a></h2>
|
||||
<p>We can assemble the three functions we just defined in quotes and give
|
||||
them them to the <code class="docutils literal notranslate"><span class="pre">ifte</span></code> combinator. With some arrangement to show off
|
||||
the symmetry of the two branches, we have:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[[[abs] ii <=] [[<>] [pop !-] ||] &&]
|
||||
[[ !-] [[++]] [[--]] ifte dip]
|
||||
[[pop !-] [--] [++] ifte ]
|
||||
ifte
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>As I was writing this up I realized that, since the <code class="docutils literal notranslate"><span class="pre">&&</span></code> combinator
|
||||
doesn’t consume the stack (below its quoted args), I can unquote the
|
||||
predicate, swap the branches, and use the <code class="docutils literal notranslate"><span class="pre">branch</span></code> combinator instead
|
||||
of <code class="docutils literal notranslate"><span class="pre">ifte</span></code>:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[[abs] ii <=] [[<>] [pop !-] ||] &&
|
||||
[[pop !-] [--] [++] ifte ]
|
||||
[[ !-] [[++]] [[--]] ifte dip]
|
||||
branch
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Let’s try it out:</p>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'0 0 spiral_next'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">0</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'1 0 spiral_next'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="o">-</span><span class="mi">1</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'1 -1 spiral_next'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="o">-</span><span class="mi">1</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'0 -1 spiral_next'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mi">1</span> <span class="o">-</span><span class="mi">1</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
<section id="turning-it-into-a-generator-with-x">
|
||||
<h2>Turning it into a Generator with <code class="docutils literal notranslate"><span class="pre">x</span></code><a class="headerlink" href="#turning-it-into-a-generator-with-x" title="Permalink to this headline">¶</a></h2>
|
||||
<p>It can be used with the x combinator to make a kind of generator for
|
||||
spiral square coordinates.</p>
|
||||
<p>We can use <code class="docutils literal notranslate"><span class="pre">codireco</span></code> to make a generator</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">codireco</span> <span class="p">:</span><span class="o">:=</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>It will look like this:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">value</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Here’s a trace of how it works:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span> <span class="n">x</span>
|
||||
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span> <span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span>
|
||||
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="mi">0</span> <span class="o">.</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span>
|
||||
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">codireco</span>
|
||||
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||
<span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="p">[</span><span class="mi">0</span> <span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||
<span class="o">.</span> <span class="mi">0</span> <span class="n">dup</span> <span class="o">++</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||
<span class="mi">0</span> <span class="o">.</span> <span class="n">dup</span> <span class="o">++</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||
<span class="mi">0</span> <span class="mi">0</span> <span class="o">.</span> <span class="o">++</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||
<span class="mi">0</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||
<span class="mi">0</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">0</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||
<span class="mi">0</span> <span class="mi">1</span> <span class="p">[[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span>
|
||||
<span class="mi">0</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="o">++</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span> <span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>But first we have to change the <code class="docutils literal notranslate"><span class="pre">spiral_next</span></code> function to work on a
|
||||
quoted pair of integers, and leave a copy of the pair on the stack.
|
||||
From:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">y</span> <span class="n">x</span> <span class="n">spiral_next</span>
|
||||
<span class="o">---------------------</span>
|
||||
<span class="n">y</span><span class="s1">' x'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>to:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">x</span> <span class="n">y</span><span class="p">]</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span>
|
||||
<span class="o">-------------------------------</span>
|
||||
<span class="p">[</span><span class="n">x</span><span class="s1">' y'</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 0] [spiral_next] infra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">1</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>So our generator is:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="n">x</span> <span class="n">y</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Or rather:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>There is a function <code class="docutils literal notranslate"><span class="pre">make_generator</span></code> that will build the generator for
|
||||
us out of the value and stepper function:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">make_generator</span>
|
||||
<span class="o">----------------------------------------------------</span>
|
||||
<span class="p">[[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">dup</span> <span class="p">[</span><span class="n">spiral_next</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Here it is in action:</p>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 0] [dup [spiral_next] infra] make_generator x x x x pop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span> <span class="mi">0</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Four <code class="docutils literal notranslate"><span class="pre">x</span></code> combinators, four pairs of coordinates.</p>
|
||||
</section>
|
||||
<section id="conclusion">
|
||||
<h2>Conclusion<a class="headerlink" href="#conclusion" title="Permalink to this headline">¶</a></h2>
|
||||
<p>So that’s an example of Joy code. It’s a straightforward translation of
|
||||
the original. It’s a little long for a single definition, you might
|
||||
break it up like so:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> _spn_P ::= [[abs] ii <=] [[<>] [pop !-] ||] &&
|
||||
|
||||
_spn_T ::= [ !-] [[++]] [[--]] ifte dip
|
||||
_spn_E ::= [pop !-] [--] [++] ifte
|
||||
|
||||
spiral_next ::= _spn_P [_spn_E] [_spn_T] branch
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>This way it’s easy to see that the function is a branch with two
|
||||
quasi-symmetrical paths.</p>
|
||||
<p>We then used this function to make a simple generator of coordinate
|
||||
pairs, where the next pair in the series can be generated at any time by
|
||||
using the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator on the generator (which is just a quoted
|
||||
expression containing a copy of the current pair and the “stepper
|
||||
function” to generate the next pair from that.)</p>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'_spn_T [!-] [[++]] [[--]] ifte dip'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'_spn_E [pop !-] [--] [++] ifte'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'spiral_next _spn_P [_spn_E] [_spn_T] branch'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'23 18 spiral_next'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> . 23 18 spiral_next
|
||||
23 . 18 spiral_next
|
||||
23 18 . spiral_next
|
||||
23 18 . _spn_P [_spn_E] [_spn_T] branch
|
||||
23 18 . [[abs] ii <=] [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] . [[<>] [pop !-] ||] && [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . && [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[<>] [pop !-] ||] . [nullary] cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[<>] [pop !-] ||] [nullary] . cons [nullary [0]] dip branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] . [nullary [0]] dip branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [[[<>] [pop !-] ||] nullary] [nullary [0]] . dip branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] . nullary [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] . [stack] dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [stack] . dinfrirst [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [[abs] ii <=] [stack] . dip infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . stack [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [18 23] . [[abs] ii <=] infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [18 23] [[abs] ii <=] . infra first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . [abs] ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] . ii <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] . [dip] dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] [dip] . dupdip i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] . dip [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 . abs 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 . 18 [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . [abs] i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [abs] . i <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . abs <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 . <= [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
False . [18 23] swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
False [18 23] . swaack first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 [False] . first [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 False . [0] [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 False [0] . [[[<>] [pop !-] ||] nullary] branch [_spn_E] [_spn_T] branch
|
||||
23 18 False [0] [[[<>] [pop !-] ||] nullary] . branch [_spn_E] [_spn_T] branch
|
||||
23 18 . 0 [_spn_E] [_spn_T] branch
|
||||
23 18 0 . [_spn_E] [_spn_T] branch
|
||||
23 18 0 [_spn_E] . [_spn_T] branch
|
||||
23 18 0 [_spn_E] [_spn_T] . branch
|
||||
23 18 . _spn_E
|
||||
23 18 . [pop !-] [--] [++] ifte
|
||||
23 18 [pop !-] . [--] [++] ifte
|
||||
23 18 [pop !-] [--] . [++] ifte
|
||||
23 18 [pop !-] [--] [++] . ifte
|
||||
23 18 [pop !-] [--] [++] . [nullary not] dipd branch
|
||||
23 18 [pop !-] [--] [++] [nullary not] . dipd branch
|
||||
23 18 [pop !-] . nullary not [--] [++] branch
|
||||
23 18 [pop !-] . [stack] dinfrirst not [--] [++] branch
|
||||
23 18 [pop !-] [stack] . dinfrirst not [--] [++] branch
|
||||
23 18 [pop !-] [stack] . dip infra first not [--] [++] branch
|
||||
23 18 . stack [pop !-] infra first not [--] [++] branch
|
||||
23 18 [18 23] . [pop !-] infra first not [--] [++] branch
|
||||
23 18 [18 23] [pop !-] . infra first not [--] [++] branch
|
||||
23 18 . pop !- [18 23] swaack first not [--] [++] branch
|
||||
23 . !- [18 23] swaack first not [--] [++] branch
|
||||
23 . 0 >= [18 23] swaack first not [--] [++] branch
|
||||
23 0 . >= [18 23] swaack first not [--] [++] branch
|
||||
True . [18 23] swaack first not [--] [++] branch
|
||||
True [18 23] . swaack first not [--] [++] branch
|
||||
23 18 [True] . first not [--] [++] branch
|
||||
23 18 True . not [--] [++] branch
|
||||
23 18 False . [--] [++] branch
|
||||
23 18 False [--] . [++] branch
|
||||
23 18 False [--] [++] . branch
|
||||
23 18 . --
|
||||
23 17 .
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
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|
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|
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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|
||||
@@ -148,10 +148,10 @@ the desired outcome.</p>
|
||||
</section>
|
||||
<section id="define-treestep">
|
||||
<h2>Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code><a class="headerlink" href="#define-treestep" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span><span class="p">,</span> <span class="n">DefinitionWrapper</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1"> _treestep_0 == [[not] swap] dip</span>
|
||||
<span class="s1"> _treestep_1 == [dip] cons [uncons] swoncat</span>
|
||||
@@ -169,7 +169,7 @@ all nodes in a tree with this function:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sumtree</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="nb">sum</span> <span class="o">+</span><span class="p">]</span> <span class="n">treestep</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'sumtree == [pop 0] [] [sum +] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'sumtree == [pop 0] [] [sum +] treestep'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Running this function on an empty tree value gives zero:</p>
|
||||
@@ -178,7 +178,7 @@ all nodes in a tree with this function:</p>
|
||||
<span class="mi">0</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] sumtree'</span><span class="p">)</span> <span class="c1"># Empty tree.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[] sumtree'</span><span class="p">)</span> <span class="c1"># Empty tree.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span>
|
||||
@@ -192,61 +192,61 @@ all nodes in a tree with this function:</p>
|
||||
<span class="n">n</span><span class="o">+</span><span class="n">m</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23] sumtree'</span><span class="p">)</span> <span class="c1"># No child trees.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23] sumtree'</span><span class="p">)</span> <span class="c1"># No child trees.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 []] sumtree'</span><span class="p">)</span> <span class="c1"># Child tree, empty.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 []] sumtree'</span><span class="p">)</span> <span class="c1"># Child tree, empty.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [4]] [3]] sumtree'</span><span class="p">)</span> <span class="c1"># Non-empty child trees.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [4]] [3]] sumtree'</span><span class="p">)</span> <span class="c1"># Non-empty child trees.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">32</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] sumtree'</span><span class="p">)</span> <span class="c1"># Etc...</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] sumtree'</span><span class="p">)</span> <span class="c1"># Etc...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep'</span><span class="p">)</span> <span class="c1"># Alternate "spelling".</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep'</span><span class="p">)</span> <span class="c1"># Alternate "spelling".</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep'</span><span class="p">)</span> <span class="c1"># Replace each node.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep'</span><span class="p">)</span> <span class="c1"># Replace each node.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[]]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep'</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep'</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep'</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep'</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span>
|
||||
@@ -277,7 +277,7 @@ all nodes in a tree with this function:</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>This doesn’t quite work:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="s1">'B'</span> <span class="s1">'B'</span>
|
||||
@@ -299,7 +299,7 @@ depositing our results directly on the stack.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="p">[</span><span class="n">flatten</span> <span class="n">cons</span><span class="p">]</span> <span class="n">treestep</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">9</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">8</span> <span class="mi">6</span> <span class="mi">7</span><span class="p">]</span>
|
||||
@@ -322,7 +322,7 @@ depositing our results directly on the stack.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">i</span> <span class="n">roll</span><span class="o"><</span> <span class="n">swons</span> <span class="n">concat</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="n">treestep</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span><span class="p">]</span>
|
||||
@@ -343,7 +343,7 @@ non-empty node is:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">N</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">C</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'key'</span> <span class="s1">'value'</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[[</span><span class="s1">'left'</span><span class="p">]</span> <span class="p">[</span><span class="s1">'right'</span><span class="p">]]</span> <span class="p">[[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="s1">'B'</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="s1">'N'</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="s1">'C'</span><span class="p">]</span> <span class="n">genrec</span><span class="p">]</span> <span class="s1">'C'</span>
|
||||
@@ -353,21 +353,21 @@ non-empty node is:</p>
|
||||
<section id="treegrind-with-step">
|
||||
<h2><code class="docutils literal notranslate"><span class="pre">treegrind</span></code> with <code class="docutils literal notranslate"><span class="pre">step</span></code><a class="headerlink" href="#treegrind-with-step" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Iteration through the nodes</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Sum the nodes’ keys.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">44</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Rebuild the tree using <code class="docutils literal notranslate"><span class="pre">map</span></code> (imitating <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">103</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">102</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">109</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">105</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">104</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">108</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">106</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">107</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]]</span> <span class="p">[]]]</span> <span class="p">[]]]</span>
|
||||
@@ -449,7 +449,7 @@ equal):</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>To me, that seems simpler than the <code class="docutils literal notranslate"><span class="pre">genrec</span></code> version.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1"> T> == pop [first] dip i</span>
|
||||
<span class="s1"> T< == pop [second] dip i</span>
|
||||
@@ -461,7 +461,7 @@ equal):</p>
|
||||
<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span><span class="se">\</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span><span class="se">\</span>
|
||||
|
||||
<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
|
||||
|
||||
@@ -473,7 +473,7 @@ equal):</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span><span class="se">\</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span><span class="se">\</span>
|
||||
|
||||
<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
|
||||
|
||||
|
||||
@@ -35,7 +35,7 @@
|
||||
|
||||
<section id="type-checking">
|
||||
<h1>Type Checking<a class="headerlink" href="#type-checking" title="Permalink to this headline">¶</a></h1>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">logging</span><span class="o">,</span> <span class="nn">sys</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">logging</span><span class="o">,</span> <span class="nn">sys</span>
|
||||
|
||||
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span>
|
||||
<span class="nb">format</span><span class="o">=</span><span class="s1">'</span><span class="si">%(message)s</span><span class="s1">'</span><span class="p">,</span>
|
||||
@@ -44,7 +44,7 @@
|
||||
<span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.types</span> <span class="kn">import</span> <span class="p">(</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.types</span> <span class="kn">import</span> <span class="p">(</span>
|
||||
<span class="n">doc_from_stack_effect</span><span class="p">,</span>
|
||||
<span class="n">infer</span><span class="p">,</span>
|
||||
<span class="n">reify</span><span class="p">,</span>
|
||||
@@ -54,14 +54,14 @@
|
||||
<span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
|
||||
<span class="k">del</span> <span class="n">D</span><span class="p">[</span><span class="s1">'product'</span><span class="p">]</span>
|
||||
<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="an-example">
|
||||
<h2>An Example<a class="headerlink" href="#an-example" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ pop swap rolldown rrest ccons
|
||||
@@ -72,31 +72,31 @@
|
||||
40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">text_to_expression</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">text_to_expression</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">stack_to_string</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'0 1 2 [3 4]'</span><span class="p">)</span> <span class="c1"># reverse order</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'0 1 2 [3 4]'</span><span class="p">)</span> <span class="c1"># reverse order</span>
|
||||
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<span class="n">u</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a4</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">a5</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -106,17 +106,17 @@
|
||||
</section>
|
||||
<section id="unification-works-in-reverse">
|
||||
<h2>Unification Works “in Reverse”<a class="headerlink" href="#unification-works-in-reverse" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[2 3]'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[2 3]'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># output side, not input side</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># output side, not input side</span>
|
||||
<span class="n">u</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</span><span class="p">:</span> <span class="p">()}</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -126,7 +126,7 @@
|
||||
</section>
|
||||
<section id="failing-a-check">
|
||||
<h2>Failing a Check<a class="headerlink" href="#failing-a-check" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ dup mul
|
||||
@@ -135,14 +135,14 @@
|
||||
31 (i1 -- i2) ∘
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'"two"'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'"two"'</span><span class="p">)</span>
|
||||
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'two'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
|
||||
<span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)</span>
|
||||
<span class="k">except</span> <span class="n">JoyTypeError</span><span class="p">,</span> <span class="n">err</span><span class="p">:</span>
|
||||
<span class="nb">print</span> <span class="n">err</span>
|
||||
|
||||
@@ -182,7 +182,7 @@ terms in the forms:</p>
|
||||
<section id="compiling-popswaproll">
|
||||
<h3>Compiling <code class="docutils literal notranslate"><span class="pre">pop∘swap∘roll<</span></code><a class="headerlink" href="#compiling-popswaproll" title="Permalink to this headline">¶</a></h3>
|
||||
<p>The simplest way to “compile” this function would be something like:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="n">rolldown</span><span class="p">(</span><span class="o">*</span><span class="n">swap</span><span class="p">(</span><span class="o">*</span><span class="n">pop</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">d</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -193,7 +193,7 @@ terms in the forms:</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>We should be able to directly write out a Python function like:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">poswrd</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
<span class="k">return</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
@@ -335,7 +335,7 @@ actually pretty easy. I’ll explain below.</p>
|
||||
</div>
|
||||
<p>From this stack effect comment it should be possible to construct the
|
||||
following Python code:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
<span class="k">return</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span>
|
||||
</pre></div>
|
||||
@@ -348,7 +348,7 @@ following Python code:</p>
|
||||
<h3>Representing Stack Effect Comments in Python<a class="headerlink" href="#representing-stack-effect-comments-in-python" title="Permalink to this headline">¶</a></h3>
|
||||
<p>I’m going to use pairs of tuples of type descriptors, which will be
|
||||
integers or tuples of type descriptors:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">roll_dn</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">roll_dn</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||
|
||||
<span class="n">pop</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,),</span> <span class="p">()</span>
|
||||
|
||||
@@ -358,7 +358,7 @@ integers or tuples of type descriptors:</p>
|
||||
</section>
|
||||
<section id="compose">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">compose()</span></code><a class="headerlink" href="#compose" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
|
||||
<span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
|
||||
|
||||
@@ -403,7 +403,7 @@ integers or tuples of type descriptors:</p>
|
||||
</section>
|
||||
<section id="unify">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">unify()</span></code><a class="headerlink" href="#unify" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
|
||||
@@ -420,7 +420,7 @@ integers or tuples of type descriptors:</p>
|
||||
</section>
|
||||
<section id="update">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">update()</span></code><a class="headerlink" href="#update" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">term</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">term</span><span class="p">):</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="n">s</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">term</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">inner</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">term</span><span class="p">)</span>
|
||||
@@ -429,7 +429,7 @@ integers or tuples of type descriptors:</p>
|
||||
</section>
|
||||
<section id="relabel">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">relabel()</span></code><a class="headerlink" href="#relabel" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">relabel</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">relabel</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="n">left</span><span class="p">,</span> <span class="n">_1000</span><span class="p">(</span><span class="n">right</span><span class="p">)</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">_1000</span><span class="p">(</span><span class="n">right</span><span class="p">):</span>
|
||||
@@ -446,7 +446,7 @@ integers or tuples of type descriptors:</p>
|
||||
</section>
|
||||
<section id="delabel">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">delabel()</span></code><a class="headerlink" href="#delabel" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="p">{</span><span class="n">u</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">u</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">_unique</span><span class="p">(</span><span class="n">f</span><span class="p">)))}</span>
|
||||
<span class="k">return</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
|
||||
|
||||
@@ -472,38 +472,38 @@ integers or tuples of type descriptors:</p>
|
||||
<p>At last we put it all together in a function <code class="docutils literal notranslate"><span class="pre">C()</span></code> that accepts two
|
||||
stack effect comments and returns their composition (or raises and
|
||||
exception if they can’t be composed due to type conflicts.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
<span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span>
|
||||
<span class="n">fg</span> <span class="o">=</span> <span class="n">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">delabel</span><span class="p">(</span><span class="n">fg</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Let’s try it out.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">),</span> <span class="n">roll_dn</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">),</span> <span class="n">roll_dn</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">poswrd</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">poswrd</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">))</span>
|
||||
<span class="n">poswrd</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -516,12 +516,12 @@ exception if they can’t be composed due to type conflicts.)</p>
|
||||
<p>Here’s that trick to represent functions like <code class="docutils literal notranslate"><span class="pre">rest</span></code> and <code class="docutils literal notranslate"><span class="pre">cons</span></code> that
|
||||
manipulate stacks. We use a cons-list of tuples and give the tails their
|
||||
own numbers. Then everything above already works.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">rest</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">rest</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,)</span>
|
||||
|
||||
<span class="n">cons</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">poswrd</span><span class="p">,</span> <span class="n">rest</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">poswrd</span><span class="p">,</span> <span class="n">rest</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
|
||||
@@ -542,7 +542,7 @@ own numbers. Then everything above already works.</p>
|
||||
<span class="p">}</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">roll_dn</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span>
|
||||
|
||||
<span class="n">F</span>
|
||||
</pre></div>
|
||||
@@ -560,10 +560,10 @@ own numbers. Then everything above already works.</p>
|
||||
<h3>Dealing with <code class="docutils literal notranslate"><span class="pre">cons</span></code> and <code class="docutils literal notranslate"><span class="pre">uncons</span></code><a class="headerlink" href="#dealing-with-cons-and-uncons" title="Permalink to this headline">¶</a></h3>
|
||||
<p>However, if we try to compose e.g. <code class="docutils literal notranslate"><span class="pre">cons</span></code> and <code class="docutils literal notranslate"><span class="pre">uncons</span></code> it won’t
|
||||
work:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">uncons</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">uncons</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
|
||||
<span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
|
||||
<span class="k">except</span> <span class="ne">Exception</span><span class="p">,</span> <span class="n">e</span><span class="p">:</span>
|
||||
<span class="nb">print</span> <span class="n">e</span>
|
||||
@@ -577,7 +577,7 @@ work:</p>
|
||||
<p>The problem is that the <code class="docutils literal notranslate"><span class="pre">unify()</span></code> function as written doesn’t handle
|
||||
the case when both terms are tuples. We just have to add a clause to
|
||||
deal with this recursively:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
|
||||
@@ -606,7 +606,7 @@ deal with this recursively:</p>
|
||||
<span class="k">return</span> <span class="n">s</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
|
||||
@@ -618,13 +618,13 @@ deal with this recursively:</p>
|
||||
<section id="part-iii-compiling-yin-functions">
|
||||
<h2>Part III: Compiling Yin Functions<a class="headerlink" href="#part-iii-compiling-yin-functions" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Now consider the Python function we would like to derive:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
<span class="k">return</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>And compare it to the input stack effect comment tuple we just computed:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||
@@ -646,7 +646,7 @@ stack effect comment tuple, just in the reverse order:</p>
|
||||
</div>
|
||||
<p>Eh?</p>
|
||||
<p>And the return tuple</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">)),)</span>
|
||||
@@ -666,7 +666,7 @@ effect.)</p>
|
||||
<h3>Python Identifiers<a class="headerlink" href="#python-identifiers" title="Permalink to this headline">¶</a></h3>
|
||||
<p>We want to substitute Python identifiers for the integers. I’m going to
|
||||
repurpose <code class="docutils literal notranslate"><span class="pre">joy.parser.Symbol</span></code> class for this:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.parser</span> <span class="kn">import</span> <span class="n">Symbol</span>
|
||||
|
||||
|
||||
@@ -690,7 +690,7 @@ repurpose <code class="docutils literal notranslate"><span class="pre">joy.parse
|
||||
effect comment tuples to reasonable text format. There are some details
|
||||
in how this code works that related to stuff later in the notebook, so
|
||||
you should skip it for now and read it later if you’re interested.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="s1">'(</span><span class="si">%s</span><span class="s1">--</span><span class="si">%s</span><span class="s1">)'</span> <span class="o">%</span> <span class="p">(</span>
|
||||
<span class="s1">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_to_str</span><span class="p">,</span> <span class="n">inputs</span> <span class="o">+</span> <span class="p">(</span><span class="s1">''</span><span class="p">,))),</span>
|
||||
<span class="s1">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">_to_str</span><span class="p">,</span> <span class="p">(</span><span class="s1">''</span><span class="p">,)</span> <span class="o">+</span> <span class="n">outputs</span><span class="p">))</span>
|
||||
@@ -728,7 +728,7 @@ you should skip it for now and read it later if you’re interested.</p>
|
||||
<p>Now we can write a compiler function to emit Python source code. (The
|
||||
underscore suffix distiguishes it from the built-in <code class="docutils literal notranslate"><span class="pre">compile()</span></code>
|
||||
function.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
|
||||
<span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">identifiers</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
|
||||
@@ -744,7 +744,7 @@ function.)</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Here it is in action:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">source</span> <span class="o">=</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">'F'</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">source</span> <span class="o">=</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">'F'</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
|
||||
|
||||
<span class="nb">print</span> <span class="n">source</span>
|
||||
</pre></div>
|
||||
@@ -756,13 +756,13 @@ function.)</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Compare:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F_python</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="p">((</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
<span class="k">return</span> <span class="p">((</span><span class="n">d</span><span class="p">,</span> <span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">S0</span><span class="p">)),</span> <span class="n">stack</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Next steps:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
|
||||
<span class="nb">eval</span><span class="p">(</span><span class="nb">compile</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="s1">'__main__'</span><span class="p">,</span> <span class="s1">'single'</span><span class="p">),</span> <span class="p">{},</span> <span class="n">L</span><span class="p">)</span>
|
||||
|
||||
@@ -773,14 +773,14 @@ function.)</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Let’s try it out:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">'F'</span><span class="p">]</span> <span class="o">=</span> <span class="n">SimpleFunctionWrapper</span><span class="p">(</span><span class="n">L</span><span class="p">[</span><span class="s1">'F'</span><span class="p">])</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span><span class="p">[</span><span class="s1">'F'</span><span class="p">]</span> <span class="o">=</span> <span class="n">SimpleFunctionWrapper</span><span class="p">(</span><span class="n">L</span><span class="p">[</span><span class="s1">'F'</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[4 5 ...] 2 3 1 F'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[4 5 ...] 2 3 1 F'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">3</span> <span class="mi">2</span> <span class="o">...</span><span class="p">]</span>
|
||||
@@ -800,7 +800,7 @@ this might be less helpful.</p>
|
||||
<h3>Compiling Library Functions<a class="headerlink" href="#compiling-library-functions" title="Permalink to this headline">¶</a></h3>
|
||||
<p>We can use <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> to generate many primitives in the library
|
||||
from their stack effect comments:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span>
|
||||
|
||||
<span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||
|
||||
@@ -823,7 +823,7 @@ from their stack effect comments:</p>
|
||||
<span class="k">return</span> <span class="nb">locals</span><span class="p">()</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
|
||||
<span class="nb">print</span>
|
||||
<span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span><span class="p">)</span>
|
||||
<span class="nb">print</span>
|
||||
@@ -966,7 +966,7 @@ and <code class="docutils literal notranslate"><span class="pre">t</span></code>
|
||||
Python class hierarchy of Joy types and use the <code class="docutils literal notranslate"><span class="pre">issubclass()</span></code> method
|
||||
to establish domain ordering, as well as other handy behaviour that will
|
||||
make it fairly easy to reuse most of the code above.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">AnyJoyType</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">AnyJoyType</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
||||
|
||||
<span class="n">prefix</span> <span class="o">=</span> <span class="s1">'a'</span>
|
||||
|
||||
@@ -1010,12 +1010,12 @@ make it fairly easy to reuse most of the code above.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Mess with it a little:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">permutations</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">permutations</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>“Any” types can be specialized to numbers and stacks, but not vice
|
||||
versa:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="mi">2</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="mi">2</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">a</span><span class="p">,</span> <span class="s1">'>='</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="s1">'->'</span><span class="p">,</span> <span class="n">a</span> <span class="o">>=</span> <span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1030,7 +1030,7 @@ versa:</p>
|
||||
<p>Our crude <a class="reference external" href="https://en.wikipedia.org/wiki/Numerical_tower">Numerical
|
||||
Tower</a> of <em>numbers</em> >
|
||||
<em>floats</em> > <em>integers</em> works as well (but we’re not going to use it yet):</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">FloatJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">IntJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">)),</span> <span class="mi">2</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">permutations</span><span class="p">((</span><span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">FloatJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">IntJoyType</span><span class="p">(</span><span class="mi">0</span><span class="p">)),</span> <span class="mi">2</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">a</span><span class="p">,</span> <span class="s1">'>='</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="s1">'->'</span><span class="p">,</span> <span class="n">a</span> <span class="o">>=</span> <span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1051,18 +1051,18 @@ Tower</a> of <em>numbers</em> >
|
||||
</section>
|
||||
<section id="typing-sqr">
|
||||
<h3>Typing <code class="docutils literal notranslate"><span class="pre">sqr</span></code><a class="headerlink" href="#typing-sqr" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||
|
||||
<span class="n">mul</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">dup</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">mul</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">mul</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">),</span> <span class="p">(</span><span class="n">n3</span><span class="p">,))</span>
|
||||
@@ -1072,7 +1072,7 @@ Tower</a> of <em>numbers</em> >
|
||||
<section id="modifying-the-inferencer">
|
||||
<h3>Modifying the Inferencer<a class="headerlink" href="#modifying-the-inferencer" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Re-labeling still works fine:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">foo</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">foo</span> <span class="o">=</span> <span class="n">relabel</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
|
||||
|
||||
<span class="n">foo</span>
|
||||
</pre></div>
|
||||
@@ -1084,7 +1084,7 @@ Tower</a> of <em>numbers</em> >
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">delabel()</span></code> version 2<a class="headerlink" href="#delabel-version-2" title="Permalink to this headline">¶</a></h4>
|
||||
<p>The <code class="docutils literal notranslate"><span class="pre">delabel()</span></code> function needs an overhaul. It now has to keep track
|
||||
of how many labels of each domain it has “seen”.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">Counter</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">Counter</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">delabel</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">seen</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
@@ -1105,7 +1105,7 @@ of how many labels of each domain it has “seen”.</p>
|
||||
<span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">delabel</span><span class="p">(</span><span class="n">inner</span><span class="p">,</span> <span class="n">seen</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span> <span class="k">for</span> <span class="n">inner</span> <span class="ow">in</span> <span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">delabel</span><span class="p">(</span><span class="n">foo</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">delabel</span><span class="p">(</span><span class="n">foo</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">a1</span><span class="p">)),</span> <span class="p">((</span><span class="n">n1</span><span class="p">,</span> <span class="n">n2</span><span class="p">),</span> <span class="p">(</span><span class="n">n3</span><span class="p">,)))</span>
|
||||
@@ -1114,7 +1114,7 @@ of how many labels of each domain it has “seen”.</p>
|
||||
</section>
|
||||
<section id="unify-version-3">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 3<a class="headerlink" href="#unify-version-3" title="Permalink to this headline">¶</a></h4>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
|
||||
@@ -1162,7 +1162,7 @@ of how many labels of each domain it has “seen”.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Rewrite the stack effect comments:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">defs</span><span class="p">():</span>
|
||||
|
||||
<span class="n">rolldown</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||
|
||||
@@ -1215,10 +1215,10 @@ of how many labels of each domain it has “seen”.</p>
|
||||
<span class="k">return</span> <span class="nb">locals</span><span class="p">()</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">DEFS</span> <span class="o">=</span> <span class="n">defs</span><span class="p">()</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">DEFS</span> <span class="o">=</span> <span class="n">defs</span><span class="p">()</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
|
||||
<span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">'='</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1250,27 +1250,27 @@ of how many labels of each domain it has “seen”.</p>
|
||||
<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">DEFS</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">DEFS</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</section>
|
||||
<section id="compose-dup-and-mul">
|
||||
<h4>Compose <code class="docutils literal notranslate"><span class="pre">dup</span></code> and <code class="docutils literal notranslate"><span class="pre">mul</span></code><a class="headerlink" href="#compose-dup-and-mul" title="Permalink to this headline">¶</a></h4>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">n1</span><span class="p">,),</span> <span class="p">(</span><span class="n">n2</span><span class="p">,))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Revisit the <code class="docutils literal notranslate"><span class="pre">F</span></code> function, works fine.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">rest</span><span class="p">,</span> <span class="n">cons</span><span class="p">,</span> <span class="n">cons</span><span class="p">))</span>
|
||||
<span class="n">F</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(((</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">a3</span><span class="p">,</span> <span class="n">a4</span><span class="p">,</span> <span class="n">a5</span><span class="p">),</span> <span class="p">((</span><span class="n">a4</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">F</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">F</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a1</span> <span class="n">a2</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a4</span> <span class="n">a5</span> <span class="o">--</span> <span class="p">[</span><span class="n">a4</span> <span class="n">a3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
@@ -1278,25 +1278,25 @@ of how many labels of each domain it has “seen”.</p>
|
||||
</div>
|
||||
<p>Some otherwise inefficient functions are no longer to be feared. We can
|
||||
also get the effect of combinators in some limited cases.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">neato</span><span class="p">(</span><span class="o">*</span><span class="n">funcs</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">neato</span><span class="p">(</span><span class="o">*</span><span class="n">funcs</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="n">funcs</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [swap] dip</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [swap] dip</span>
|
||||
<span class="n">neato</span><span class="p">(</span><span class="n">rollup</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">--</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a3</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [popop] dipd</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># e.g. [popop] dipd</span>
|
||||
<span class="n">neato</span><span class="p">(</span><span class="n">popdd</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">pop</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="n">a4</span> <span class="o">--</span> <span class="n">a3</span> <span class="n">a4</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Reverse the order of the top three items.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Reverse the order of the top three items.</span>
|
||||
<span class="n">neato</span><span class="p">(</span><span class="n">rollup</span><span class="p">,</span> <span class="n">swap</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1308,7 +1308,7 @@ also get the effect of combinators in some limited cases.</p>
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">compile_()</span></code> version 2<a class="headerlink" href="#compile-version-2" title="Permalink to this headline">¶</a></h4>
|
||||
<p>Because the type labels represent themselves as valid Python identifiers
|
||||
the <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> function doesn’t need to generate them anymore:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">f</span>
|
||||
<span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">)</span>
|
||||
@@ -1323,7 +1323,7 @@ the <code class="docutils literal notranslate"><span class="pre">compile_()</spa
|
||||
<span class="s1"> return </span><span class="si">%s</span><span class="s1">'''</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">'F'</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">'F'</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
@@ -1334,7 +1334,7 @@ the <code class="docutils literal notranslate"><span class="pre">compile_()</spa
|
||||
</div>
|
||||
<p>But it cannot magically create new functions that involve e.g. math and
|
||||
such. Note that this is <em>not</em> a <code class="docutils literal notranslate"><span class="pre">sqr</span></code> function implementation:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">'sqr'</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">'sqr'</span><span class="p">,</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sqr</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
@@ -1356,14 +1356,14 @@ functions (at least) are already wrappers it should be straightforward.)</p>
|
||||
<p>The functions that <em>can</em> be compiled are the ones that have only
|
||||
<code class="docutils literal notranslate"><span class="pre">AnyJoyType</span></code> and <code class="docutils literal notranslate"><span class="pre">StackJoyType</span></code> labels in their stack effect
|
||||
comments. We can write a function to check that:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">imap</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">imap</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">compilable</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">(</span><span class="n">imap</span><span class="p">(</span><span class="n">compilable</span><span class="p">,</span> <span class="n">f</span><span class="p">))</span> <span class="ow">or</span> <span class="n">stacky</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">defs</span><span class="p">()</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
|
||||
<span class="k">if</span> <span class="n">compilable</span><span class="p">(</span><span class="n">stack_effect_comment</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">'='</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
@@ -1465,7 +1465,7 @@ first two rules’ <code class="docutils literal notranslate"><span class="pre">
|
||||
the “truthiness” of <code class="docutils literal notranslate"><span class="pre">StackJoyType</span></code> to false to let e.g.
|
||||
<code class="docutils literal notranslate"><span class="pre">joy.utils.stack.concat</span></code> work with our stack effect comment cons-list
|
||||
tuples.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
<span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">s</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span> <span class="c1"># s can also be the empty dict, which is ok.</span>
|
||||
@@ -1475,7 +1475,7 @@ tuples.)</p>
|
||||
</div>
|
||||
<p>I don’t want to rewrite all the defs myself, so I’ll write a little
|
||||
conversion function instead. This is programmer’s laziness.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sequence_to_stack</span><span class="p">(</span><span class="n">seq</span><span class="p">,</span> <span class="n">stack</span><span class="o">=</span><span class="n">StackJoyType</span><span class="p">(</span><span class="mi">23</span><span class="p">)):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">sequence_to_stack</span><span class="p">(</span><span class="n">seq</span><span class="p">,</span> <span class="n">stack</span><span class="o">=</span><span class="n">StackJoyType</span><span class="p">(</span><span class="mi">23</span><span class="p">)):</span>
|
||||
<span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">seq</span><span class="p">:</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">item</span><span class="p">,</span> <span class="n">stack</span>
|
||||
<span class="k">return</span> <span class="n">stack</span>
|
||||
|
||||
@@ -1488,13 +1488,13 @@ conversion function instead. This is programmer’s laziness.</p>
|
||||
<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">),</span> <span class="p">(</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="p">(</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s1</span><span class="p">))))))</span>
|
||||
@@ -1506,7 +1506,7 @@ conversion function instead. This is programmer’s laziness.</p>
|
||||
<section id="doc-from-stack-effect-version-2">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">doc_from_stack_effect()</span></code> version 2<a class="headerlink" href="#doc-from-stack-effect-version-2" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Clunky junk, but it will suffice for now.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">doc_from_stack_effect</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">outputs</span><span class="p">):</span>
|
||||
<span class="n">switch</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="c1"># Do we need to display the '...' for the rest of the main stack?</span>
|
||||
<span class="n">i</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">_f</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">switch</span><span class="p">),</span> <span class="n">_f</span><span class="p">(</span><span class="n">outputs</span><span class="p">,</span> <span class="n">switch</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">switch</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
|
||||
@@ -1553,7 +1553,7 @@ conversion function instead. This is programmer’s laziness.</p>
|
||||
<span class="k">return</span> <span class="s1">'[</span><span class="si">%s</span><span class="s1">]'</span> <span class="o">%</span> <span class="s1">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">NEW_DEFS</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
|
||||
<span class="nb">print</span> <span class="n">name</span><span class="p">,</span> <span class="s1">'='</span><span class="p">,</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack_effect_comment</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1587,7 +1587,7 @@ conversion function instead. This is programmer’s laziness.</p>
|
||||
<span class="n">uncons</span> <span class="o">=</span> <span class="p">([</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">stack</span><span class="p">)</span>
|
||||
<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">))</span>
|
||||
<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">uncons</span><span class="p">)))</span>
|
||||
<span class="nb">print</span> <span class="p">;</span> <span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">reduce</span><span class="p">(</span><span class="n">C</span><span class="p">,</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">uncons</span><span class="p">,</span> <span class="n">cons</span><span class="p">)))</span>
|
||||
@@ -1602,13 +1602,13 @@ conversion function instead. This is programmer’s laziness.</p>
|
||||
<span class="p">(</span><span class="o">...</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="n">a1</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="p">[[</span><span class="n">a2</span> <span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">...</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">Q</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">ccons</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span>
|
||||
|
||||
<span class="n">Q</span>
|
||||
</pre></div>
|
||||
@@ -1620,7 +1620,7 @@ conversion function instead. This is programmer’s laziness.</p>
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">compile_()</span></code> version 3<a class="headerlink" href="#compile-version-3" title="Permalink to this headline">¶</a></h4>
|
||||
<p>This makes the <code class="docutils literal notranslate"><span class="pre">compile_()</span></code> function pretty simple as the stack effect
|
||||
comments are now already in the form needed for the Python code:</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compile_</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">doc</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="n">i</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">f</span>
|
||||
<span class="k">if</span> <span class="n">doc</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">doc</span> <span class="o">=</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
|
||||
@@ -1630,7 +1630,7 @@ comments are now already in the form needed for the Python code:</p>
|
||||
<span class="s1"> return </span><span class="si">%s</span><span class="s1">'''</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">doc</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">o</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">'Q'</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">compile_</span><span class="p">(</span><span class="s1">'Q'</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">Q</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
@@ -1639,35 +1639,35 @@ comments are now already in the form needed for the Python code:</p>
|
||||
<span class="k">return</span> <span class="p">(((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">),</span> <span class="p">((</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">s2</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">unstack</span> <span class="o">=</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">unstack</span> <span class="o">=</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
|
||||
<span class="n">enstacken</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">unstack</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">unstack</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">enstacken</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">enstacken</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">enstacken</span><span class="p">))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">enstacken</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">.</span><span class="mf">2.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">C</span><span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="n">unstack</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((</span><span class="n">s1</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)),</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span>
|
||||
@@ -1679,14 +1679,14 @@ comments are now already in the form needed for the Python code:</p>
|
||||
<section id="part-vi-multiple-stack-effects">
|
||||
<h2>Part VI: Multiple Stack Effects<a class="headerlink" href="#part-vi-multiple-stack-effects" title="Permalink to this headline">¶</a></h2>
|
||||
<p>…</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">IntJoyType</span><span class="p">(</span><span class="n">NumberJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">'i'</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">IntJoyType</span><span class="p">(</span><span class="n">NumberJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">'i'</span>
|
||||
|
||||
|
||||
<span class="n">F</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">FloatJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
|
||||
<span class="n">I</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">IntJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">muls</span> <span class="o">=</span> <span class="p">[</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">muls</span> <span class="o">=</span> <span class="p">[</span>
|
||||
<span class="p">((</span><span class="n">I</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
|
||||
<span class="p">((</span><span class="n">F</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">I</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
|
||||
<span class="p">((</span><span class="n">I</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span> <span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])),</span>
|
||||
@@ -1694,7 +1694,7 @@ comments are now already in the form needed for the Python code:</p>
|
||||
<span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1704,7 +1704,7 @@ comments are now already in the form needed for the Python code:</p>
|
||||
<span class="p">(</span><span class="n">f1</span> <span class="n">f2</span> <span class="o">--</span> <span class="n">f3</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">muls</span><span class="p">:</span>
|
||||
<span class="k">try</span><span class="p">:</span>
|
||||
<span class="n">e</span> <span class="o">=</span> <span class="n">C</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span>
|
||||
<span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||||
@@ -1716,7 +1716,7 @@ comments are now already in the form needed for the Python code:</p>
|
||||
<span class="p">(</span><span class="n">a1</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a1</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="n">f2</span> <span class="o">--</span> <span class="n">f3</span><span class="p">)</span> <span class="p">(</span><span class="n">f1</span> <span class="o">--</span> <span class="n">f2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
|
||||
@@ -1731,14 +1731,14 @@ comments are now already in the form needed for the Python code:</p>
|
||||
<span class="k">return</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">mul</span><span class="p">]):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">mul</span><span class="p">]):</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">n1</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1793,7 +1793,7 @@ disappears:</p>
|
||||
<span class="p">{</span><span class="n">c</span><span class="p">:</span> <span class="n">a</span><span class="p">,</span> <span class="n">d</span><span class="p">:</span> <span class="n">e</span><span class="p">,</span> <span class="o">.</span><span class="mf">1.</span><span class="p">:</span> <span class="n">A</span><span class="o">*</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">}</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">KleeneStar</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">KleeneStar</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
||||
|
||||
<span class="n">kind</span> <span class="o">=</span> <span class="n">AnyJoyType</span>
|
||||
|
||||
@@ -1840,7 +1840,7 @@ disappears:</p>
|
||||
<section id="unify-version-4">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 4<a class="headerlink" href="#unify-version-4" title="Permalink to this headline">¶</a></h4>
|
||||
<p>Can now return multiple results…</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">unify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="k">if</span> <span class="n">s</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="k">elif</span> <span class="n">s</span><span class="p">:</span>
|
||||
@@ -1911,21 +1911,21 @@ disappears:</p>
|
||||
<span class="k">return</span> <span class="n">thing</span><span class="o">.</span><span class="vm">__class__</span> <span class="ow">in</span> <span class="p">{</span><span class="n">AnyJoyType</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">}</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||
<span class="n">a</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
|
||||
<span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">s2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">'->'</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1933,7 +1933,7 @@ disappears:</p>
|
||||
<span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a10001</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)}</span> <span class="o">-></span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span> <span class="p">(</span><span class="n">a10001</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">'->'</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">a</span><span class="p">),</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1948,7 +1948,7 @@ disappears:</p>
|
||||
<span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">)</span> <span class="p">[</span><span class="n">a1</span><span class="o">*</span><span class="p">]</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="n">s1</span><span class="p">))</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a1</span><span class="o">*</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">((</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">((</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||||
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">sum_</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
@@ -1956,7 +1956,7 @@ disappears:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]))),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">]))),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
@@ -1964,7 +1964,7 @@ disappears:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">--</span> <span class="p">[</span><span class="n">n1</span> <span class="n">n2</span> <span class="n">n3</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">sum_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">sum_</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">f</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">result</span><span class="p">,</span> <span class="s1">'->'</span><span class="p">,</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">sum_</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1978,7 +1978,7 @@ disappears:</p>
|
||||
<section id="compose-version-3">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">compose()</span></code> version 3<a class="headerlink" href="#compose-version-3" title="Permalink to this headline">¶</a></h4>
|
||||
<p>This function has to be modified to yield multiple results.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">compose</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
<span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">),</span> <span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">)</span> <span class="o">=</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">g_in</span><span class="p">,</span> <span class="n">f_out</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">s</span><span class="p">:</span>
|
||||
@@ -1987,7 +1987,7 @@ disappears:</p>
|
||||
<span class="k">yield</span> <span class="n">update</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="p">(</span><span class="n">f_in</span><span class="p">,</span> <span class="n">g_out</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">meta_compose</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
|
||||
<span class="k">for</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span> <span class="ow">in</span> <span class="n">product</span><span class="p">(</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
|
||||
<span class="k">try</span><span class="p">:</span>
|
||||
<span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">C</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
|
||||
@@ -2002,7 +2002,7 @@ disappears:</p>
|
||||
<span class="k">yield</span> <span class="n">delabel</span><span class="p">(</span><span class="n">fg</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="n">muls</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2010,14 +2010,14 @@ disappears:</p>
|
||||
<span class="p">(</span><span class="n">i1</span> <span class="o">--</span> <span class="n">i2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">dup</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="n">n1</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">cons</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">cons</span><span class="p">],</span> <span class="p">[</span><span class="n">sum_</span><span class="p">]):</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">f</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2025,7 +2025,7 @@ disappears:</p>
|
||||
<span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">(((</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">sum_</span> <span class="o">=</span> <span class="p">(((</span><span class="n">N</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">Ns</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])),</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">N</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">cons</span><span class="p">),</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">sum_</span><span class="p">),</span>
|
||||
|
||||
@@ -2036,21 +2036,21 @@ disappears:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="p">[</span><span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span> <span class="p">([</span><span class="n">n1</span> <span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n0</span><span class="p">)</span> <span class="p">(</span><span class="n">n1</span> <span class="p">[</span><span class="n">n1</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">]</span> <span class="o">--</span> <span class="n">n2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="p">(</span><span class="n">As</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">1</span><span class="p">])))</span>
|
||||
<span class="n">a</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a4</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">]))</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">]))</span>
|
||||
<span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="p">(</span><span class="n">a2</span><span class="p">,</span> <span class="n">s2</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">result</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2058,7 +2058,7 @@ disappears:</p>
|
||||
<span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="n">a4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(</span><span class="n">a1</span><span class="o">*</span><span class="p">,</span> <span class="p">(</span><span class="n">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)),</span> <span class="n">a2</span><span class="p">:</span> <span class="n">a10003</span><span class="p">}</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">result</span> <span class="ow">in</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">result</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2111,7 +2111,7 @@ stack effect we have to “split universes” again and return both.</p>
|
||||
<p>We need a type variable for Joy functions that can go in our expressions
|
||||
and be used by the hybrid inferencer/interpreter. They have to store a
|
||||
name and a list of stack effects.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">FunctionJoyType</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">FunctionJoyType</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">):</span>
|
||||
|
||||
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">sec</span><span class="p">,</span> <span class="n">number</span><span class="p">):</span>
|
||||
<span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">name</span>
|
||||
@@ -2131,12 +2131,12 @@ name and a list of stack effects.</p>
|
||||
<h4>Specialized for Simple Functions and Combinators<a class="headerlink" href="#specialized-for-simple-functions-and-combinators" title="Permalink to this headline">¶</a></h4>
|
||||
<p>For non-combinator functions the stack effects list contains stack
|
||||
effect comments (represented by pairs of cons-lists as described above.)</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">SymbolJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">SymbolJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span>
|
||||
<span class="n">prefix</span> <span class="o">=</span> <span class="s1">'F'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>For combinators the list contains Python functions.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">CombinatorJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">CombinatorJoyType</span><span class="p">(</span><span class="n">FunctionJoyType</span><span class="p">):</span>
|
||||
|
||||
<span class="n">prefix</span> <span class="o">=</span> <span class="s1">'C'</span>
|
||||
|
||||
@@ -2155,7 +2155,7 @@ effect comments (represented by pairs of cons-lists as described above.)</p>
|
||||
</div>
|
||||
<p>For simple combinators that have only one effect (like <code class="docutils literal notranslate"><span class="pre">dip</span></code>) you only
|
||||
need one function and it can be the combinator itself.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span>
|
||||
|
||||
<span class="n">dip</span> <span class="o">=</span> <span class="n">CombinatorJoyType</span><span class="p">(</span><span class="s1">'dip'</span><span class="p">,</span> <span class="p">[</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">],</span> <span class="mi">23</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
@@ -2163,7 +2163,7 @@ need one function and it can be the combinator itself.</p>
|
||||
<p>For combinators that can have more than one effect (like <code class="docutils literal notranslate"><span class="pre">branch</span></code>) you
|
||||
have to write functions that each implement the action of one of the
|
||||
effects.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">branch_true</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">branch_true</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">):</span>
|
||||
<span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="p">(</span><span class="n">else_</span><span class="p">,</span> <span class="p">(</span><span class="n">flag</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">concat</span><span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
|
||||
|
||||
@@ -2189,7 +2189,7 @@ that expression.</p>
|
||||
updated along with the stack effects after doing unification or we risk
|
||||
losing useful information. This was a straightforward, if awkward,
|
||||
modification to the call structure of <code class="docutils literal notranslate"><span class="pre">meta_compose()</span></code> et. al.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">ID</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># Identity function.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">ID</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">S</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># Identity function.</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">infer</span><span class="p">(</span><span class="o">*</span><span class="n">expression</span><span class="p">):</span>
|
||||
@@ -2249,7 +2249,7 @@ module (FIXME link to its docs here!) should be explained… There is
|
||||
cruft to convert the definitions in <code class="docutils literal notranslate"><span class="pre">DEFS</span></code> to the new
|
||||
<code class="docutils literal notranslate"><span class="pre">SymbolJoyType</span></code> objects, and some combinators. Here is an example of
|
||||
output from the current code :</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span><span class="o">/</span><span class="mi">0</span> <span class="c1"># (Don't try to run this cell! It's not going to work. This is "read only" code heh..)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span><span class="o">/</span><span class="mi">0</span> <span class="c1"># (Don't try to run this cell! It's not going to work. This is "read only" code heh..)</span>
|
||||
|
||||
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span><span class="nb">format</span><span class="o">=</span><span class="s1">'</span><span class="si">%(message)s</span><span class="s1">'</span><span class="p">,</span> <span class="n">stream</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stdout</span><span class="p">,</span> <span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span><span class="p">)</span>
|
||||
|
||||
@@ -2366,7 +2366,7 @@ relational</em> nature of the stack effect comments to “compute in reverse”
|
||||
as it were. There’s a working demo of this at the end of the <code class="docutils literal notranslate"><span class="pre">types</span></code>
|
||||
module. But if you’re interested in all that you should just use Prolog!</p>
|
||||
<p>Anyhow, type <em>checking</em> is a few easy steps away.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_ge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_ge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="p">(</span><span class="nb">issubclass</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">)</span>
|
||||
<span class="ow">or</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'accept'</span><span class="p">)</span>
|
||||
<span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">accept</span><span class="p">))</span>
|
||||
|
||||
@@ -42,7 +42,7 @@ the original paper: <a class="reference external" href="https://www.st.cs.uni-sa
|
||||
Huet</a></p>
|
||||
<p>Given a datastructure on the stack we can navigate through it, modify
|
||||
it, and rebuild it using the “zipper” technique.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<section id="trees">
|
||||
@@ -52,7 +52,7 @@ strings, Symbols (strings that are names of functions) and sequences
|
||||
(aka lists, aka quoted literals, aka aggregates, etc…), but we can build
|
||||
<a class="reference external" href="https://en.wikipedia.org/wiki/Tree_%28data_structure%29">trees</a> out
|
||||
of sequences.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8]'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8]'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
|
||||
@@ -75,13 +75,13 @@ datastructure used to keep track of these items is the zipper.)</p>
|
||||
show the trace so you can see how it works. If we were going to use
|
||||
these a lot it would make sense to write Python versions for efficiency,
|
||||
but see below.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'z-down == [] swap uncons swap'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'z-down == [] swap uncons swap'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'z-up == swons swap shunt'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'z-right == [swons] cons dip uncons swap'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'z-left == swons [uncons swap] dip swap'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8] z-down'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8] z-down'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">z</span><span class="o">-</span><span class="n">down</span>
|
||||
@@ -93,7 +93,7 @@ but see below.</p>
|
||||
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[] [[2 [3 4 25 6] 7] 8] 1 z-right'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[] [[2 [3 4 25 6] 7] 8] 1 z-right'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span>
|
||||
@@ -113,43 +113,43 @@ but see below.</p>
|
||||
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2 [3 4 25 6] 7] z-down'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2 [3 4 25 6] 7] z-down'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">2</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [] [[3 4 25 6] 7] 2 z-right'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [] [[3 4 25 6] 7] 2 z-right'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [3 4 25 6] z-down'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [3 4 25 6] z-down'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">3</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [] [4 25 6] 3 z-right'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [] [4 25 6] 3 z-right'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">4</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [3] [25 6] 4 z-right'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [3] [25 6] 4 z-right'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">25</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [4 3] [6] 25 sqr'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [4 3] [6] 25 sqr'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [4 3] [6] 625 z-up'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [4 3] [6] 625 z-up'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||
@@ -168,13 +168,13 @@ but see below.</p>
|
||||
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [3 4 625 6] z-up'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [3 4 625 6] z-up'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2 [3 4 625 6] 7] z-up'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1] [8] [2 [3 4 625 6] 7] z-up'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
|
||||
@@ -185,7 +185,7 @@ but see below.</p>
|
||||
<h2><code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code><a class="headerlink" href="#dip-and-infra" title="Permalink to this headline">¶</a></h2>
|
||||
<p>In Joy we have the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators which can “target”
|
||||
or “address” any particular item in a Joy tree structure.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span>
|
||||
@@ -236,11 +236,11 @@ been embedded in a nested series of quoted programs, e.g.:</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>The <code class="docutils literal notranslate"><span class="pre">Z</span></code> function isn’t hard to make.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Z == [[] cons cons] step i'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'Z == [[] cons cons] step i'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Here it is in action in a simplified scenario.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'1 [2 3 4] Z'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'1 [2 3 4] Z'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="n">Z</span>
|
||||
@@ -273,7 +273,7 @@ been embedded in a nested series of quoted programs, e.g.:</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>And here it is doing the main thing.</p>
|
||||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
|
||||
|
||||
@@ -110,6 +110,14 @@
|
||||
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a><ul>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#original-form">Original Form</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#translation-to-joy">Translation to Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#putting-the-pieces-together">Putting the Pieces Together</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#turning-it-into-a-generator-with-x">Turning it into a Generator with <code class="docutils literal notranslate"><span class="pre">x</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html#conclusion">Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a><ul>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#trees">Trees</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#zipper-in-joy">Zipper in Joy</a></li>
|
||||
@@ -194,6 +202,7 @@
|
||||
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Square_Spiral.html">Square Spiral Example Joy Code</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>
|
||||
|
||||
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Reference in New Issue
Block a user