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Simon Forman
2020-05-17 16:40:58 -07:00
parent ef6411205d
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docs/sphinx_docs/notebooks/Zipper.rst
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@@ -1,14 +1,14 @@
Traversing Datastructures with Zippers
======================================
This notebook is about using the "zipper" with joy datastructures. See
This notebook is about using the “zipper” with joy datastructures. See
the `Zipper wikipedia
entry <https://en.wikipedia.org/wiki/Zipper_%28data_structure%29>`__ or
the original paper: `"FUNCTIONAL PEARL The Zipper" by Gérard
the original paper: `“FUNCTIONAL PEARL The Zipper” by Gérard
Huet <https://www.st.cs.uni-saarland.de/edu/seminare/2005/advanced-fp/docs/huet-zipper.pdf>`__
Given a datastructure on the stack we can navigate through it, modify
it, and rebuild it using the "zipper" technique.
it, and rebuild it using the “zipper” technique.
.. code:: ipython2
@@ -17,10 +17,9 @@ it, and rebuild it using the "zipper" technique.
Trees
-----
In Joypy there aren't any complex datastructures, just ints, floats,
In Joypy there aren’t any complex datastructures, just ints, floats,
strings, Symbols (strings that are names of functions) and sequences
(aka lists, aka quoted literals, aka aggregates, etc...), but we can
build
(aka lists, aka quoted literals, aka aggregates, etc…), but we can build
`trees <https://en.wikipedia.org/wiki/Tree_%28data_structure%29>`__ out
of sequences.
@@ -45,12 +44,12 @@ In Joy we can do this with the following words:
::
z-down == [] swap uncons swap
z-up == swons swap shunt
z-right == [swons] cons dip uncons swap
z-left == swons [uncons swap] dip swap
z-down == [] swap uncons swap
z-up == swons swap shunt
z-right == [swons] cons dip uncons swap
z-left == swons [uncons swap] dip swap
Let's use them to change 25 into 625. The first time a word is used I
Let’s use them to change 25 into 625. The first time a word is used I
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.
@@ -208,8 +207,8 @@ but see below.
``dip`` and ``infra``
---------------------
In Joy we have the ``dip`` and ``infra`` combinators which can "target"
or "address" any particular item in a Joy tree structure.
In Joy we have the ``dip`` and ``infra`` combinators which can “target”
or “address” any particular item in a Joy tree structure.
.. code:: ipython2
@@ -247,8 +246,8 @@ or "address" any particular item in a Joy tree structure.
[1 [2 [3 4 625 6] 7] 8] .
If you read the trace carefully you'll see that about half of it is the
``dip`` and ``infra`` combinators de-quoting programs and "digging" into
If you read the trace carefully you’ll see that about half of it is the
``dip`` and ``infra`` combinators de-quoting programs and “digging” into
the subject datastructure. Instead of maintaining temporary results on
the stack they are pushed into the pending expression (continuation).
When ``sqr`` has run the rest of the pending expression rebuilds the
@@ -264,12 +263,12 @@ been embedded in a nested series of quoted programs, e.g.:
::
[...] [Q] [dip dip infra dip infra dip infra] Z
-------------------------------------------------------------
[...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra
[...] [Q] [dip dip infra dip infra dip infra] Z
-------------------------------------------------------------
[...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra
The ``Z`` function isn't hard to make.
The ``Z`` function isn’t hard to make.
.. code:: ipython2
@@ -333,21 +332,21 @@ a string made from only two characters.
::
[...] [Q] 'ddididi' Zstr
-------------------------------------------------------------
[...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra
[...] [Q] 'ddididi' Zstr
-------------------------------------------------------------
[...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra
The string can be considered a name or address for an item in the
subject datastructure.
Determining the right "path" for an item in a tree.
Determining the right “path” for an item in a tree.
---------------------------------------------------
It's easy to read off (in reverse) the right sequence of "d" and "i"
It’s easy to read off (in reverse) the right sequence of “d” and “i”
from the subject datastructure:
::
[ n [ n [ n n x ...
i d i d i d d Bingo!
[ n [ n [ n n x ...
i d i d i d d Bingo!