Type inference of Joy expressions.
More remains to be done but it seems to work.
This commit is contained in:
Simon Forman
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@@ -1,5 +1,5 @@
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# Type Inference
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# The Blissful Elegance of Typing Joy
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This notebook presents a simple type inferencer for Joy code. It can infer the stack effect of most Joy expressions. It's built largely by means of existing ideas and research. (A great overview of the existing knowledge is a talk ["Type Inference in Stack-Based Programming Languages"](http://prl.ccs.neu.edu/blog/2017/03/10/type-inference-in-stack-based-programming-languages/) given by Rob Kleffner on or about 2017-03-10 as part of a course on the history of programming languages.)
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@@ -345,6 +345,8 @@ def unify(u, v, s=None):
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s[u] = v
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elif isinstance(v, int):
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s[v] = u
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else:
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s = False
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return s
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```
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@@ -556,6 +558,9 @@ except Exception, e:
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print e
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```
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Cannot unify (1, 2) and (1001, 1002).
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#### `unify()` version 2
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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:
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@@ -584,6 +589,8 @@ def unify(u, v, s=None):
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s = unify(a, c, s)
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if s != False:
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s = unify(b, d, s)
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else:
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s = False
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return s
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```
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@@ -1413,7 +1420,7 @@ print compile_('sqr', C(dup, mul))
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return (n2, stack)
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(Eventually I should come back around to this becuase it's not tooo difficult to exend this code to be able to compile e.g. `n3 = mul(n1, n2)` for `mul` and insert it in the right place with the right variable names. It requires a little more support from the library functions, in that we need to know to call `mul()` the Python function for `mul` the Joy function, but since *most* of the math functions (at least) are already wrappers it should be straightforward.)
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(Eventually I should come back around to this becuase it's not tooo difficult to exend this code to be able to compile e.g. `n2 = mul(n1, n1)` for `mul` with the right variable names and insert it in the right place. It requires a little more support from the library functions, in that we need to know to call `mul()` the Python function for `mul` the Joy function, but since *most* of the math functions (at least) are already wrappers it should be straightforward.)
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#### `compilable()`
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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:
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@@ -2227,7 +2234,7 @@ for result in unify(a, b):
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## Part VII: Typing Combinators
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In order to compute the stack effect of combinators you kinda have to have the quoted programs they expect available. In the most general case, the `i` combinator, you can't say anything about it's stack effect other than it expects one quote:
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In order to compute the stack effect of combinators you kinda have to have the quoted programs they expect available. In the most general case, the `i` combinator, you can't say anything about its stack effect other than it expects one quote:
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i (... [.1.] -- ... .1.)
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@@ -2250,7 +2257,11 @@ Obviously it would be:
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Without any information about the contents of the quote we can't say much about the result.
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I think there's a way forward. If we convert our list of terms we are composing into a stack structure we can use it as a *Joy expression*, then we can treat the *output half* of a function's stack effect comment as a Joy interpreter stack, and just execute combinators directly. We can hybridize the compostition function with an interpreter to evaluate combinators, compose non-combinator functions, and put type variables on the stack. For combinators like `branch` that can have more than one stack effect we have to "split universes" again and return both.
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### Hybrid Inferencer/Interpreter
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I think there's a way forward. If we convert our list (of terms we are composing) into a stack structure we can use it as a *Joy expression*, then we can treat the *output half* of a function's stack effect comment as a Joy interpreter stack, and just execute combinators directly. We can hybridize the compostition function with an interpreter to evaluate combinators, compose non-combinator functions, and put type variables on the stack. For combinators like `branch` that can have more than one stack effect we have to "split universes" again and return both.
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#### Joy Types for Functions
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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.
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```python
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@@ -2267,211 +2278,183 @@ class FunctionJoyType(AnyJoyType):
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def __repr__(self):
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return self.name
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class SymbolJoyType(FunctionJoyType): prefix = 'F'
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class CombinatorJoyType(FunctionJoyType): prefix = 'C'
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```
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#### Specialized for Simple Functions and Combinators
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For non-combinator functions the stack effects list contains stack effect comments (represented by pairs of cons-lists as described above.)
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```python
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def flatten(g):
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return list(chain.from_iterable(g))
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class SymbolJoyType(FunctionJoyType):
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prefix = 'F'
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```
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For combinators the list contains Python functions.
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```python
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class CombinatorJoyType(FunctionJoyType):
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prefix = 'C'
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def __init__(self, name, sec, number, expect=None):
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super(CombinatorJoyType, self).__init__(name, sec, number)
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self.expect = expect
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def enter_guard(self, f):
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if self.expect is None:
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return f
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g = self.expect, self.expect
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new_f = list(compose(f, g, ()))
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assert len(new_f) == 1, repr(new_f)
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return new_f[0][1]
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```
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For simple combinators that have only one effect (like ``dip``) you only need one function and it can be the combinator itself.
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```python
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import joy.library
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dip = CombinatorJoyType('dip', [joy.library.dip], 23)
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```
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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.
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```python
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def branch_true(stack, expression, dictionary):
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(then, (else_, (flag, stack))) = stack
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return stack, concat(then, expression), dictionary
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def branch_false(stack, expression, dictionary):
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(then, (else_, (flag, stack))) = stack
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return stack, concat(else_, expression), dictionary
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branch = CombinatorJoyType('branch', [branch_true, branch_false], 100)
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```
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You can also provide an optional stack effect, input-side only, that will then be used as an identity function (that accepts and returns stacks that match the "guard" stack effect) which will be used to guard against type mismatches going into the evaluation of the combinator.
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#### `infer()`
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With those in place, we can define a function that accepts a sequence of Joy type variables, including ones representing functions (not just values), and attempts to grind out all the possible stack effects of that expression.
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One tricky thing is that type variables *in the expression* have to be 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.
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```python
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ID = S[0], S[0] # Identity function.
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def infer(e, F=ID):
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def infer(*expression):
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return sorted(set(_infer(list_to_stack(expression))))
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def _infer(e, F=ID):
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_log_it(e, F)
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if not e:
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return [F]
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n, e = e
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if isinstance(n, SymbolJoyType):
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res = flatten(infer(e, Fn) for Fn in MC([F], n.stack_effects))
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eFG = meta_compose([F], n.stack_effects, e)
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res = flatten(_infer(e, Fn) for e, Fn in eFG)
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elif isinstance(n, CombinatorJoyType):
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res = []
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for combinator in n.stack_effects:
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fi, fo = F
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new_fo, ee, _ = combinator(fo, e, {})
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ee = update(FUNCTIONS, ee) # Fix Symbols.
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new_F = fi, new_fo
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res.extend(infer(ee, new_F))
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fi, fo = n.enter_guard(F)
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res = flatten(_interpret(f, fi, fo, e) for f in n.stack_effects)
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elif isinstance(n, Symbol):
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assert n not in FUNCTIONS, repr(n)
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func = joy.library._dictionary[n]
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res = _interpret(func, F[0], F[1], e)
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else:
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lit = s9, (n, s9)
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res = flatten(infer(e, Fn) for Fn in MC([F], [lit]))
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fi, fo = F
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res = _infer(e, (fi, (n, fo)))
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return res
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def _interpret(f, fi, fo, e):
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new_fo, ee, _ = f(fo, e, {})
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ee = update(FUNCTIONS, ee) # Fix Symbols.
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new_F = fi, new_fo
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return _infer(ee, new_F)
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def _log_it(e, F):
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_log.info(
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u'%3i %s ∘ %s',
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len(inspect_stack()),
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doc_from_stack_effect(*F),
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expression_to_string(e),
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)
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```
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#### Work in Progress
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And that brings us to current Work-In-Progress. The mixed-mode inferencer/interpreter `infer()` function seems to work well. There are details I should document, and the rest of the code in the "polytypes" module (FIXME link to its docs here!) should be explained... There is 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 :
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```python
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f0, f1, f2, f3, f4, f5, f6, f7, f8, f9 = F = map(FloatJoyType, _R)
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i0, i1, i2, i3, i4, i5, i6, i7, i8, i9 = I = map(IntJoyType, _R)
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n0, n1, n2, n3, n4, n5, n6, n7, n8, n9 = N
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s0, s1, s2, s3, s4, s5, s6, s7, s8, s9 = S
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```
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1/0 # (Don't try to run this cell! It's not going to work. This is "read only" code heh..)
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logging.basicConfig(format='%(message)s', stream=sys.stdout, level=logging.INFO)
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```python
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import joy.library
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FNs = '''ccons cons divmod_ dup dupd first
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over pm pop popd popdd popop pred
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rest rolldown rollup rrest second
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sqrt stack succ swaack swap swons
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third tuck uncons'''
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FUNCTIONS = {
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name: SymbolJoyType(name, [NEW_DEFS[name]], i)
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for i, name in enumerate(FNs.strip().split())
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}
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FUNCTIONS['sum'] = SymbolJoyType('sum', [(((Ns[1], s1), s0), (n0, s0))], 100)
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FUNCTIONS['mul'] = SymbolJoyType('mul', [
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((i2, (i1, s0)), (i3, s0)),
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((f2, (i1, s0)), (f3, s0)),
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((i2, (f1, s0)), (f3, s0)),
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((f2, (f1, s0)), (f3, s0)),
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], 101)
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FUNCTIONS.update({
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combo.__name__: CombinatorJoyType(combo.__name__, [combo], i)
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for i, combo in enumerate((
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joy.library.i,
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joy.library.dip,
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joy.library.dipd,
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joy.library.dipdd,
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joy.library.dupdip,
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joy.library.b,
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joy.library.x,
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joy.library.infra,
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))
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})
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def branch_true(stack, expression, dictionary):
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(then, (else_, (flag, stack))) = stack
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return stack, CONCAT(then, expression), dictionary
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def branch_false(stack, expression, dictionary):
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(then, (else_, (flag, stack))) = stack
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return stack, CONCAT(else_, expression), dictionary
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FUNCTIONS['branch'] = CombinatorJoyType('branch', [branch_true, branch_false], 100)
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```
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```python
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globals().update(FUNCTIONS)
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h = infer((pred, s2), (mul, s3), (div, s4), (nullary, (bool, s5)), dipd, branch)
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print '-' * 40
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for fi, fo in h:
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print doc_from_stack_effect(fi, fo)
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```
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The numbers at the start of the lines are the current depth of the Python call stack. They're followed by the current computed stack effect (initialized to `ID`) then the pending expression (the inference of the stack effect of which is the whole object of the current example.)
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```python
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from itertools import chain
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from joy.utils.stack import list_to_stack as l2s
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```
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In this example we are implementing (and inferring) `ifte` as `[nullary bool] dipd branch` which shows off a lot of the current implementation in action.
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```python
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expression = l2s([n1, n2, (mul, s2), (stack, s3), dip, infra, first])
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```
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```python
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expression
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```
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(n1, (n2, ((mul, s2), ((stack, s3), (dip, (infra, (first, ())))))))
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```python
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expression = l2s([n1, n2, mul])
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```
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```python
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expression
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```
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(n1, (n2, (mul, ())))
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```python
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infer(expression)
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```
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[(s1, (f1, s1)), (s1, (i1, s1))]
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```python
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infer(expression)
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```
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[(s1, (f1, s1)), (s1, (i1, s1))]
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```python
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for stack_effect_comment in infer(expression):
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print doc_from_stack_effect(*stack_effect_comment)
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```
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(-- f1)
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(-- i1)
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```python
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expression
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```
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(n1, (n2, (mul, ())))
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```python
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infer(expression)
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```
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[(s1, (f1, s1)), (s1, (i1, s1))]
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And that brings us to current Work-In-Progress. I'm pretty hopeful that the mixed-mode inferencer/interpreter `infer()` function along with the ability to specify multiple implementations for the combinators will permit modelling of the stack effects of e.g. `ifte`. If I can keep up the pace I should be able to verify that conjecture by the end of June.
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7 (--) ∘ [pred] [mul] [div] [nullary bool] dipd branch
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8 (-- [pred ...2]) ∘ [mul] [div] [nullary bool] dipd branch
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9 (-- [pred ...2] [mul ...3]) ∘ [div] [nullary bool] dipd branch
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10 (-- [pred ...2] [mul ...3] [div ...4]) ∘ [nullary bool] dipd branch
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11 (-- [pred ...2] [mul ...3] [div ...4] [nullary bool ...5]) ∘ dipd branch
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15 (-- [pred ...5]) ∘ nullary bool [mul] [div] branch
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19 (-- [pred ...2]) ∘ [stack] dinfrirst bool [mul] [div] branch
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20 (-- [pred ...2] [stack ]) ∘ dinfrirst bool [mul] [div] branch
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22 (-- [pred ...2] [stack ]) ∘ dip infra first bool [mul] [div] branch
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26 (--) ∘ stack [pred] infra first bool [mul] [div] branch
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29 (... -- ... [...]) ∘ [pred] infra first bool [mul] [div] branch
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30 (... -- ... [...] [pred ...1]) ∘ infra first bool [mul] [div] branch
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34 (--) ∘ pred s1 swaack first bool [mul] [div] branch
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37 (n1 -- n2) ∘ [n1] swaack first bool [mul] [div] branch
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38 (... n1 -- ... n2 [n1 ...]) ∘ swaack first bool [mul] [div] branch
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41 (... n1 -- ... n1 [n2 ...]) ∘ first bool [mul] [div] branch
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44 (n1 -- n1 n2) ∘ bool [mul] [div] branch
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47 (n1 -- n1 b1) ∘ [mul] [div] branch
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48 (n1 -- n1 b1 [mul ...1]) ∘ [div] branch
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49 (n1 -- n1 b1 [mul ...1] [div ...2]) ∘ branch
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53 (n1 -- n1) ∘ div
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56 (f2 f1 -- f3) ∘
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56 (i1 f1 -- f2) ∘
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56 (f1 i1 -- f2) ∘
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56 (i2 i1 -- f1) ∘
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53 (n1 -- n1) ∘ mul
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56 (f2 f1 -- f3) ∘
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56 (i1 f1 -- f2) ∘
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56 (f1 i1 -- f2) ∘
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56 (i2 i1 -- i3) ∘
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----------------------------------------
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(f2 f1 -- f3)
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(i1 f1 -- f2)
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(f1 i1 -- f2)
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(i2 i1 -- f1)
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(i2 i1 -- i3)
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## Conclusion
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(for now...)
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We built a simple type inferencer, and a kind of crude "compiler" for a subset of Joy functions. Then we built a more powerful inferencer that actually does some evaluation and explores branching code paths
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Work remains to be done:
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||||
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@@ -2489,12 +2472,11 @@ Work remains to be done:
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- docstrings all around
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||||
- improve this notebook (it kinda falls apart at the end narratively. I went off and just started writing code to see if it would work. It does, but now I have to come back and describe here what I did.
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I'm starting to realize that, with the inferencer/checker/compiler coming along, and with the UI ready to be rewritten in Joy, I'm close to a time when my ephasis is going to have to shift from crunchy code stuff to squishy human stuff. I'm going to have to put normal people in front of this and see if, in fact, they *can* learn the basics of programming with it.
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The rest of this stuff is junk and/or unfinished material.
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## Appendix: Joy in the Logical Paradigm
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For this to work the type label classes have to be modified to let `T >= t` succeed, where e.g. `T` is `IntJoyType` and `t` is `int`
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For *type checking* to work the type label classes have to be modified to let `T >= t` succeed, where e.g. `T` is `IntJoyType` and `t` is `int`. If you do that you can take advantage of the *logical relational* 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 `polytypes` module. But if you're interested in all that you should just use Prolog!
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|
||||
Anyhow, type *checking* is a few easy steps away.
|
||||
|
||||
|
||||
```python
|
||||
@@ -2507,373 +2489,3 @@ AnyJoyType.__ge__ = _ge
|
||||
AnyJoyType.accept = tuple, int, float, long, str, unicode, bool, Symbol
|
||||
StackJoyType.accept = tuple
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
F = infer(l2s((pop, swap, rolldown, rest, rest, cons, cons)))
|
||||
|
||||
for f in F:
|
||||
print doc_from_stack_effect(*f)
|
||||
```
|
||||
|
||||
([a4 a5 .1.] a3 a2 a1 -- [a2 a3 .1.])
|
||||
|
||||
|
||||
|
||||
```python
|
||||
from joy.parser import text_to_expression
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
F = infer(l2s((pop, pop, pop)))
|
||||
|
||||
for f in F:
|
||||
print doc_from_stack_effect(*f)
|
||||
```
|
||||
|
||||
(a3 a2 a1 --)
|
||||
|
||||
|
||||
|
||||
```python
|
||||
s = text_to_expression('0 1 2')
|
||||
s
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
(0, (1, (2, ())))
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
F[0][0]
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
(a1, (a2, (a3, s1)))
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
L = unify(s, F[0][0])
|
||||
L
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
s = text_to_expression('0 1 2 [3 4]')
|
||||
s
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
(0, (1, (2, ((3, (4, ())), ()))))
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
F[0][0]
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
(a1, (a2, (a3, s1)))
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
L = unify(s, F[0][0])
|
||||
L
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
L = unify(F[0][0], s)
|
||||
L
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
F[1][0]
|
||||
```
|
||||
|
||||
|
||||
---------------------------------------------------------------------------
|
||||
|
||||
IndexError Traceback (most recent call last)
|
||||
|
||||
<ipython-input-133-58a8e44e9cba> in <module>()
|
||||
----> 1 F[1][0]
|
||||
|
||||
|
||||
IndexError: list index out of range
|
||||
|
||||
|
||||
|
||||
```python
|
||||
s[0]
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
A[1] >= 23
|
||||
```
|
||||
|
||||
## [Abstract Interpretation](https://en.wikipedia.org/wiki/Abstract_interpretation)
|
||||
I *think* this might be sorta what I'm doing above with the `kav()` function...
|
||||
In any event "mixed-mode" interpreters that include values and type variables and can track constraints, etc. will be, uh, super-useful. And Abstract Interpretation should be a rich source of ideas.
|
||||
|
||||
|
||||
## Junk
|
||||
|
||||
|
||||
```python
|
||||
class SymbolJoyType(AnyJoyType): prefix = 'F'
|
||||
|
||||
W = map(SymbolJoyType, _R)
|
||||
|
||||
k = S[0], ((W[1], S[2]), S[0])
|
||||
Symbol('cons')
|
||||
print doc_from_stack_effect(*k)
|
||||
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
dip_a = ((W[1], S[2]), (A[1], S[0]))
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
d = relabel(S[0], dip_a)
|
||||
print doc_from_stack_effect(*d)
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
s = list(unify(d[1], k[1]))[0]
|
||||
s
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
j = update(s, k)
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
print doc_from_stack_effect(*j)
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
j
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
cons
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
for f in MC([k], [dup]):
|
||||
print doc_from_stack_effect(*f)
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
l = S[0], ((cons, S[2]), (A[1], S[0]))
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
print doc_from_stack_effect(*l)
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
|
||||
def dip_t(F):
|
||||
(quote, (a1, sec)) = F[1]
|
||||
G = F[0], sec
|
||||
P = S[3], (a1, S[3])
|
||||
a = [P]
|
||||
while isinstance(quote, tuple):
|
||||
term, quote = quote
|
||||
a.append(term)
|
||||
a.append(G)
|
||||
return a[::-1]
|
||||
|
||||
|
||||
|
||||
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
from joy.utils.stack import iter_stack
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
a, b, c = dip_t(l)
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
a
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
b
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
c
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
MC([a], [b])
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
kjs = MC(MC([a], [b]), [c])
|
||||
kjs
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
print doc_from_stack_effect(*kjs[0])
|
||||
```
|
||||
|
||||
(a0 [.0.] -- [a0 .0.] a1)
|
||||
|
||||
a0 [.0.] a1 [cons] dip
|
||||
----------------------------
|
||||
[a0 .0.] a1
|
||||
|
||||
### `concat`
|
||||
|
||||
How to deal with `concat`?
|
||||
|
||||
concat ([.0.] [.1.] -- [.0. .1.])
|
||||
|
||||
We would like to represent this in Python somehow...
|
||||
|
||||
|
||||
```python
|
||||
concat = (S[0], S[1]), ((S[0], S[1]),)
|
||||
```
|
||||
|
||||
But this is actually `cons` with the first argument restricted to be a stack:
|
||||
|
||||
([.0.] [.1.] -- [[.0.] .1.])
|
||||
|
||||
What we have implemented so far would actually only permit:
|
||||
|
||||
([.0.] [.1.] -- [.2.])
|
||||
|
||||
|
||||
```python
|
||||
concat = (S[0], S[1]), (S[2],)
|
||||
```
|
||||
|
||||
|
||||
Which works but can lose information. Consider `cons concat`, this is how much information we *could* retain:
|
||||
|
||||
(1 [.0.] [.1.] -- [1 .0. .1.])
|
||||
|
||||
As opposed to just:
|
||||
|
||||
(1 [.0.] [.1.] -- [.2.])
|
||||
|
||||
### represent `concat`
|
||||
|
||||
([.0.] [.1.] -- [A*(.0.) .1.])
|
||||
|
||||
Meaning that `A*` on the right-hand side should all the crap from `.0.`.
|
||||
|
||||
([ .0.] [.1.] -- [ A* .1.])
|
||||
([a .0.] [.1.] -- [a A* .1.])
|
||||
([a b .0.] [.1.] -- [a b A* .1.])
|
||||
([a b c .0.] [.1.] -- [a b c A* .1.])
|
||||
|
||||
|
||||
|
||||
or...
|
||||
|
||||
([ .0.] [.1.] -- [ .1.])
|
||||
([a .0.] [.1.] -- [a .1.])
|
||||
([a b .0.] [.1.] -- [a b .1.])
|
||||
([a b c .0.] [.1.] -- [a b c .1.])
|
||||
([a A* c .0.] [.1.] -- [a A* c .1.])
|
||||
|
||||
|
||||
|
||||
(a, (b, S0)) . S1 = (a, (b, (A*, S1)))
|
||||
|
||||
|
||||
```python
|
||||
class Astar(object):
|
||||
def __repr__(self):
|
||||
return 'A*'
|
||||
|
||||
|
||||
def concat(s0, s1):
|
||||
a = []
|
||||
while isinstance(s0, tuple):
|
||||
term, s0 = s0
|
||||
a.append(term)
|
||||
assert isinstance(s0, StackJoyType), repr(s0)
|
||||
s1 = Astar(), s1
|
||||
for term in reversed(a):
|
||||
s1 = term, s1
|
||||
return s1
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
a, b = (A[1], S[0]), (A[2], S[1])
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
concat(a, b)
|
||||
```
|
||||
|
||||
+210
-578
@@ -1,6 +1,6 @@
|
||||
|
||||
Type Inference
|
||||
==============
|
||||
The Blissful Elegance of Typing Joy
|
||||
===================================
|
||||
|
||||
This notebook presents a simple type inferencer for Joy code. It can
|
||||
infer the stack effect of most Joy expressions. It's built largely by
|
||||
@@ -476,6 +476,8 @@ integers or tuples of type descriptors:
|
||||
s[u] = v
|
||||
elif isinstance(v, int):
|
||||
s[v] = u
|
||||
else:
|
||||
s = False
|
||||
|
||||
return s
|
||||
|
||||
@@ -709,6 +711,12 @@ work:
|
||||
except Exception, e:
|
||||
print e
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
Cannot unify (1, 2) and (1001, 1002).
|
||||
|
||||
|
||||
``unify()`` version 2
|
||||
^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
@@ -741,6 +749,8 @@ deal with this recursively:
|
||||
s = unify(a, c, s)
|
||||
if s != False:
|
||||
s = unify(b, d, s)
|
||||
else:
|
||||
s = False
|
||||
|
||||
return s
|
||||
|
||||
@@ -1674,8 +1684,8 @@ such. Note that this is *not* a ``sqr`` function implementation:
|
||||
|
||||
(Eventually I should come back around to this becuase it's not tooo
|
||||
difficult to exend this code to be able to compile e.g.
|
||||
``n3 = mul(n1, n2)`` for ``mul`` and insert it in the right place with
|
||||
the right variable names. It requires a little more support from the
|
||||
``n2 = mul(n1, n1)`` for ``mul`` with the right variable names and
|
||||
insert it in the right place. It requires a little more support from the
|
||||
library functions, in that we need to know to call ``mul()`` the Python
|
||||
function for ``mul`` the Joy function, but since *most* of the math
|
||||
functions (at least) are already wrappers it should be straightforward.)
|
||||
@@ -2612,7 +2622,7 @@ Part VII: Typing Combinators
|
||||
|
||||
In order to compute the stack effect of combinators you kinda have to
|
||||
have the quoted programs they expect available. In the most general
|
||||
case, the ``i`` combinator, you can't say anything about it's stack
|
||||
case, the ``i`` combinator, you can't say anything about its stack
|
||||
effect other than it expects one quote:
|
||||
|
||||
::
|
||||
@@ -2646,8 +2656,11 @@ Obviously it would be:
|
||||
Without any information about the contents of the quote we can't say
|
||||
much about the result.
|
||||
|
||||
I think there's a way forward. If we convert our list of terms we are
|
||||
composing into a stack structure we can use it as a *Joy expression*,
|
||||
Hybrid Inferencer/Interpreter
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
I think there's a way forward. If we convert our list (of terms we are
|
||||
composing) into a stack structure we can use it as a *Joy expression*,
|
||||
then we can treat the *output half* of a function's stack effect comment
|
||||
as a Joy interpreter stack, and just execute combinators directly. We
|
||||
can hybridize the compostition function with an interpreter to evaluate
|
||||
@@ -2655,6 +2668,13 @@ combinators, compose non-combinator functions, and put type variables on
|
||||
the stack. For combinators like ``branch`` that can have more than one
|
||||
stack effect we have to "split universes" again and return both.
|
||||
|
||||
Joy Types for Functions
|
||||
^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
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:: ipython2
|
||||
|
||||
class FunctionJoyType(AnyJoyType):
|
||||
@@ -2670,217 +2690,212 @@ stack effect we have to "split universes" again and return both.
|
||||
|
||||
def __repr__(self):
|
||||
return self.name
|
||||
|
||||
|
||||
class SymbolJoyType(FunctionJoyType): prefix = 'F'
|
||||
class CombinatorJoyType(FunctionJoyType): prefix = 'C'
|
||||
|
||||
|
||||
|
||||
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:: ipython2
|
||||
|
||||
def flatten(g):
|
||||
return list(chain.from_iterable(g))
|
||||
class SymbolJoyType(FunctionJoyType):
|
||||
prefix = 'F'
|
||||
|
||||
For combinators the list contains Python functions.
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
class CombinatorJoyType(FunctionJoyType):
|
||||
|
||||
prefix = 'C'
|
||||
|
||||
def __init__(self, name, sec, number, expect=None):
|
||||
super(CombinatorJoyType, self).__init__(name, sec, number)
|
||||
self.expect = expect
|
||||
|
||||
def enter_guard(self, f):
|
||||
if self.expect is None:
|
||||
return f
|
||||
g = self.expect, self.expect
|
||||
new_f = list(compose(f, g, ()))
|
||||
assert len(new_f) == 1, repr(new_f)
|
||||
return new_f[0][1]
|
||||
|
||||
For simple combinators that have only one effect (like ``dip``) you only
|
||||
need one function and it can be the combinator itself.
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
import joy.library
|
||||
|
||||
dip = CombinatorJoyType('dip', [joy.library.dip], 23)
|
||||
|
||||
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:: ipython2
|
||||
|
||||
def branch_true(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
return stack, concat(then, expression), dictionary
|
||||
|
||||
def branch_false(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
return stack, concat(else_, expression), dictionary
|
||||
|
||||
branch = CombinatorJoyType('branch', [branch_true, branch_false], 100)
|
||||
|
||||
You can also provide an optional stack effect, input-side only, that
|
||||
will then be used as an identity function (that accepts and returns
|
||||
stacks that match the "guard" stack effect) which will be used to guard
|
||||
against type mismatches going into the evaluation of the combinator.
|
||||
|
||||
``infer()``
|
||||
^^^^^^^^^^^
|
||||
|
||||
With those in place, we can define a function that accepts a sequence of
|
||||
Joy type variables, including ones representing functions (not just
|
||||
values), and attempts to grind out all the possible stack effects of
|
||||
that expression.
|
||||
|
||||
One tricky thing is that type variables *in the expression* have to be
|
||||
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:: ipython2
|
||||
|
||||
ID = S[0], S[0] # Identity function.
|
||||
|
||||
|
||||
def infer(e, F=ID):
|
||||
def infer(*expression):
|
||||
return sorted(set(_infer(list_to_stack(expression))))
|
||||
|
||||
|
||||
def _infer(e, F=ID):
|
||||
_log_it(e, F)
|
||||
if not e:
|
||||
return [F]
|
||||
|
||||
n, e = e
|
||||
|
||||
if isinstance(n, SymbolJoyType):
|
||||
res = flatten(infer(e, Fn) for Fn in MC([F], n.stack_effects))
|
||||
eFG = meta_compose([F], n.stack_effects, e)
|
||||
res = flatten(_infer(e, Fn) for e, Fn in eFG)
|
||||
|
||||
elif isinstance(n, CombinatorJoyType):
|
||||
res = []
|
||||
for combinator in n.stack_effects:
|
||||
fi, fo = F
|
||||
new_fo, ee, _ = combinator(fo, e, {})
|
||||
ee = update(FUNCTIONS, ee) # Fix Symbols.
|
||||
new_F = fi, new_fo
|
||||
res.extend(infer(ee, new_F))
|
||||
fi, fo = n.enter_guard(F)
|
||||
res = flatten(_interpret(f, fi, fo, e) for f in n.stack_effects)
|
||||
|
||||
elif isinstance(n, Symbol):
|
||||
assert n not in FUNCTIONS, repr(n)
|
||||
func = joy.library._dictionary[n]
|
||||
res = _interpret(func, F[0], F[1], e)
|
||||
|
||||
else:
|
||||
lit = s9, (n, s9)
|
||||
res = flatten(infer(e, Fn) for Fn in MC([F], [lit]))
|
||||
fi, fo = F
|
||||
res = _infer(e, (fi, (n, fo)))
|
||||
|
||||
return res
|
||||
|
||||
|
||||
def _interpret(f, fi, fo, e):
|
||||
new_fo, ee, _ = f(fo, e, {})
|
||||
ee = update(FUNCTIONS, ee) # Fix Symbols.
|
||||
new_F = fi, new_fo
|
||||
return _infer(ee, new_F)
|
||||
|
||||
|
||||
def _log_it(e, F):
|
||||
_log.info(
|
||||
u'%3i %s ∘ %s',
|
||||
len(inspect_stack()),
|
||||
doc_from_stack_effect(*F),
|
||||
expression_to_string(e),
|
||||
)
|
||||
|
||||
Work in Progress
|
||||
^^^^^^^^^^^^^^^^
|
||||
|
||||
And that brings us to current Work-In-Progress. The mixed-mode
|
||||
inferencer/interpreter ``infer()`` function seems to work well. There
|
||||
are details I should document, and the rest of the code in the
|
||||
"polytypes" module (FIXME link to its docs here!) should be explained...
|
||||
There is 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:: ipython2
|
||||
|
||||
f0, f1, f2, f3, f4, f5, f6, f7, f8, f9 = F = map(FloatJoyType, _R)
|
||||
i0, i1, i2, i3, i4, i5, i6, i7, i8, i9 = I = map(IntJoyType, _R)
|
||||
n0, n1, n2, n3, n4, n5, n6, n7, n8, n9 = N
|
||||
s0, s1, s2, s3, s4, s5, s6, s7, s8, s9 = S
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
import joy.library
|
||||
1/0 # (Don't try to run this cell! It's not going to work. This is "read only" code heh..)
|
||||
|
||||
FNs = '''ccons cons divmod_ dup dupd first
|
||||
over pm pop popd popdd popop pred
|
||||
rest rolldown rollup rrest second
|
||||
sqrt stack succ swaack swap swons
|
||||
third tuck uncons'''
|
||||
logging.basicConfig(format='%(message)s', stream=sys.stdout, level=logging.INFO)
|
||||
|
||||
FUNCTIONS = {
|
||||
name: SymbolJoyType(name, [NEW_DEFS[name]], i)
|
||||
for i, name in enumerate(FNs.strip().split())
|
||||
}
|
||||
FUNCTIONS['sum'] = SymbolJoyType('sum', [(((Ns[1], s1), s0), (n0, s0))], 100)
|
||||
FUNCTIONS['mul'] = SymbolJoyType('mul', [
|
||||
((i2, (i1, s0)), (i3, s0)),
|
||||
((f2, (i1, s0)), (f3, s0)),
|
||||
((i2, (f1, s0)), (f3, s0)),
|
||||
((f2, (f1, s0)), (f3, s0)),
|
||||
], 101)
|
||||
FUNCTIONS.update({
|
||||
combo.__name__: CombinatorJoyType(combo.__name__, [combo], i)
|
||||
for i, combo in enumerate((
|
||||
joy.library.i,
|
||||
joy.library.dip,
|
||||
joy.library.dipd,
|
||||
joy.library.dipdd,
|
||||
joy.library.dupdip,
|
||||
joy.library.b,
|
||||
joy.library.x,
|
||||
joy.library.infra,
|
||||
))
|
||||
})
|
||||
|
||||
def branch_true(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
return stack, CONCAT(then, expression), dictionary
|
||||
|
||||
def branch_false(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
return stack, CONCAT(else_, expression), dictionary
|
||||
|
||||
FUNCTIONS['branch'] = CombinatorJoyType('branch', [branch_true, branch_false], 100)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
globals().update(FUNCTIONS)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
from itertools import chain
|
||||
from joy.utils.stack import list_to_stack as l2s
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression = l2s([n1, n2, (mul, s2), (stack, s3), dip, infra, first])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(n1, (n2, ((mul, s2), ((stack, s3), (dip, (infra, (first, ())))))))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression = l2s([n1, n2, mul])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(n1, (n2, (mul, ())))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
infer(expression)
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[(s1, (f1, s1)), (s1, (i1, s1))]
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
infer(expression)
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[(s1, (f1, s1)), (s1, (i1, s1))]
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
for stack_effect_comment in infer(expression):
|
||||
print doc_from_stack_effect(*stack_effect_comment)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(-- f1)
|
||||
(-- i1)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(n1, (n2, (mul, ())))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
infer(expression)
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[(s1, (f1, s1)), (s1, (i1, s1))]
|
||||
|
||||
|
||||
|
||||
And that brings us to current Work-In-Progress. I'm pretty hopeful that
|
||||
the mixed-mode inferencer/interpreter ``infer()`` function along with
|
||||
the ability to specify multiple implementations for the combinators will
|
||||
permit modelling of the stack effects of e.g. ``ifte``. If I can keep up
|
||||
the pace I should be able to verify that conjecture by the end of June.
|
||||
|
||||
h = infer((pred, s2), (mul, s3), (div, s4), (nullary, (bool, s5)), dipd, branch)
|
||||
|
||||
print '-' * 40
|
||||
|
||||
for fi, fo in h:
|
||||
print doc_from_stack_effect(fi, fo)
|
||||
|
||||
The numbers at the start of the lines are the current depth of the
|
||||
Python call stack. They're followed by the current computed stack effect
|
||||
(initialized to ``ID``) then the pending expression (the inference of
|
||||
the stack effect of which is the whole object of the current example.)
|
||||
|
||||
In this example we are implementing (and inferring) ``ifte`` as
|
||||
``[nullary bool] dipd branch`` which shows off a lot of the current
|
||||
implementation in action.
|
||||
|
||||
::
|
||||
|
||||
7 (--) ∘ [pred] [mul] [div] [nullary bool] dipd branch
|
||||
8 (-- [pred ...2]) ∘ [mul] [div] [nullary bool] dipd branch
|
||||
9 (-- [pred ...2] [mul ...3]) ∘ [div] [nullary bool] dipd branch
|
||||
10 (-- [pred ...2] [mul ...3] [div ...4]) ∘ [nullary bool] dipd branch
|
||||
11 (-- [pred ...2] [mul ...3] [div ...4] [nullary bool ...5]) ∘ dipd branch
|
||||
15 (-- [pred ...5]) ∘ nullary bool [mul] [div] branch
|
||||
19 (-- [pred ...2]) ∘ [stack] dinfrirst bool [mul] [div] branch
|
||||
20 (-- [pred ...2] [stack ]) ∘ dinfrirst bool [mul] [div] branch
|
||||
22 (-- [pred ...2] [stack ]) ∘ dip infra first bool [mul] [div] branch
|
||||
26 (--) ∘ stack [pred] infra first bool [mul] [div] branch
|
||||
29 (... -- ... [...]) ∘ [pred] infra first bool [mul] [div] branch
|
||||
30 (... -- ... [...] [pred ...1]) ∘ infra first bool [mul] [div] branch
|
||||
34 (--) ∘ pred s1 swaack first bool [mul] [div] branch
|
||||
37 (n1 -- n2) ∘ [n1] swaack first bool [mul] [div] branch
|
||||
38 (... n1 -- ... n2 [n1 ...]) ∘ swaack first bool [mul] [div] branch
|
||||
41 (... n1 -- ... n1 [n2 ...]) ∘ first bool [mul] [div] branch
|
||||
44 (n1 -- n1 n2) ∘ bool [mul] [div] branch
|
||||
47 (n1 -- n1 b1) ∘ [mul] [div] branch
|
||||
48 (n1 -- n1 b1 [mul ...1]) ∘ [div] branch
|
||||
49 (n1 -- n1 b1 [mul ...1] [div ...2]) ∘ branch
|
||||
53 (n1 -- n1) ∘ div
|
||||
56 (f2 f1 -- f3) ∘
|
||||
56 (i1 f1 -- f2) ∘
|
||||
56 (f1 i1 -- f2) ∘
|
||||
56 (i2 i1 -- f1) ∘
|
||||
53 (n1 -- n1) ∘ mul
|
||||
56 (f2 f1 -- f3) ∘
|
||||
56 (i1 f1 -- f2) ∘
|
||||
56 (f1 i1 -- f2) ∘
|
||||
56 (i2 i1 -- i3) ∘
|
||||
----------------------------------------
|
||||
(f2 f1 -- f3)
|
||||
(i1 f1 -- f2)
|
||||
(f1 i1 -- f2)
|
||||
(i2 i1 -- f1)
|
||||
(i2 i1 -- i3)
|
||||
|
||||
Conclusion
|
||||
----------
|
||||
|
||||
(for now...)
|
||||
We built a simple type inferencer, and a kind of crude "compiler" for a
|
||||
subset of Joy functions. Then we built a more powerful inferencer that
|
||||
actually does some evaluation and explores branching code paths
|
||||
|
||||
Work remains to be done:
|
||||
|
||||
@@ -2900,21 +2915,18 @@ Work remains to be done:
|
||||
went off and just started writing code to see if it would work. It
|
||||
does, but now I have to come back and describe here what I did.
|
||||
|
||||
I'm starting to realize that, with the inferencer/checker/compiler
|
||||
coming along, and with the UI ready to be rewritten in Joy, I'm close to
|
||||
a time when my ephasis is going to have to shift from crunchy code stuff
|
||||
to squishy human stuff. I'm going to have to put normal people in front
|
||||
of this and see if, in fact, they *can* learn the basics of programming
|
||||
with it.
|
||||
|
||||
The rest of this stuff is junk and/or unfinished material.
|
||||
|
||||
Appendix: Joy in the Logical Paradigm
|
||||
-------------------------------------
|
||||
|
||||
For this to work the type label classes have to be modified to let
|
||||
``T >= t`` succeed, where e.g. ``T`` is ``IntJoyType`` and ``t`` is
|
||||
``int``
|
||||
For *type checking* to work the type label classes have to be modified
|
||||
to let ``T >= t`` succeed, where e.g. ``T`` is ``IntJoyType`` and ``t``
|
||||
is ``int``. If you do that you can take advantage of the *logical
|
||||
relational* 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
|
||||
``polytypes`` module. But if you're interested in all that you should
|
||||
just use Prolog!
|
||||
|
||||
Anyhow, type *checking* is a few easy steps away.
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
@@ -2926,383 +2938,3 @@ For this to work the type label classes have to be modified to let
|
||||
AnyJoyType.__ge__ = _ge
|
||||
AnyJoyType.accept = tuple, int, float, long, str, unicode, bool, Symbol
|
||||
StackJoyType.accept = tuple
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F = infer(l2s((pop, swap, rolldown, rest, rest, cons, cons)))
|
||||
|
||||
for f in F:
|
||||
print doc_from_stack_effect(*f)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
([a4 a5 .1.] a3 a2 a1 -- [a2 a3 .1.])
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
from joy.parser import text_to_expression
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F = infer(l2s((pop, pop, pop)))
|
||||
|
||||
for f in F:
|
||||
print doc_from_stack_effect(*f)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a3 a2 a1 --)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
s = text_to_expression('0 1 2')
|
||||
s
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(0, (1, (2, ())))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F[0][0]
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a1, (a2, (a3, s1)))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
L = unify(s, F[0][0])
|
||||
L
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
s = text_to_expression('0 1 2 [3 4]')
|
||||
s
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(0, (1, (2, ((3, (4, ())), ()))))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F[0][0]
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a1, (a2, (a3, s1)))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
L = unify(s, F[0][0])
|
||||
L
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
L = unify(F[0][0], s)
|
||||
L
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F[1][0]
|
||||
|
||||
|
||||
::
|
||||
|
||||
|
||||
---------------------------------------------------------------------------
|
||||
|
||||
IndexError Traceback (most recent call last)
|
||||
|
||||
<ipython-input-133-58a8e44e9cba> in <module>()
|
||||
----> 1 F[1][0]
|
||||
|
||||
|
||||
IndexError: list index out of range
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
s[0]
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
A[1] >= 23
|
||||
|
||||
`Abstract Interpretation <https://en.wikipedia.org/wiki/Abstract_interpretation>`__
|
||||
-----------------------------------------------------------------------------------
|
||||
|
||||
I *think* this might be sorta what I'm doing above with the ``kav()``
|
||||
function... In any event "mixed-mode" interpreters that include values
|
||||
and type variables and can track constraints, etc. will be, uh,
|
||||
super-useful. And Abstract Interpretation should be a rich source of
|
||||
ideas.
|
||||
|
||||
Junk
|
||||
----
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
class SymbolJoyType(AnyJoyType): prefix = 'F'
|
||||
|
||||
W = map(SymbolJoyType, _R)
|
||||
|
||||
k = S[0], ((W[1], S[2]), S[0])
|
||||
Symbol('cons')
|
||||
print doc_from_stack_effect(*k)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
dip_a = ((W[1], S[2]), (A[1], S[0]))
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
d = relabel(S[0], dip_a)
|
||||
print doc_from_stack_effect(*d)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
s = list(unify(d[1], k[1]))[0]
|
||||
s
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
j = update(s, k)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*j)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
j
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
cons
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
for f in MC([k], [dup]):
|
||||
print doc_from_stack_effect(*f)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
l = S[0], ((cons, S[2]), (A[1], S[0]))
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*l)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
|
||||
def dip_t(F):
|
||||
(quote, (a1, sec)) = F[1]
|
||||
G = F[0], sec
|
||||
P = S[3], (a1, S[3])
|
||||
a = [P]
|
||||
while isinstance(quote, tuple):
|
||||
term, quote = quote
|
||||
a.append(term)
|
||||
a.append(G)
|
||||
return a[::-1]
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
from joy.utils.stack import iter_stack
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
a, b, c = dip_t(l)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
a
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
b
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
c
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
MC([a], [b])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
kjs = MC(MC([a], [b]), [c])
|
||||
kjs
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*kjs[0])
|
||||
|
||||
::
|
||||
|
||||
(a0 [.0.] -- [a0 .0.] a1)
|
||||
|
||||
a0 [.0.] a1 [cons] dip
|
||||
----------------------------
|
||||
[a0 .0.] a1
|
||||
|
||||
``concat``
|
||||
~~~~~~~~~~
|
||||
|
||||
How to deal with ``concat``?
|
||||
|
||||
::
|
||||
|
||||
concat ([.0.] [.1.] -- [.0. .1.])
|
||||
|
||||
We would like to represent this in Python somehow...
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
concat = (S[0], S[1]), ((S[0], S[1]),)
|
||||
|
||||
But this is actually ``cons`` with the first argument restricted to be a
|
||||
stack:
|
||||
|
||||
::
|
||||
|
||||
([.0.] [.1.] -- [[.0.] .1.])
|
||||
|
||||
What we have implemented so far would actually only permit:
|
||||
|
||||
::
|
||||
|
||||
([.0.] [.1.] -- [.2.])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
concat = (S[0], S[1]), (S[2],)
|
||||
|
||||
Which works but can lose information. Consider ``cons concat``, this is
|
||||
how much information we *could* retain:
|
||||
|
||||
::
|
||||
|
||||
(1 [.0.] [.1.] -- [1 .0. .1.])
|
||||
|
||||
As opposed to just:
|
||||
|
||||
::
|
||||
|
||||
(1 [.0.] [.1.] -- [.2.])
|
||||
|
||||
represent ``concat``
|
||||
~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
([.0.] [.1.] -- [A*(.0.) .1.])
|
||||
|
||||
Meaning that ``A*`` on the right-hand side should all the crap from
|
||||
``.0.``.
|
||||
|
||||
::
|
||||
|
||||
([ .0.] [.1.] -- [ A* .1.])
|
||||
([a .0.] [.1.] -- [a A* .1.])
|
||||
([a b .0.] [.1.] -- [a b A* .1.])
|
||||
([a b c .0.] [.1.] -- [a b c A* .1.])
|
||||
|
||||
or...
|
||||
|
||||
::
|
||||
|
||||
([ .0.] [.1.] -- [ .1.])
|
||||
([a .0.] [.1.] -- [a .1.])
|
||||
([a b .0.] [.1.] -- [a b .1.])
|
||||
([a b c .0.] [.1.] -- [a b c .1.])
|
||||
([a A* c .0.] [.1.] -- [a A* c .1.])
|
||||
|
||||
::
|
||||
|
||||
(a, (b, S0)) . S1 = (a, (b, (A*, S1)))
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
class Astar(object):
|
||||
def __repr__(self):
|
||||
return 'A*'
|
||||
|
||||
|
||||
def concat(s0, s1):
|
||||
a = []
|
||||
while isinstance(s0, tuple):
|
||||
term, s0 = s0
|
||||
a.append(term)
|
||||
assert isinstance(s0, StackJoyType), repr(s0)
|
||||
s1 = Astar(), s1
|
||||
for term in reversed(a):
|
||||
s1 = term, s1
|
||||
return s1
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
a, b = (A[1], S[0]), (A[2], S[1])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
concat(a, b)
|
||||
|
||||
@@ -35,8 +35,10 @@
|
||||
<li><a href="joy/library.html">joy.library</a></li>
|
||||
<li><a href="joy/parser.html">joy.parser</a></li>
|
||||
<li><a href="joy/utils/generated_library.html">joy.utils.generated_library</a></li>
|
||||
<li><a href="joy/utils/polytypes.html">joy.utils.polytypes</a></li>
|
||||
<li><a href="joy/utils/pretty_print.html">joy.utils.pretty_print</a></li>
|
||||
<li><a href="joy/utils/stack.html">joy.utils.stack</a></li>
|
||||
<li><a href="joy/utils/types.html">joy.utils.types</a></li>
|
||||
</ul>
|
||||
|
||||
</div>
|
||||
|
||||
@@ -127,7 +127,6 @@
|
||||
<span class="s1">of == swap at</span>
|
||||
<span class="s1">product == 1 swap [*] step</span>
|
||||
<span class="s1">flatten == [] swap [concat] step</span>
|
||||
<span class="s1">unit == [] cons</span>
|
||||
<span class="s1">quoted == [unit] dip</span>
|
||||
<span class="s1">unquoted == [i] dip</span>
|
||||
<span class="s1">enstacken == stack [clear] dip</span>
|
||||
@@ -153,13 +152,17 @@
|
||||
<span class="s1">anamorphism == [pop []] swap [dip swons] genrec</span>
|
||||
<span class="s1">range == [0 <=] [1 - dup] anamorphism</span>
|
||||
<span class="s1">while == swap [nullary] cons dup dipd concat loop</span>
|
||||
<span class="s1">dudipd == dup dipd</span>
|
||||
<span class="s1">dupdipd == dup dipd</span>
|
||||
<span class="s1">primrec == [i] genrec</span>
|
||||
<span class="s1">step_zero == 0 roll> step</span>
|
||||
<span class="s1">codireco == cons dip rest cons</span>
|
||||
<span class="s1">make_generator == [codireco] ccons</span>
|
||||
<span class="s1">ccons == cons cons</span>
|
||||
<span class="s1">'''</span>
|
||||
<span class="c1"># ifte == [nullary not] dipd branch</span>
|
||||
<span class="c1"># ifte == [nullary] dipd swap branch</span>
|
||||
|
||||
<span class="c1">##ccons == cons cons</span>
|
||||
<span class="c1">##unit == [] cons</span>
|
||||
<span class="c1">##second == rest first</span>
|
||||
<span class="c1">##third == rest rest first</span>
|
||||
<span class="c1">##swons == swap cons</span>
|
||||
@@ -605,12 +608,12 @@
|
||||
<span class="c1">## return second, (tos, stack)</span>
|
||||
|
||||
|
||||
<div class="viewcode-block" id="swaack"><a class="viewcode-back" href="../../library.html#joy.library.swaack">[docs]</a><span class="nd">@inscribe</span>
|
||||
<span class="nd">@SimpleFunctionWrapper</span>
|
||||
<span class="k">def</span> <span class="nf">swaack</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<span class="sd">'''swap stack'''</span>
|
||||
<span class="n">old_stack</span><span class="p">,</span> <span class="n">stack</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">old_stack</span></div>
|
||||
<span class="c1">##@inscribe</span>
|
||||
<span class="c1">##@SimpleFunctionWrapper</span>
|
||||
<span class="c1">##def swaack(stack):</span>
|
||||
<span class="c1">## '''swap stack'''</span>
|
||||
<span class="c1">## old_stack, stack = stack</span>
|
||||
<span class="c1">## return stack, old_stack</span>
|
||||
|
||||
|
||||
<span class="c1">##@inscribe</span>
|
||||
|
||||
@@ -189,7 +189,7 @@
|
||||
<span class="c1"># RuntimeError: maximum recursion depth exceeded</span>
|
||||
<span class="c1"># on quotes longer than sys.getrecursionlimit().</span>
|
||||
|
||||
<span class="c1">## return (quote[0], concat(quote[1], expression)) if quote else expression</span>
|
||||
<span class="k">return</span> <span class="p">(</span><span class="n">quote</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">concat</span><span class="p">(</span><span class="n">quote</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">expression</span><span class="p">))</span> <span class="k">if</span> <span class="n">quote</span> <span class="k">else</span> <span class="n">expression</span></div>
|
||||
|
||||
<span class="c1"># Original implementation.</span>
|
||||
|
||||
@@ -198,13 +198,13 @@
|
||||
<span class="c1"># In-lining is slightly faster (and won't break the</span>
|
||||
<span class="c1"># recursion limit on long quotes.)</span>
|
||||
|
||||
<span class="n">temp</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">while</span> <span class="n">quote</span><span class="p">:</span>
|
||||
<span class="n">item</span><span class="p">,</span> <span class="n">quote</span> <span class="o">=</span> <span class="n">quote</span>
|
||||
<span class="n">temp</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">temp</span><span class="p">):</span>
|
||||
<span class="n">expression</span> <span class="o">=</span> <span class="n">item</span><span class="p">,</span> <span class="n">expression</span>
|
||||
<span class="k">return</span> <span class="n">expression</span></div>
|
||||
<span class="c1">## temp = []</span>
|
||||
<span class="c1">## while quote:</span>
|
||||
<span class="c1">## item, quote = quote</span>
|
||||
<span class="c1">## temp.append(item)</span>
|
||||
<span class="c1">## for item in reversed(temp):</span>
|
||||
<span class="c1">## expression = item, expression</span>
|
||||
<span class="c1">## return expression</span>
|
||||
|
||||
|
||||
|
||||
|
||||
@@ -98,6 +98,7 @@ The following is specific information for this dialect of Joy.
|
||||
pretty
|
||||
library
|
||||
lib
|
||||
types
|
||||
notebooks/index
|
||||
|
||||
|
||||
|
||||
@@ -45,8 +45,10 @@
|
||||
| <a href="#H"><strong>H</strong></a>
|
||||
| <a href="#I"><strong>I</strong></a>
|
||||
| <a href="#J"><strong>J</strong></a>
|
||||
| <a href="#K"><strong>K</strong></a>
|
||||
| <a href="#L"><strong>L</strong></a>
|
||||
| <a href="#M"><strong>M</strong></a>
|
||||
| <a href="#N"><strong>N</strong></a>
|
||||
| <a href="#O"><strong>O</strong></a>
|
||||
| <a href="#P"><strong>P</strong></a>
|
||||
| <a href="#R"><strong>R</strong></a>
|
||||
@@ -67,9 +69,13 @@
|
||||
<li><a href="library.html#joy.library.DefinitionWrapper.add_def">add_def() (joy.library.DefinitionWrapper class method)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.DefinitionWrapper.add_definitions">add_definitions() (joy.library.DefinitionWrapper class method)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.types.AnyJoyType">AnyJoyType (class in joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.polytypes.AnyStarJoyType">AnyStarJoyType (class in joy.utils.polytypes)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.app1">app1() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.app2">app2() (in module joy.library)</a>
|
||||
@@ -83,10 +89,12 @@
|
||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.b">b() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.BinaryBuiltinWrapper">BinaryBuiltinWrapper() (in module joy.library)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.BinaryBuiltinWrapper">BinaryBuiltinWrapper() (in module joy.library)</a>
|
||||
<li><a href="types.html#joy.utils.types.BooleanJoyType">BooleanJoyType (class in joy.utils.types)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.branch">branch() (in module joy.library)</a>
|
||||
</li>
|
||||
@@ -103,9 +111,21 @@
|
||||
<li><a href="library.html#joy.library.clear">clear() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.cmp_">cmp_() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.CombinatorJoyType">CombinatorJoyType (class in joy.utils.polytypes)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.types.compilable">compilable() (in module joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.types.compile_">compile_() (in module joy.utils.types)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.compose">compose() (in module joy.utils.polytypes)</a>
|
||||
|
||||
<ul>
|
||||
<li><a href="types.html#joy.utils.types.compose">(in module joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></li>
|
||||
<li><a href="stack.html#joy.utils.stack.concat">concat() (in module joy.utils.stack)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.concat_">concat_() (in module joy.library)</a>
|
||||
@@ -121,17 +141,27 @@
|
||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.DefinitionWrapper">DefinitionWrapper (class in joy.library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.defs">defs() (in module joy.utils.polytypes)</a>
|
||||
|
||||
<ul>
|
||||
<li><a href="types.html#joy.utils.types.defs">(in module joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></li>
|
||||
<li><a href="types.html#joy.utils.types.delabel">delabel() (in module joy.utils.types)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.dip">dip() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.dipd">dipd() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.dipdd">dipdd() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.divmod_">divmod_() (in module joy.library)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.divmod_">divmod_() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.types.doc_from_stack_effect">doc_from_stack_effect() (in module joy.utils.types)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.drop">drop() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.dup">dup() (in module joy.utils.generated_library)</a>
|
||||
@@ -159,12 +189,16 @@
|
||||
<li><a href="library.html#joy.utils.generated_library.first">first() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.first_two">first_two() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.types.FloatJoyType">FloatJoyType (class in joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.floor">floor() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.fourth">fourth() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.FunctionJoyType">FunctionJoyType (class in joy.utils.polytypes)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.FunctionWrapper">FunctionWrapper() (in module joy.library)</a>
|
||||
</li>
|
||||
@@ -202,14 +236,22 @@
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.ifte">ifte() (in module joy.library)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.polytypes.infer">infer() (in module joy.utils.polytypes)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.infra">infra() (in module joy.library)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.initialize">initialize() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.inscribe">inscribe() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.IntJoyType">IntJoyType (class in joy.utils.polytypes)</a>
|
||||
|
||||
<ul>
|
||||
<li><a href="types.html#joy.utils.types.IntJoyType">(class in joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></li>
|
||||
<li><a href="stack.html#joy.utils.stack.iter_stack">iter_stack() (in module joy.utils.stack)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
@@ -224,15 +266,41 @@
|
||||
</li>
|
||||
<li><a href="library.html#module-joy.library">joy.library (module)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="parser.html#module-joy.parser">joy.parser (module)</a>
|
||||
</li>
|
||||
<li><a href="library.html#module-joy.utils.generated_library">joy.utils.generated_library (module)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#module-joy.utils.polytypes">joy.utils.polytypes (module)</a>
|
||||
</li>
|
||||
<li><a href="pretty.html#module-joy.utils.pretty_print">joy.utils.pretty_print (module)</a>
|
||||
</li>
|
||||
<li><a href="stack.html#module-joy.utils.stack">joy.utils.stack (module)</a>
|
||||
</li>
|
||||
<li><a href="types.html#module-joy.utils.types">joy.utils.types (module)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.types.JoyTypeError">JoyTypeError</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
</tr></table>
|
||||
|
||||
<h2 id="K">K</h2>
|
||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.polytypes.AnyStarJoyType.kind">kind (joy.utils.polytypes.AnyStarJoyType attribute)</a>
|
||||
|
||||
<ul>
|
||||
<li><a href="types.html#joy.utils.polytypes.KleeneStar.kind">(joy.utils.polytypes.KleeneStar attribute)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.NumberStarJoyType.kind">(joy.utils.polytypes.NumberStarJoyType attribute)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.StackStarJoyType.kind">(joy.utils.polytypes.StackStarJoyType attribute)</a>
|
||||
</li>
|
||||
</ul></li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.polytypes.KleeneStar">KleeneStar (class in joy.utils.polytypes)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
</tr></table>
|
||||
@@ -254,15 +322,29 @@
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.map_">map_() (in module joy.library)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.max_">max_() (in module joy.library)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.polytypes.meta_compose">meta_compose() (in module joy.utils.polytypes)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.min_">min_() (in module joy.library)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
</tr></table>
|
||||
|
||||
<h2 id="N">N</h2>
|
||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.types.NumberJoyType">NumberJoyType (class in joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.polytypes.NumberStarJoyType">NumberStarJoyType (class in joy.utils.polytypes)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
</tr></table>
|
||||
|
||||
<h2 id="O">O</h2>
|
||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
@@ -306,16 +388,18 @@
|
||||
<h2 id="R">R</h2>
|
||||
<table style="width: 100%" class="indextable genindextable"><tr>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.types.relabel">relabel() (in module joy.utils.types)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.remove">remove() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="joy.html#joy.joy.repl">repl() (in module joy.joy)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.rest">rest() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.reverse">reverse() (in module joy.library)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.reverse">reverse() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.rolldown">rolldown() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.rollup">rollup() (in module joy.utils.generated_library)</a>
|
||||
@@ -343,13 +427,19 @@
|
||||
<li><a href="library.html#joy.library.sort_">sort_() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.sqrt">sqrt() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.Ss">Ss (in module joy.utils.polytypes)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.stack">stack() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="stack.html#joy.utils.stack.stack_to_string">stack_to_string() (in module joy.utils.stack)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.types.StackJoyType">StackJoyType (class in joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="types.html#joy.utils.polytypes.StackStarJoyType">StackStarJoyType (class in joy.utils.polytypes)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.step">step() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.stuncons">stuncons() (in module joy.utils.generated_library)</a>
|
||||
@@ -360,13 +450,15 @@
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.sum_">sum_() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.swaack">swaack() (in module joy.library)</a>
|
||||
<li><a href="library.html#joy.utils.generated_library.swaack">swaack() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.swap">swap() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.swons">swons() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="parser.html#joy.parser.Symbol">Symbol (class in joy.parser)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.SymbolJoyType">SymbolJoyType (class in joy.utils.polytypes)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
</tr></table>
|
||||
@@ -398,13 +490,23 @@
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.uncons">uncons() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.polytypes.unify">unify() (in module joy.utils.polytypes)</a>
|
||||
|
||||
<ul>
|
||||
<li><a href="types.html#joy.utils.types.unify">(in module joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></li>
|
||||
</ul></td>
|
||||
<td style="width: 33%; vertical-align: top;"><ul>
|
||||
<li><a href="library.html#joy.library.unique">unique() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.unit">unit() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.library.unstack">unstack() (in module joy.library)</a>
|
||||
</li>
|
||||
<li><a href="library.html#joy.utils.generated_library.unswons">unswons() (in module joy.utils.generated_library)</a>
|
||||
</li>
|
||||
<li><a href="types.html#joy.utils.types.update">update() (in module joy.utils.types)</a>
|
||||
</li>
|
||||
</ul></td>
|
||||
</tr></table>
|
||||
|
||||
@@ -131,6 +131,11 @@ interesting aspects. It’s quite a treasure trove.</p>
|
||||
<li class="toctree-l2"><a class="reference internal" href="lib.html#void"><code class="docutils literal notranslate"><span class="pre">void</span></code></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="types.html">Type Inference of Joy Expressions</a><ul>
|
||||
<li class="toctree-l2"><a class="reference internal" href="types.html#joy-utils-types"><code class="docutils literal notranslate"><span class="pre">joy.utils.types</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="types.html#joy-utils-polytypes"><code class="docutils literal notranslate"><span class="pre">joy.utils.polytypes</span></code></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="notebooks/index.html">Essays about Programming in Joy</a><ul>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Developing.html">Developing a Program in Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Quadratic.html">Quadratic formula</a></li>
|
||||
@@ -141,7 +146,7 @@ interesting aspects. It’s quite a treasure trove.</p>
|
||||
<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/Zipper.html">Traversing Datastructures with Zippers</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Types.html">Type Inference</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/NoUpdates.html">No Updates</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="notebooks/Categorical.html">Categorical Programming</a></li>
|
||||
</ul>
|
||||
|
||||
@@ -612,12 +612,6 @@ on top of the stack.</p>
|
||||
<p>sum == 0 swap [+] step</p>
|
||||
</dd></dl>
|
||||
|
||||
<dl class="function">
|
||||
<dt id="joy.library.swaack">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">swaack</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#swaack"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.swaack" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>swap stack</p>
|
||||
</dd></dl>
|
||||
|
||||
<dl class="function">
|
||||
<dt id="joy.library.take">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">take</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#take"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.take" title="Permalink to this definition">¶</a></dt>
|
||||
@@ -708,7 +702,7 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.ccons">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">ccons</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#ccons"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.ccons" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a1</span> <span class="n">a0</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="n">a0</span> <span class="o">...</span><span class="mi">0</span><span class="p">])</span>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">a2</span> <span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">]</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="mi">1</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -756,7 +750,7 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.first_two">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">first_two</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#first_two"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.first_two" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a0</span> <span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="n">a0</span> <span class="n">a1</span><span class="p">)</span>
|
||||
<dd><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="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span> <span class="n">a2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -764,7 +758,7 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.fourth">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">fourth</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#fourth"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.fourth" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a0</span> <span class="n">a1</span> <span class="n">a2</span> <span class="n">a3</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
|
||||
<dd><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="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a4</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -852,7 +846,7 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.rrest">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">rrest</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#rrest"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.rrest" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a0</span> <span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">])</span>
|
||||
<dd><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="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -860,7 +854,7 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.second">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">second</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#second"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.second" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a0</span> <span class="n">a1</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="n">a1</span><span class="p">)</span>
|
||||
<dd><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="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -876,7 +870,7 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.stuncons">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">stuncons</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#stuncons"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.stuncons" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="n">a0</span> <span class="o">--</span> <span class="o">...</span> <span class="n">a0</span> <span class="n">a0</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><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="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -884,7 +878,15 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.stununcons">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">stununcons</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#stununcons"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.stununcons" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="o">...</span> <span class="n">a1</span> <span class="n">a0</span> <span class="o">--</span> <span class="o">...</span> <span class="n">a1</span> <span class="n">a0</span> <span class="n">a0</span> <span class="n">a1</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span>
|
||||
<dd><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="o">--</span> <span class="o">...</span> <span class="n">a2</span> <span class="n">a1</span> <span class="n">a1</span> <span class="n">a2</span> <span class="p">[</span><span class="o">...</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.swaack">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">swaack</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#swaack"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.swaack" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -900,7 +902,7 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.swons">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">swons</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#swons"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.swons" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="n">a0</span> <span class="o">--</span> <span class="p">[</span><span class="n">a0</span> <span class="o">...</span><span class="mi">0</span><span class="p">])</span>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a1</span> <span class="o">...</span><span class="mi">1</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -908,7 +910,7 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.third">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">third</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#third"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.third" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a0</span> <span class="n">a1</span> <span class="n">a2</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="n">a2</span><span class="p">)</span>
|
||||
<dd><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="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="n">a3</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
@@ -929,10 +931,18 @@ from each list. The smallest list sets the length of the result list.</p>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.unit">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">unit</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#unit"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.unit" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><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">a1</span> <span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
||||
<dl class="function">
|
||||
<dt id="joy.utils.generated_library.unswons">
|
||||
<code class="descclassname">joy.utils.generated_library.</code><code class="descname">unswons</code><span class="sig-paren">(</span><em>stack</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/utils/generated_library.html#unswons"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.generated_library.unswons" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a0</span> <span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">0</span><span class="p">]</span> <span class="n">a0</span><span class="p">)</span>
|
||||
<dd><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="mi">1</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a1</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
||||
@@ -6,7 +6,7 @@
|
||||
<head>
|
||||
<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
||||
<title>Type Inference — Thun 0.2.0 documentation</title>
|
||||
<title>The Blissful Elegance of Typing Joy — Thun 0.2.0 documentation</title>
|
||||
<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
|
||||
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
|
||||
<script type="text/javascript" src="../_static/documentation_options.js"></script>
|
||||
@@ -32,8 +32,8 @@
|
||||
<div class="bodywrapper">
|
||||
<div class="body" role="main">
|
||||
|
||||
<div class="section" id="type-inference">
|
||||
<h1>Type Inference<a class="headerlink" href="#type-inference" title="Permalink to this headline">¶</a></h1>
|
||||
<div class="section" id="the-blissful-elegance-of-typing-joy">
|
||||
<h1>The Blissful Elegance of Typing Joy<a class="headerlink" href="#the-blissful-elegance-of-typing-joy" title="Permalink to this headline">¶</a></h1>
|
||||
<p>This notebook presents a simple type inferencer for Joy code. It can
|
||||
infer the stack effect of most Joy expressions. It’s built largely by
|
||||
means of existing ideas and research. (A great overview of the existing
|
||||
@@ -410,6 +410,8 @@ integers or tuples of type descriptors:</p>
|
||||
<span class="n">s</span><span class="p">[</span><span class="n">u</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
|
||||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
|
||||
<span class="n">s</span><span class="p">[</span><span class="n">v</span><span class="p">]</span> <span class="o">=</span> <span class="n">u</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="kc">False</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">s</span>
|
||||
</pre></div>
|
||||
@@ -566,6 +568,9 @@ work:</p>
|
||||
<span class="nb">print</span> <span class="n">e</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Cannot</span> <span class="n">unify</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="ow">and</span> <span class="p">(</span><span class="mi">1001</span><span class="p">,</span> <span class="mi">1002</span><span class="p">)</span><span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="unify-version-2">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">unify()</span></code> version 2<a class="headerlink" href="#unify-version-2" title="Permalink to this headline">¶</a></h4>
|
||||
<p>The problem is that the <code class="docutils literal notranslate"><span class="pre">unify()</span></code> function as written doesn’t handle
|
||||
@@ -594,6 +599,8 @@ deal with this recursively:</p>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">s</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="n">s</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">d</span><span class="p">,</span> <span class="n">s</span><span class="p">)</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">s</span> <span class="o">=</span> <span class="kc">False</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">s</span>
|
||||
</pre></div>
|
||||
@@ -1337,8 +1344,8 @@ such. Note that this is <em>not</em> a <code class="docutils literal notranslate
|
||||
</div>
|
||||
<p>(Eventually I should come back around to this becuase it’s not tooo
|
||||
difficult to exend this code to be able to compile e.g.
|
||||
<code class="docutils literal notranslate"><span class="pre">n3</span> <span class="pre">=</span> <span class="pre">mul(n1,</span> <span class="pre">n2)</span></code> for <code class="docutils literal notranslate"><span class="pre">mul</span></code> and insert it in the right place with
|
||||
the right variable names. It requires a little more support from the
|
||||
<code class="docutils literal notranslate"><span class="pre">n2</span> <span class="pre">=</span> <span class="pre">mul(n1,</span> <span class="pre">n1)</span></code> for <code class="docutils literal notranslate"><span class="pre">mul</span></code> with the right variable names and
|
||||
insert it in the right place. It requires a little more support from the
|
||||
library functions, in that we need to know to call <code class="docutils literal notranslate"><span class="pre">mul()</span></code> the Python
|
||||
function for <code class="docutils literal notranslate"><span class="pre">mul</span></code> the Joy function, but since <em>most</em> of the math
|
||||
functions (at least) are already wrappers it should be straightforward.)</p>
|
||||
@@ -2065,7 +2072,7 @@ disappears:</p>
|
||||
<h2>Part VII: Typing Combinators<a class="headerlink" href="#part-vii-typing-combinators" title="Permalink to this headline">¶</a></h2>
|
||||
<p>In order to compute the stack effect of combinators you kinda have to
|
||||
have the quoted programs they expect available. In the most general
|
||||
case, the <code class="docutils literal notranslate"><span class="pre">i</span></code> combinator, you can’t say anything about it’s stack
|
||||
case, the <code class="docutils literal notranslate"><span class="pre">i</span></code> combinator, you can’t say anything about its stack
|
||||
effect other than it expects one quote:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">i</span> <span class="p">(</span><span class="o">...</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="o">.</span><span class="mf">1.</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
@@ -2088,14 +2095,21 @@ effect other than it expects one quote:</p>
|
||||
</div>
|
||||
<p>Without any information about the contents of the quote we can’t say
|
||||
much about the result.</p>
|
||||
<p>I think there’s a way forward. If we convert our list of terms we are
|
||||
composing into a stack structure we can use it as a <em>Joy expression</em>,
|
||||
<div class="section" id="hybrid-inferencer-interpreter">
|
||||
<h3>Hybrid Inferencer/Interpreter<a class="headerlink" href="#hybrid-inferencer-interpreter" title="Permalink to this headline">¶</a></h3>
|
||||
<p>I think there’s a way forward. If we convert our list (of terms we are
|
||||
composing) into a stack structure we can use it as a <em>Joy expression</em>,
|
||||
then we can treat the <em>output half</em> of a function’s stack effect comment
|
||||
as a Joy interpreter stack, and just execute combinators directly. We
|
||||
can hybridize the compostition function with an interpreter to evaluate
|
||||
combinators, compose non-combinator functions, and put type variables on
|
||||
the stack. For combinators like <code class="docutils literal notranslate"><span class="pre">branch</span></code> that can have more than one
|
||||
stack effect we have to “split universes” again and return both.</p>
|
||||
<div class="section" id="joy-types-for-functions">
|
||||
<h4>Joy Types for Functions<a class="headerlink" href="#joy-types-for-functions" title="Permalink to this headline">¶</a></h4>
|
||||
<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="code ipython2 highlight-default 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="nf">__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>
|
||||
@@ -2109,159 +2123,198 @@ stack effect we have to “split universes” again and return both.</p>
|
||||
|
||||
<span class="k">def</span> <span class="nf">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</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>
|
||||
<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>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">flatten</span><span class="p">(</span><span class="n">g</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="n">chain</span><span class="o">.</span><span class="n">from_iterable</span><span class="p">(</span><span class="n">g</span><span class="p">))</span>
|
||||
</div>
|
||||
<div class="section" id="specialized-for-simple-functions-and-combinators">
|
||||
<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="code ipython2 highlight-default 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="code ipython2 highlight-default 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>
|
||||
|
||||
<span class="k">def</span> <span class="nf">__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="n">expect</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="nb">super</span><span class="p">(</span><span class="n">CombinatorJoyType</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</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">expect</span> <span class="o">=</span> <span class="n">expect</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">enter_guard</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="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">expect</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">f</span>
|
||||
<span class="n">g</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">expect</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">expect</span>
|
||||
<span class="n">new_f</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</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="p">()))</span>
|
||||
<span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">new_f</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> <span class="nb">repr</span><span class="p">(</span><span class="n">new_f</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">new_f</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</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="code ipython2 highlight-default 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>
|
||||
</div>
|
||||
<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="code ipython2 highlight-default 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>
|
||||
|
||||
<span class="k">def</span> <span class="nf">branch_false</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">else_</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
|
||||
|
||||
<span class="n">branch</span> <span class="o">=</span> <span class="n">CombinatorJoyType</span><span class="p">(</span><span class="s1">'branch'</span><span class="p">,</span> <span class="p">[</span><span class="n">branch_true</span><span class="p">,</span> <span class="n">branch_false</span><span class="p">],</span> <span class="mi">100</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>You can also provide an optional stack effect, input-side only, that
|
||||
will then be used as an identity function (that accepts and returns
|
||||
stacks that match the “guard” stack effect) which will be used to guard
|
||||
against type mismatches going into the evaluation of the combinator.</p>
|
||||
</div>
|
||||
<div class="section" id="infer">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">infer()</span></code><a class="headerlink" href="#infer" title="Permalink to this headline">¶</a></h4>
|
||||
<p>With those in place, we can define a function that accepts a sequence of
|
||||
Joy type variables, including ones representing functions (not just
|
||||
values), and attempts to grind out all the possible stack effects of
|
||||
that expression.</p>
|
||||
<p>One tricky thing is that type variables <em>in the expression</em> have to be
|
||||
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="code ipython2 highlight-default 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="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>
|
||||
<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">_infer</span><span class="p">(</span><span class="n">list_to_stack</span><span class="p">(</span><span class="n">expression</span><span class="p">))))</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">F</span><span class="o">=</span><span class="n">ID</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">_infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">F</span><span class="o">=</span><span class="n">ID</span><span class="p">):</span>
|
||||
<span class="n">_log_it</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">F</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">e</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span>
|
||||
|
||||
<span class="n">n</span><span class="p">,</span> <span class="n">e</span> <span class="o">=</span> <span class="n">e</span>
|
||||
|
||||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">SymbolJoyType</span><span class="p">):</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">flatten</span><span class="p">(</span><span class="n">infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">Fn</span><span class="p">)</span> <span class="k">for</span> <span class="n">Fn</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">F</span><span class="p">],</span> <span class="n">n</span><span class="o">.</span><span class="n">stack_effects</span><span class="p">))</span>
|
||||
<span class="n">eFG</span> <span class="o">=</span> <span class="n">meta_compose</span><span class="p">([</span><span class="n">F</span><span class="p">],</span> <span class="n">n</span><span class="o">.</span><span class="n">stack_effects</span><span class="p">,</span> <span class="n">e</span><span class="p">)</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">flatten</span><span class="p">(</span><span class="n">_infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">Fn</span><span class="p">)</span> <span class="k">for</span> <span class="n">e</span><span class="p">,</span> <span class="n">Fn</span> <span class="ow">in</span> <span class="n">eFG</span><span class="p">)</span>
|
||||
|
||||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">CombinatorJoyType</span><span class="p">):</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">combinator</span> <span class="ow">in</span> <span class="n">n</span><span class="o">.</span><span class="n">stack_effects</span><span class="p">:</span>
|
||||
<span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">F</span>
|
||||
<span class="n">new_fo</span><span class="p">,</span> <span class="n">ee</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">combinator</span><span class="p">(</span><span class="n">fo</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="p">{})</span>
|
||||
<span class="n">ee</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">FUNCTIONS</span><span class="p">,</span> <span class="n">ee</span><span class="p">)</span> <span class="c1"># Fix Symbols.</span>
|
||||
<span class="n">new_F</span> <span class="o">=</span> <span class="n">fi</span><span class="p">,</span> <span class="n">new_fo</span>
|
||||
<span class="n">res</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">infer</span><span class="p">(</span><span class="n">ee</span><span class="p">,</span> <span class="n">new_F</span><span class="p">))</span>
|
||||
<span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">n</span><span class="o">.</span><span class="n">enter_guard</span><span class="p">(</span><span class="n">F</span><span class="p">)</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">flatten</span><span class="p">(</span><span class="n">_interpret</span><span class="p">(</span><span class="n">f</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="n">e</span><span class="p">)</span> <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">n</span><span class="o">.</span><span class="n">stack_effects</span><span class="p">)</span>
|
||||
|
||||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">Symbol</span><span class="p">):</span>
|
||||
<span class="k">assert</span> <span class="n">n</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">FUNCTIONS</span><span class="p">,</span> <span class="nb">repr</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<span class="n">func</span> <span class="o">=</span> <span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">_dictionary</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">_interpret</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">F</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="mi">1</span><span class="p">],</span> <span class="n">e</span><span class="p">)</span>
|
||||
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">lit</span> <span class="o">=</span> <span class="n">s9</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">s9</span><span class="p">)</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">flatten</span><span class="p">(</span><span class="n">infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">Fn</span><span class="p">)</span> <span class="k">for</span> <span class="n">Fn</span> <span class="ow">in</span> <span class="n">MC</span><span class="p">([</span><span class="n">F</span><span class="p">],</span> <span class="p">[</span><span class="n">lit</span><span class="p">]))</span>
|
||||
<span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">F</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">_infer</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">fo</span><span class="p">)))</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">res</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">f0</span><span class="p">,</span> <span class="n">f1</span><span class="p">,</span> <span class="n">f2</span><span class="p">,</span> <span class="n">f3</span><span class="p">,</span> <span class="n">f4</span><span class="p">,</span> <span class="n">f5</span><span class="p">,</span> <span class="n">f6</span><span class="p">,</span> <span class="n">f7</span><span class="p">,</span> <span class="n">f8</span><span class="p">,</span> <span class="n">f9</span> <span class="o">=</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">i0</span><span class="p">,</span> <span class="n">i1</span><span class="p">,</span> <span class="n">i2</span><span class="p">,</span> <span class="n">i3</span><span class="p">,</span> <span class="n">i4</span><span class="p">,</span> <span class="n">i5</span><span class="p">,</span> <span class="n">i6</span><span class="p">,</span> <span class="n">i7</span><span class="p">,</span> <span class="n">i8</span><span class="p">,</span> <span class="n">i9</span> <span class="o">=</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>
|
||||
<span class="n">n0</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="n">n3</span><span class="p">,</span> <span class="n">n4</span><span class="p">,</span> <span class="n">n5</span><span class="p">,</span> <span class="n">n6</span><span class="p">,</span> <span class="n">n7</span><span class="p">,</span> <span class="n">n8</span><span class="p">,</span> <span class="n">n9</span> <span class="o">=</span> <span class="n">N</span>
|
||||
<span class="n">s0</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="n">s3</span><span class="p">,</span> <span class="n">s4</span><span class="p">,</span> <span class="n">s5</span><span class="p">,</span> <span class="n">s6</span><span class="p">,</span> <span class="n">s7</span><span class="p">,</span> <span class="n">s8</span><span class="p">,</span> <span class="n">s9</span> <span class="o">=</span> <span class="n">S</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span>
|
||||
|
||||
<span class="n">FNs</span> <span class="o">=</span> <span class="s1">'''ccons cons divmod_ dup dupd first</span>
|
||||
<span class="s1"> over pm pop popd popdd popop pred</span>
|
||||
<span class="s1"> rest rolldown rollup rrest second</span>
|
||||
<span class="s1"> sqrt stack succ swaack swap swons</span>
|
||||
<span class="s1"> third tuck uncons'''</span>
|
||||
|
||||
<span class="n">FUNCTIONS</span> <span class="o">=</span> <span class="p">{</span>
|
||||
<span class="n">name</span><span class="p">:</span> <span class="n">SymbolJoyType</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">[</span><span class="n">NEW_DEFS</span><span class="p">[</span><span class="n">name</span><span class="p">]],</span> <span class="n">i</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">name</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">FNs</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span><span class="o">.</span><span class="n">split</span><span class="p">())</span>
|
||||
<span class="p">}</span>
|
||||
<span class="n">FUNCTIONS</span><span class="p">[</span><span class="s1">'sum'</span><span class="p">]</span> <span class="o">=</span> <span class="n">SymbolJoyType</span><span class="p">(</span><span class="s1">'sum'</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">s1</span><span class="p">),</span> <span class="n">s0</span><span class="p">),</span> <span class="p">(</span><span class="n">n0</span><span class="p">,</span> <span class="n">s0</span><span class="p">))],</span> <span class="mi">100</span><span class="p">)</span>
|
||||
<span class="n">FUNCTIONS</span><span class="p">[</span><span class="s1">'mul'</span><span class="p">]</span> <span class="o">=</span> <span class="n">SymbolJoyType</span><span class="p">(</span><span class="s1">'mul'</span><span class="p">,</span> <span class="p">[</span>
|
||||
<span class="p">((</span><span class="n">i2</span><span class="p">,</span> <span class="p">(</span><span class="n">i1</span><span class="p">,</span> <span class="n">s0</span><span class="p">)),</span> <span class="p">(</span><span class="n">i3</span><span class="p">,</span> <span class="n">s0</span><span class="p">)),</span>
|
||||
<span class="p">((</span><span class="n">f2</span><span class="p">,</span> <span class="p">(</span><span class="n">i1</span><span class="p">,</span> <span class="n">s0</span><span class="p">)),</span> <span class="p">(</span><span class="n">f3</span><span class="p">,</span> <span class="n">s0</span><span class="p">)),</span>
|
||||
<span class="p">((</span><span class="n">i2</span><span class="p">,</span> <span class="p">(</span><span class="n">f1</span><span class="p">,</span> <span class="n">s0</span><span class="p">)),</span> <span class="p">(</span><span class="n">f3</span><span class="p">,</span> <span class="n">s0</span><span class="p">)),</span>
|
||||
<span class="p">((</span><span class="n">f2</span><span class="p">,</span> <span class="p">(</span><span class="n">f1</span><span class="p">,</span> <span class="n">s0</span><span class="p">)),</span> <span class="p">(</span><span class="n">f3</span><span class="p">,</span> <span class="n">s0</span><span class="p">)),</span>
|
||||
<span class="p">],</span> <span class="mi">101</span><span class="p">)</span>
|
||||
<span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">update</span><span class="p">({</span>
|
||||
<span class="n">combo</span><span class="o">.</span><span class="vm">__name__</span><span class="p">:</span> <span class="n">CombinatorJoyType</span><span class="p">(</span><span class="n">combo</span><span class="o">.</span><span class="vm">__name__</span><span class="p">,</span> <span class="p">[</span><span class="n">combo</span><span class="p">],</span> <span class="n">i</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">combo</span> <span class="ow">in</span> <span class="nb">enumerate</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">i</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="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dipd</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">dipdd</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">dupdip</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">b</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">x</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">infra</span><span class="p">,</span>
|
||||
<span class="p">))</span>
|
||||
<span class="p">})</span>
|
||||
<span class="k">def</span> <span class="nf">_interpret</span><span class="p">(</span><span class="n">f</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="n">e</span><span class="p">):</span>
|
||||
<span class="n">new_fo</span><span class="p">,</span> <span class="n">ee</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">fo</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="p">{})</span>
|
||||
<span class="n">ee</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">FUNCTIONS</span><span class="p">,</span> <span class="n">ee</span><span class="p">)</span> <span class="c1"># Fix Symbols.</span>
|
||||
<span class="n">new_F</span> <span class="o">=</span> <span class="n">fi</span><span class="p">,</span> <span class="n">new_fo</span>
|
||||
<span class="k">return</span> <span class="n">_infer</span><span class="p">(</span><span class="n">ee</span><span class="p">,</span> <span class="n">new_F</span><span class="p">)</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>
|
||||
|
||||
<span class="k">def</span> <span class="nf">branch_false</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">else_</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
|
||||
<span class="k">def</span> <span class="nf">_log_it</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">F</span><span class="p">):</span>
|
||||
<span class="n">_log</span><span class="o">.</span><span class="n">info</span><span class="p">(</span>
|
||||
<span class="sa">u</span><span class="s1">'</span><span class="si">%3i</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="p">,</span>
|
||||
<span class="nb">len</span><span class="p">(</span><span class="n">inspect_stack</span><span class="p">()),</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">expression_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">),</span>
|
||||
<span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="work-in-progress">
|
||||
<h4>Work in Progress<a class="headerlink" href="#work-in-progress" title="Permalink to this headline">¶</a></h4>
|
||||
<p>And that brings us to current Work-In-Progress. The mixed-mode
|
||||
inferencer/interpreter <code class="docutils literal notranslate"><span class="pre">infer()</span></code> function seems to work well. There
|
||||
are details I should document, and the rest of the code in the
|
||||
“polytypes” 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="code ipython2 highlight-default 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">FUNCTIONS</span><span class="p">[</span><span class="s1">'branch'</span><span class="p">]</span> <span class="o">=</span> <span class="n">CombinatorJoyType</span><span class="p">(</span><span class="s1">'branch'</span><span class="p">,</span> <span class="p">[</span><span class="n">branch_true</span><span class="p">,</span> <span class="n">branch_false</span><span class="p">],</span> <span class="mi">100</span><span class="p">)</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>
|
||||
|
||||
<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">FUNCTIONS</span><span class="p">)</span>
|
||||
|
||||
<span class="n">h</span> <span class="o">=</span> <span class="n">infer</span><span class="p">((</span><span class="n">pred</span><span class="p">,</span> <span class="n">s2</span><span class="p">),</span> <span class="p">(</span><span class="n">mul</span><span class="p">,</span> <span class="n">s3</span><span class="p">),</span> <span class="p">(</span><span class="n">div</span><span class="p">,</span> <span class="n">s4</span><span class="p">),</span> <span class="p">(</span><span class="n">nullary</span><span class="p">,</span> <span class="p">(</span><span class="nb">bool</span><span class="p">,</span> <span class="n">s5</span><span class="p">)),</span> <span class="n">dipd</span><span class="p">,</span> <span class="n">branch</span><span class="p">)</span>
|
||||
|
||||
<span class="nb">print</span> <span class="s1">'-'</span> <span class="o">*</span> <span class="mi">40</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="ow">in</span> <span class="n">h</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">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default 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">FUNCTIONS</span><span class="p">)</span>
|
||||
<p>The numbers at the start of the lines are the current depth of the
|
||||
Python call stack. They’re followed by the current computed stack effect
|
||||
(initialized to <code class="docutils literal notranslate"><span class="pre">ID</span></code>) then the pending expression (the inference of
|
||||
the stack effect of which is the whole object of the current example.)</p>
|
||||
<p>In this example we are implementing (and inferring) <code class="docutils literal notranslate"><span class="pre">ifte</span></code> as
|
||||
<code class="docutils literal notranslate"><span class="pre">[nullary</span> <span class="pre">bool]</span> <span class="pre">dipd</span> <span class="pre">branch</span></code> which shows off a lot of the current
|
||||
implementation in action.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> 7 (--) ∘ [pred] [mul] [div] [nullary bool] dipd branch
|
||||
8 (-- [pred ...2]) ∘ [mul] [div] [nullary bool] dipd branch
|
||||
9 (-- [pred ...2] [mul ...3]) ∘ [div] [nullary bool] dipd branch
|
||||
10 (-- [pred ...2] [mul ...3] [div ...4]) ∘ [nullary bool] dipd branch
|
||||
11 (-- [pred ...2] [mul ...3] [div ...4] [nullary bool ...5]) ∘ dipd branch
|
||||
15 (-- [pred ...5]) ∘ nullary bool [mul] [div] branch
|
||||
19 (-- [pred ...2]) ∘ [stack] dinfrirst bool [mul] [div] branch
|
||||
20 (-- [pred ...2] [stack ]) ∘ dinfrirst bool [mul] [div] branch
|
||||
22 (-- [pred ...2] [stack ]) ∘ dip infra first bool [mul] [div] branch
|
||||
26 (--) ∘ stack [pred] infra first bool [mul] [div] branch
|
||||
29 (... -- ... [...]) ∘ [pred] infra first bool [mul] [div] branch
|
||||
30 (... -- ... [...] [pred ...1]) ∘ infra first bool [mul] [div] branch
|
||||
34 (--) ∘ pred s1 swaack first bool [mul] [div] branch
|
||||
37 (n1 -- n2) ∘ [n1] swaack first bool [mul] [div] branch
|
||||
38 (... n1 -- ... n2 [n1 ...]) ∘ swaack first bool [mul] [div] branch
|
||||
41 (... n1 -- ... n1 [n2 ...]) ∘ first bool [mul] [div] branch
|
||||
44 (n1 -- n1 n2) ∘ bool [mul] [div] branch
|
||||
47 (n1 -- n1 b1) ∘ [mul] [div] branch
|
||||
48 (n1 -- n1 b1 [mul ...1]) ∘ [div] branch
|
||||
49 (n1 -- n1 b1 [mul ...1] [div ...2]) ∘ branch
|
||||
53 (n1 -- n1) ∘ div
|
||||
56 (f2 f1 -- f3) ∘
|
||||
56 (i1 f1 -- f2) ∘
|
||||
56 (f1 i1 -- f2) ∘
|
||||
56 (i2 i1 -- f1) ∘
|
||||
53 (n1 -- n1) ∘ mul
|
||||
56 (f2 f1 -- f3) ∘
|
||||
56 (i1 f1 -- f2) ∘
|
||||
56 (f1 i1 -- f2) ∘
|
||||
56 (i2 i1 -- i3) ∘
|
||||
----------------------------------------
|
||||
(f2 f1 -- f3)
|
||||
(i1 f1 -- f2)
|
||||
(f1 i1 -- f2)
|
||||
(i2 i1 -- f1)
|
||||
(i2 i1 -- i3)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">itertools</span> <span class="k">import</span> <span class="n">chain</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">list_to_stack</span> <span class="k">as</span> <span class="n">l2s</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">expression</span> <span class="o">=</span> <span class="n">l2s</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">mul</span><span class="p">,</span> <span class="n">s2</span><span class="p">),</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">s3</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">first</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">expression</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> <span class="p">((</span><span class="n">mul</span><span class="p">,</span> <span class="n">s2</span><span class="p">),</span> <span class="p">((</span><span class="n">stack</span><span class="p">,</span> <span class="n">s3</span><span class="p">),</span> <span class="p">(</span><span class="n">dip</span><span class="p">,</span> <span class="p">(</span><span class="n">infra</span><span class="p">,</span> <span class="p">(</span><span class="n">first</span><span class="p">,</span> <span class="p">())))))))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">expression</span> <span class="o">=</span> <span class="n">l2s</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="n">mul</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">expression</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> <span class="p">(</span><span class="n">mul</span><span class="p">,</span> <span class="p">())))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">infer</span><span class="p">(</span><span class="n">expression</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">f1</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">i1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">infer</span><span class="p">(</span><span class="n">expression</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">f1</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">i1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">stack_effect_comment</span> <span class="ow">in</span> <span class="n">infer</span><span class="p">(</span><span class="n">expression</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_effect_comment</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">f1</span><span class="p">)</span>
|
||||
<span class="p">(</span><span class="o">--</span> <span class="n">i1</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">expression</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> <span class="p">(</span><span class="n">mul</span><span class="p">,</span> <span class="p">())))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">infer</span><span class="p">(</span><span class="n">expression</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">f1</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">i1</span><span class="p">,</span> <span class="n">s1</span><span class="p">))]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>And that brings us to current Work-In-Progress. I’m pretty hopeful that
|
||||
the mixed-mode inferencer/interpreter <code class="docutils literal notranslate"><span class="pre">infer()</span></code> function along with
|
||||
the ability to specify multiple implementations for the combinators will
|
||||
permit modelling of the stack effects of e.g. <code class="docutils literal notranslate"><span class="pre">ifte</span></code>. If I can keep up
|
||||
the pace I should be able to verify that conjecture by the end of June.</p>
|
||||
</div>
|
||||
<div class="section" id="conclusion">
|
||||
<h2>Conclusion<a class="headerlink" href="#conclusion" title="Permalink to this headline">¶</a></h2>
|
||||
<p>(for now…)</p>
|
||||
<p>We built a simple type inferencer, and a kind of crude “compiler” for a
|
||||
subset of Joy functions. Then we built a more powerful inferencer that
|
||||
actually does some evaluation and explores branching code paths</p>
|
||||
<p>Work remains to be done:</p>
|
||||
<ul class="simple">
|
||||
<li>the rest of the library has to be covered</li>
|
||||
@@ -2280,19 +2333,17 @@ the pace I should be able to verify that conjecture by the end of June.</p>
|
||||
went off and just started writing code to see if it would work. It
|
||||
does, but now I have to come back and describe here what I did.</li>
|
||||
</ul>
|
||||
<p>I’m starting to realize that, with the inferencer/checker/compiler
|
||||
coming along, and with the UI ready to be rewritten in Joy, I’m close to
|
||||
a time when my ephasis is going to have to shift from crunchy code stuff
|
||||
to squishy human stuff. I’m going to have to put normal people in front
|
||||
of this and see if, in fact, they <em>can</em> learn the basics of programming
|
||||
with it.</p>
|
||||
<p>The rest of this stuff is junk and/or unfinished material.</p>
|
||||
</div>
|
||||
<div class="section" id="appendix-joy-in-the-logical-paradigm">
|
||||
<h2>Appendix: Joy in the Logical Paradigm<a class="headerlink" href="#appendix-joy-in-the-logical-paradigm" title="Permalink to this headline">¶</a></h2>
|
||||
<p>For this to work the type label classes have to be modified to let
|
||||
<code class="docutils literal notranslate"><span class="pre">T</span> <span class="pre">>=</span> <span class="pre">t</span></code> succeed, where e.g. <code class="docutils literal notranslate"><span class="pre">T</span></code> is <code class="docutils literal notranslate"><span class="pre">IntJoyType</span></code> and <code class="docutils literal notranslate"><span class="pre">t</span></code> is
|
||||
<code class="docutils literal notranslate"><span class="pre">int</span></code></p>
|
||||
<p>For <em>type checking</em> to work the type label classes have to be modified
|
||||
to let <code class="docutils literal notranslate"><span class="pre">T</span> <span class="pre">>=</span> <span class="pre">t</span></code> succeed, where e.g. <code class="docutils literal notranslate"><span class="pre">T</span></code> is <code class="docutils literal notranslate"><span class="pre">IntJoyType</span></code> and <code class="docutils literal notranslate"><span class="pre">t</span></code>
|
||||
is <code class="docutils literal notranslate"><span class="pre">int</span></code>. If you do that you can take advantage of the <em>logical
|
||||
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">polytypes</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="code ipython2 highlight-default 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>
|
||||
@@ -2303,271 +2354,6 @@ with it.</p>
|
||||
<span class="n">StackJoyType</span><span class="o">.</span><span class="n">accept</span> <span class="o">=</span> <span class="nb">tuple</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">l2s</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="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">F</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">a4</span> <span class="n">a5</span> <span class="o">.</span><span class="mf">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="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.parser</span> <span class="k">import</span> <span class="n">text_to_expression</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">l2s</span><span class="p">((</span><span class="n">pop</span><span class="p">,</span> <span class="n">pop</span><span class="p">,</span> <span class="n">pop</span><span class="p">)))</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">F</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">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'0 1 2'</span><span class="p">)</span>
|
||||
<span class="n">s</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="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">())))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default 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><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="n">a1</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">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">])</span>
|
||||
<span class="n">L</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">()</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">s</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="n">s</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="p">(</span><span class="mi">1</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">3</span><span class="p">,</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">())),</span> <span class="p">()))))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default 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><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="n">a1</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">a3</span><span class="p">,</span> <span class="n">s1</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">])</span>
|
||||
<span class="n">L</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">()</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">L</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">F</span><span class="p">[</span><span class="mi">0</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="n">L</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">()</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default 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><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="o">---------------------------------------------------------------------------</span>
|
||||
|
||||
<span class="ne">IndexError</span> <span class="n">Traceback</span> <span class="p">(</span><span class="n">most</span> <span class="n">recent</span> <span class="n">call</span> <span class="n">last</span><span class="p">)</span>
|
||||
|
||||
<span class="o"><</span><span class="n">ipython</span><span class="o">-</span><span class="nb">input</span><span class="o">-</span><span class="mi">133</span><span class="o">-</span><span class="mi">58</span><span class="n">a8e44e9cba</span><span class="o">></span> <span class="ow">in</span> <span class="o"><</span><span class="n">module</span><span class="o">></span><span class="p">()</span>
|
||||
<span class="o">----></span> <span class="mi">1</span> <span class="n">F</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="ne">IndexError</span><span class="p">:</span> <span class="nb">list</span> <span class="n">index</span> <span class="n">out</span> <span class="n">of</span> <span class="nb">range</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">>=</span> <span class="mi">23</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="abstract-interpretation">
|
||||
<h2><a class="reference external" href="https://en.wikipedia.org/wiki/Abstract_interpretation">Abstract Interpretation</a><a class="headerlink" href="#abstract-interpretation" title="Permalink to this headline">¶</a></h2>
|
||||
<p>I <em>think</em> this might be sorta what I’m doing above with the <code class="docutils literal notranslate"><span class="pre">kav()</span></code>
|
||||
function… In any event “mixed-mode” interpreters that include values
|
||||
and type variables and can track constraints, etc. will be, uh,
|
||||
super-useful. And Abstract Interpretation should be a rich source of
|
||||
ideas.</p>
|
||||
</div>
|
||||
<div class="section" id="junk">
|
||||
<h2>Junk<a class="headerlink" href="#junk" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">SymbolJoyType</span><span class="p">(</span><span class="n">AnyJoyType</span><span class="p">):</span> <span class="n">prefix</span> <span class="o">=</span> <span class="s1">'F'</span>
|
||||
|
||||
<span class="n">W</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">SymbolJoyType</span><span class="p">,</span> <span class="n">_R</span><span class="p">)</span>
|
||||
|
||||
<span class="n">k</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">W</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">S</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||||
<span class="n">Symbol</span><span class="p">(</span><span class="s1">'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">k</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">dip_a</span> <span class="o">=</span> <span class="p">((</span><span class="n">W</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="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">0</span><span class="p">]))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">d</span> <span class="o">=</span> <span class="n">relabel</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">dip_a</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">d</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">s</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">unify</span><span class="p">(</span><span class="n">d</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">k</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="n">s</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">j</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default 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">j</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">j</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">cons</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default 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">k</span><span class="p">],</span> <span class="p">[</span><span class="n">dup</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="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">l</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">cons</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="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">0</span><span class="p">]))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default 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">l</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">dip_t</span><span class="p">(</span><span class="n">F</span><span class="p">):</span>
|
||||
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">sec</span><span class="p">))</span> <span class="o">=</span> <span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
|
||||
<span class="n">G</span> <span class="o">=</span> <span class="n">F</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">sec</span>
|
||||
<span class="n">P</span> <span class="o">=</span> <span class="n">S</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">S</span><span class="p">[</span><span class="mi">3</span><span class="p">])</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="k">while</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
|
||||
<span class="n">term</span><span class="p">,</span> <span class="n">quote</span> <span class="o">=</span> <span class="n">quote</span>
|
||||
<span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
|
||||
<span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">a</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">iter_stack</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="n">dip_t</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">c</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">MC</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>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">kjs</span> <span class="o">=</span> <span class="n">MC</span><span class="p">(</span><span class="n">MC</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">kjs</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default 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">kjs</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="n">a0</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="o">--</span> <span class="p">[</span><span class="n">a0</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">a1</span><span class="p">)</span>
|
||||
|
||||
<span class="n">a0</span> <span class="p">[</span><span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">a1</span> <span class="p">[</span><span class="n">cons</span><span class="p">]</span> <span class="n">dip</span>
|
||||
<span class="o">----------------------------</span>
|
||||
<span class="p">[</span><span class="n">a0</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="n">a1</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="concat">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">concat</span></code><a class="headerlink" href="#concat" title="Permalink to this headline">¶</a></h3>
|
||||
<p>How to deal with <code class="docutils literal notranslate"><span class="pre">concat</span></code>?</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">concat</span> <span class="p">([</span><span class="o">.</span><span class="mf">0.</span><span class="p">]</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="o">.</span><span class="mf">0.</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>We would like to represent this in Python somehow…</p>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">concat</span> <span class="o">=</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="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>
|
||||
<p>But this is actually <code class="docutils literal notranslate"><span class="pre">cons</span></code> with the first argument restricted to be a
|
||||
stack:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">.</span><span class="mf">0.</span><span class="p">]</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="o">.</span><span class="mf">0.</span><span class="p">]</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>What we have implemented so far would actually only permit:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">.</span><span class="mf">0.</span><span class="p">]</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="o">.</span><span class="mf">2.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">concat</span> <span class="o">=</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="p">(</span><span class="n">S</span><span class="p">[</span><span class="mi">2</span><span class="p">],)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Which works but can lose information. Consider <code class="docutils literal notranslate"><span class="pre">cons</span> <span class="pre">concat</span></code>, this is
|
||||
how much information we <em>could</em> retain:</p>
|
||||
<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="o">.</span><span class="mf">0.</span><span class="p">]</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="mi">1</span> <span class="o">.</span><span class="mf">0.</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>As opposed to just:</p>
|
||||
<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="o">.</span><span class="mf">0.</span><span class="p">]</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="o">.</span><span class="mf">2.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="represent-concat">
|
||||
<h3>represent <code class="docutils literal notranslate"><span class="pre">concat</span></code><a class="headerlink" href="#represent-concat" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="o">.</span><span class="mf">0.</span><span class="p">]</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">A</span><span class="o">*</span><span class="p">(</span><span class="o">.</span><span class="mf">0.</span><span class="p">)</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Meaning that <code class="docutils literal notranslate"><span class="pre">A*</span></code> on the right-hand side should all the crap from
|
||||
<code class="docutils literal notranslate"><span class="pre">.0.</span></code>.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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">A</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
<span class="p">([</span><span class="n">a</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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">a</span> <span class="n">A</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
<span class="p">([</span><span class="n">a</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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">a</span> <span class="n">b</span> <span class="n">A</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
<span class="p">([</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">A</span><span class="o">*</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>or…</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
<span class="p">([</span><span class="n">a</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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">a</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
<span class="p">([</span><span class="n">a</span> <span class="n">b</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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">a</span> <span class="n">b</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
<span class="p">([</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">.</span><span class="mf">1.</span><span class="p">])</span>
|
||||
<span class="p">([</span><span class="n">a</span> <span class="n">A</span><span class="o">*</span> <span class="n">c</span> <span class="o">.</span><span class="mf">0.</span><span class="p">]</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">a</span> <span class="n">A</span><span class="o">*</span> <span class="n">c</span> <span class="o">.</span><span class="mf">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="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="o">.</span> <span class="n">S1</span> <span class="o">=</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">A</span><span class="o">*</span><span class="p">,</span> <span class="n">S1</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Astar</span><span class="p">(</span><span class="nb">object</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="s1">'A*'</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">concat</span><span class="p">(</span><span class="n">s0</span><span class="p">,</span> <span class="n">s1</span><span class="p">):</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">while</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">s0</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
|
||||
<span class="n">term</span><span class="p">,</span> <span class="n">s0</span> <span class="o">=</span> <span class="n">s0</span>
|
||||
<span class="n">a</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
|
||||
<span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">s0</span><span class="p">,</span> <span class="n">StackJoyType</span><span class="p">),</span> <span class="nb">repr</span><span class="p">(</span><span class="n">s0</span><span class="p">)</span>
|
||||
<span class="n">s1</span> <span class="o">=</span> <span class="n">Astar</span><span class="p">(),</span> <span class="n">s1</span>
|
||||
<span class="k">for</span> <span class="n">term</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||
<span class="n">s1</span> <span class="o">=</span> <span class="n">term</span><span class="p">,</span> <span class="n">s1</span>
|
||||
<span class="k">return</span> <span class="n">s1</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span><span class="p">,</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">0</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">1</span><span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">concat</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -2579,7 +2365,7 @@ how much information we <em>could</em> retain:</p>
|
||||
<div class="sphinxsidebarwrapper">
|
||||
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||
<ul>
|
||||
<li><a class="reference internal" href="#">Type Inference</a><ul>
|
||||
<li><a class="reference internal" href="#">The Blissful Elegance of Typing Joy</a><ul>
|
||||
<li><a class="reference internal" href="#part-i-poial-s-rules">Part I: Pöial’s Rules</a><ul>
|
||||
<li><a class="reference internal" href="#first-rule">First Rule</a></li>
|
||||
<li><a class="reference internal" href="#second-rule">Second Rule</a></li>
|
||||
@@ -2652,17 +2438,20 @@ how much information we <em>could</em> retain:</p>
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#part-vii-typing-combinators">Part VII: Typing Combinators</a></li>
|
||||
<li><a class="reference internal" href="#conclusion">Conclusion</a></li>
|
||||
<li><a class="reference internal" href="#appendix-joy-in-the-logical-paradigm">Appendix: Joy in the Logical Paradigm</a></li>
|
||||
<li><a class="reference internal" href="#abstract-interpretation">Abstract Interpretation</a></li>
|
||||
<li><a class="reference internal" href="#junk">Junk</a><ul>
|
||||
<li><a class="reference internal" href="#concat"><code class="docutils literal notranslate"><span class="pre">concat</span></code></a></li>
|
||||
<li><a class="reference internal" href="#represent-concat">represent <code class="docutils literal notranslate"><span class="pre">concat</span></code></a></li>
|
||||
<li><a class="reference internal" href="#part-vii-typing-combinators">Part VII: Typing Combinators</a><ul>
|
||||
<li><a class="reference internal" href="#hybrid-inferencer-interpreter">Hybrid Inferencer/Interpreter</a><ul>
|
||||
<li><a class="reference internal" href="#joy-types-for-functions">Joy Types for Functions</a></li>
|
||||
<li><a class="reference internal" href="#specialized-for-simple-functions-and-combinators">Specialized for Simple Functions and Combinators</a></li>
|
||||
<li><a class="reference internal" href="#infer"><code class="docutils literal notranslate"><span class="pre">infer()</span></code></a></li>
|
||||
<li><a class="reference internal" href="#work-in-progress">Work in Progress</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#conclusion">Conclusion</a></li>
|
||||
<li><a class="reference internal" href="#appendix-joy-in-the-logical-paradigm">Appendix: Joy in the Logical Paradigm</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
<div class="relations">
|
||||
<h3>Related Topics</h3>
|
||||
|
||||
@@ -16,7 +16,7 @@
|
||||
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
|
||||
<link rel="index" title="Index" href="../genindex.html" />
|
||||
<link rel="search" title="Search" href="../search.html" />
|
||||
<link rel="next" title="Type Inference" href="Types.html" />
|
||||
<link rel="next" title="The Blissful Elegance of Typing Joy" href="Types.html" />
|
||||
<link rel="prev" title="Newton’s method" href="Newton-Raphson.html" />
|
||||
|
||||
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
|
||||
@@ -327,7 +327,7 @@ i d i d i d d Bingo!
|
||||
<li><a href="../index.html">Documentation overview</a><ul>
|
||||
<li><a href="index.html">Essays about Programming in Joy</a><ul>
|
||||
<li>Previous: <a href="Newton-Raphson.html" title="previous chapter">Newton’s method</a></li>
|
||||
<li>Next: <a href="Types.html" title="next chapter">Type Inference</a></li>
|
||||
<li>Next: <a href="Types.html" title="next chapter">The Blissful Elegance of Typing Joy</a></li>
|
||||
</ul></li>
|
||||
</ul></li>
|
||||
</ul>
|
||||
|
||||
@@ -17,7 +17,7 @@
|
||||
<link rel="index" title="Index" href="../genindex.html" />
|
||||
<link rel="search" title="Search" href="../search.html" />
|
||||
<link rel="next" title="Developing a Program in Joy" href="Developing.html" />
|
||||
<link rel="prev" title="Functions Grouped by, er, Function with Examples" href="../lib.html" />
|
||||
<link rel="prev" title="Type Inference of Joy Expressions" href="../types.html" />
|
||||
|
||||
<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
|
||||
|
||||
@@ -118,7 +118,7 @@
|
||||
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#determining-the-right-path-for-an-item-in-a-tree">Determining the right “path” for an item in a tree.</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Types.html">Type Inference</a><ul>
|
||||
<li class="toctree-l1"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a><ul>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-i-poial-s-rules">Part I: Pöial’s Rules</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-ii-implementation">Part II: Implementation</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-iii-compiling-yin-functions">Part III: Compiling Yin Functions</a></li>
|
||||
@@ -128,8 +128,6 @@
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-vii-typing-combinators">Part VII: Typing Combinators</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#conclusion">Conclusion</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#appendix-joy-in-the-logical-paradigm">Appendix: Joy in the Logical Paradigm</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#abstract-interpretation">Abstract Interpretation</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html#junk">Junk</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
|
||||
@@ -147,7 +145,7 @@
|
||||
<h3>Related Topics</h3>
|
||||
<ul>
|
||||
<li><a href="../index.html">Documentation overview</a><ul>
|
||||
<li>Previous: <a href="../lib.html" title="previous chapter">Functions Grouped by, er, Function with Examples</a></li>
|
||||
<li>Previous: <a href="../types.html" title="previous chapter">Type Inference of Joy Expressions</a></li>
|
||||
<li>Next: <a href="Developing.html" title="next chapter">Developing a Program in Joy</a></li>
|
||||
</ul></li>
|
||||
</ul>
|
||||
|
||||
Binary file not shown.
@@ -70,6 +70,11 @@
|
||||
<td>   
|
||||
<a href="library.html#module-joy.utils.generated_library"><code class="xref">joy.utils.generated_library</code></a></td><td>
|
||||
<em></em></td></tr>
|
||||
<tr class="cg-1">
|
||||
<td></td>
|
||||
<td>   
|
||||
<a href="types.html#module-joy.utils.polytypes"><code class="xref">joy.utils.polytypes</code></a></td><td>
|
||||
<em></em></td></tr>
|
||||
<tr class="cg-1">
|
||||
<td></td>
|
||||
<td>   
|
||||
@@ -80,6 +85,11 @@
|
||||
<td>   
|
||||
<a href="stack.html#module-joy.utils.stack"><code class="xref">joy.utils.stack</code></a></td><td>
|
||||
<em></em></td></tr>
|
||||
<tr class="cg-1">
|
||||
<td></td>
|
||||
<td>   
|
||||
<a href="types.html#module-joy.utils.types"><code class="xref">joy.utils.types</code></a></td><td>
|
||||
<em></em></td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
|
||||
File diff suppressed because one or more lines are too long
@@ -98,6 +98,7 @@ The following is specific information for this dialect of Joy.
|
||||
pretty
|
||||
library
|
||||
lib
|
||||
types
|
||||
notebooks/index
|
||||
|
||||
|
||||
|
||||
@@ -1,6 +1,6 @@
|
||||
|
||||
Type Inference
|
||||
==============
|
||||
The Blissful Elegance of Typing Joy
|
||||
===================================
|
||||
|
||||
This notebook presents a simple type inferencer for Joy code. It can
|
||||
infer the stack effect of most Joy expressions. It's built largely by
|
||||
@@ -476,6 +476,8 @@ integers or tuples of type descriptors:
|
||||
s[u] = v
|
||||
elif isinstance(v, int):
|
||||
s[v] = u
|
||||
else:
|
||||
s = False
|
||||
|
||||
return s
|
||||
|
||||
@@ -709,6 +711,12 @@ work:
|
||||
except Exception, e:
|
||||
print e
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
Cannot unify (1, 2) and (1001, 1002).
|
||||
|
||||
|
||||
``unify()`` version 2
|
||||
^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
@@ -741,6 +749,8 @@ deal with this recursively:
|
||||
s = unify(a, c, s)
|
||||
if s != False:
|
||||
s = unify(b, d, s)
|
||||
else:
|
||||
s = False
|
||||
|
||||
return s
|
||||
|
||||
@@ -1674,8 +1684,8 @@ such. Note that this is *not* a ``sqr`` function implementation:
|
||||
|
||||
(Eventually I should come back around to this becuase it's not tooo
|
||||
difficult to exend this code to be able to compile e.g.
|
||||
``n3 = mul(n1, n2)`` for ``mul`` and insert it in the right place with
|
||||
the right variable names. It requires a little more support from the
|
||||
``n2 = mul(n1, n1)`` for ``mul`` with the right variable names and
|
||||
insert it in the right place. It requires a little more support from the
|
||||
library functions, in that we need to know to call ``mul()`` the Python
|
||||
function for ``mul`` the Joy function, but since *most* of the math
|
||||
functions (at least) are already wrappers it should be straightforward.)
|
||||
@@ -2612,7 +2622,7 @@ Part VII: Typing Combinators
|
||||
|
||||
In order to compute the stack effect of combinators you kinda have to
|
||||
have the quoted programs they expect available. In the most general
|
||||
case, the ``i`` combinator, you can't say anything about it's stack
|
||||
case, the ``i`` combinator, you can't say anything about its stack
|
||||
effect other than it expects one quote:
|
||||
|
||||
::
|
||||
@@ -2646,8 +2656,11 @@ Obviously it would be:
|
||||
Without any information about the contents of the quote we can't say
|
||||
much about the result.
|
||||
|
||||
I think there's a way forward. If we convert our list of terms we are
|
||||
composing into a stack structure we can use it as a *Joy expression*,
|
||||
Hybrid Inferencer/Interpreter
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
I think there's a way forward. If we convert our list (of terms we are
|
||||
composing) into a stack structure we can use it as a *Joy expression*,
|
||||
then we can treat the *output half* of a function's stack effect comment
|
||||
as a Joy interpreter stack, and just execute combinators directly. We
|
||||
can hybridize the compostition function with an interpreter to evaluate
|
||||
@@ -2655,6 +2668,13 @@ combinators, compose non-combinator functions, and put type variables on
|
||||
the stack. For combinators like ``branch`` that can have more than one
|
||||
stack effect we have to "split universes" again and return both.
|
||||
|
||||
Joy Types for Functions
|
||||
^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
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:: ipython2
|
||||
|
||||
class FunctionJoyType(AnyJoyType):
|
||||
@@ -2670,217 +2690,212 @@ stack effect we have to "split universes" again and return both.
|
||||
|
||||
def __repr__(self):
|
||||
return self.name
|
||||
|
||||
|
||||
class SymbolJoyType(FunctionJoyType): prefix = 'F'
|
||||
class CombinatorJoyType(FunctionJoyType): prefix = 'C'
|
||||
|
||||
|
||||
|
||||
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:: ipython2
|
||||
|
||||
def flatten(g):
|
||||
return list(chain.from_iterable(g))
|
||||
class SymbolJoyType(FunctionJoyType):
|
||||
prefix = 'F'
|
||||
|
||||
For combinators the list contains Python functions.
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
class CombinatorJoyType(FunctionJoyType):
|
||||
|
||||
prefix = 'C'
|
||||
|
||||
def __init__(self, name, sec, number, expect=None):
|
||||
super(CombinatorJoyType, self).__init__(name, sec, number)
|
||||
self.expect = expect
|
||||
|
||||
def enter_guard(self, f):
|
||||
if self.expect is None:
|
||||
return f
|
||||
g = self.expect, self.expect
|
||||
new_f = list(compose(f, g, ()))
|
||||
assert len(new_f) == 1, repr(new_f)
|
||||
return new_f[0][1]
|
||||
|
||||
For simple combinators that have only one effect (like ``dip``) you only
|
||||
need one function and it can be the combinator itself.
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
import joy.library
|
||||
|
||||
dip = CombinatorJoyType('dip', [joy.library.dip], 23)
|
||||
|
||||
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:: ipython2
|
||||
|
||||
def branch_true(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
return stack, concat(then, expression), dictionary
|
||||
|
||||
def branch_false(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
return stack, concat(else_, expression), dictionary
|
||||
|
||||
branch = CombinatorJoyType('branch', [branch_true, branch_false], 100)
|
||||
|
||||
You can also provide an optional stack effect, input-side only, that
|
||||
will then be used as an identity function (that accepts and returns
|
||||
stacks that match the "guard" stack effect) which will be used to guard
|
||||
against type mismatches going into the evaluation of the combinator.
|
||||
|
||||
``infer()``
|
||||
^^^^^^^^^^^
|
||||
|
||||
With those in place, we can define a function that accepts a sequence of
|
||||
Joy type variables, including ones representing functions (not just
|
||||
values), and attempts to grind out all the possible stack effects of
|
||||
that expression.
|
||||
|
||||
One tricky thing is that type variables *in the expression* have to be
|
||||
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:: ipython2
|
||||
|
||||
ID = S[0], S[0] # Identity function.
|
||||
|
||||
|
||||
def infer(e, F=ID):
|
||||
def infer(*expression):
|
||||
return sorted(set(_infer(list_to_stack(expression))))
|
||||
|
||||
|
||||
def _infer(e, F=ID):
|
||||
_log_it(e, F)
|
||||
if not e:
|
||||
return [F]
|
||||
|
||||
n, e = e
|
||||
|
||||
if isinstance(n, SymbolJoyType):
|
||||
res = flatten(infer(e, Fn) for Fn in MC([F], n.stack_effects))
|
||||
eFG = meta_compose([F], n.stack_effects, e)
|
||||
res = flatten(_infer(e, Fn) for e, Fn in eFG)
|
||||
|
||||
elif isinstance(n, CombinatorJoyType):
|
||||
res = []
|
||||
for combinator in n.stack_effects:
|
||||
fi, fo = F
|
||||
new_fo, ee, _ = combinator(fo, e, {})
|
||||
ee = update(FUNCTIONS, ee) # Fix Symbols.
|
||||
new_F = fi, new_fo
|
||||
res.extend(infer(ee, new_F))
|
||||
fi, fo = n.enter_guard(F)
|
||||
res = flatten(_interpret(f, fi, fo, e) for f in n.stack_effects)
|
||||
|
||||
elif isinstance(n, Symbol):
|
||||
assert n not in FUNCTIONS, repr(n)
|
||||
func = joy.library._dictionary[n]
|
||||
res = _interpret(func, F[0], F[1], e)
|
||||
|
||||
else:
|
||||
lit = s9, (n, s9)
|
||||
res = flatten(infer(e, Fn) for Fn in MC([F], [lit]))
|
||||
fi, fo = F
|
||||
res = _infer(e, (fi, (n, fo)))
|
||||
|
||||
return res
|
||||
|
||||
|
||||
def _interpret(f, fi, fo, e):
|
||||
new_fo, ee, _ = f(fo, e, {})
|
||||
ee = update(FUNCTIONS, ee) # Fix Symbols.
|
||||
new_F = fi, new_fo
|
||||
return _infer(ee, new_F)
|
||||
|
||||
|
||||
def _log_it(e, F):
|
||||
_log.info(
|
||||
u'%3i %s ∘ %s',
|
||||
len(inspect_stack()),
|
||||
doc_from_stack_effect(*F),
|
||||
expression_to_string(e),
|
||||
)
|
||||
|
||||
Work in Progress
|
||||
^^^^^^^^^^^^^^^^
|
||||
|
||||
And that brings us to current Work-In-Progress. The mixed-mode
|
||||
inferencer/interpreter ``infer()`` function seems to work well. There
|
||||
are details I should document, and the rest of the code in the
|
||||
"polytypes" module (FIXME link to its docs here!) should be explained...
|
||||
There is 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:: ipython2
|
||||
|
||||
f0, f1, f2, f3, f4, f5, f6, f7, f8, f9 = F = map(FloatJoyType, _R)
|
||||
i0, i1, i2, i3, i4, i5, i6, i7, i8, i9 = I = map(IntJoyType, _R)
|
||||
n0, n1, n2, n3, n4, n5, n6, n7, n8, n9 = N
|
||||
s0, s1, s2, s3, s4, s5, s6, s7, s8, s9 = S
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
import joy.library
|
||||
1/0 # (Don't try to run this cell! It's not going to work. This is "read only" code heh..)
|
||||
|
||||
FNs = '''ccons cons divmod_ dup dupd first
|
||||
over pm pop popd popdd popop pred
|
||||
rest rolldown rollup rrest second
|
||||
sqrt stack succ swaack swap swons
|
||||
third tuck uncons'''
|
||||
logging.basicConfig(format='%(message)s', stream=sys.stdout, level=logging.INFO)
|
||||
|
||||
FUNCTIONS = {
|
||||
name: SymbolJoyType(name, [NEW_DEFS[name]], i)
|
||||
for i, name in enumerate(FNs.strip().split())
|
||||
}
|
||||
FUNCTIONS['sum'] = SymbolJoyType('sum', [(((Ns[1], s1), s0), (n0, s0))], 100)
|
||||
FUNCTIONS['mul'] = SymbolJoyType('mul', [
|
||||
((i2, (i1, s0)), (i3, s0)),
|
||||
((f2, (i1, s0)), (f3, s0)),
|
||||
((i2, (f1, s0)), (f3, s0)),
|
||||
((f2, (f1, s0)), (f3, s0)),
|
||||
], 101)
|
||||
FUNCTIONS.update({
|
||||
combo.__name__: CombinatorJoyType(combo.__name__, [combo], i)
|
||||
for i, combo in enumerate((
|
||||
joy.library.i,
|
||||
joy.library.dip,
|
||||
joy.library.dipd,
|
||||
joy.library.dipdd,
|
||||
joy.library.dupdip,
|
||||
joy.library.b,
|
||||
joy.library.x,
|
||||
joy.library.infra,
|
||||
))
|
||||
})
|
||||
|
||||
def branch_true(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
return stack, CONCAT(then, expression), dictionary
|
||||
|
||||
def branch_false(stack, expression, dictionary):
|
||||
(then, (else_, (flag, stack))) = stack
|
||||
return stack, CONCAT(else_, expression), dictionary
|
||||
|
||||
FUNCTIONS['branch'] = CombinatorJoyType('branch', [branch_true, branch_false], 100)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
globals().update(FUNCTIONS)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
from itertools import chain
|
||||
from joy.utils.stack import list_to_stack as l2s
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression = l2s([n1, n2, (mul, s2), (stack, s3), dip, infra, first])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(n1, (n2, ((mul, s2), ((stack, s3), (dip, (infra, (first, ())))))))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression = l2s([n1, n2, mul])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(n1, (n2, (mul, ())))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
infer(expression)
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[(s1, (f1, s1)), (s1, (i1, s1))]
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
infer(expression)
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[(s1, (f1, s1)), (s1, (i1, s1))]
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
for stack_effect_comment in infer(expression):
|
||||
print doc_from_stack_effect(*stack_effect_comment)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(-- f1)
|
||||
(-- i1)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
expression
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(n1, (n2, (mul, ())))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
infer(expression)
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[(s1, (f1, s1)), (s1, (i1, s1))]
|
||||
|
||||
|
||||
|
||||
And that brings us to current Work-In-Progress. I'm pretty hopeful that
|
||||
the mixed-mode inferencer/interpreter ``infer()`` function along with
|
||||
the ability to specify multiple implementations for the combinators will
|
||||
permit modelling of the stack effects of e.g. ``ifte``. If I can keep up
|
||||
the pace I should be able to verify that conjecture by the end of June.
|
||||
|
||||
h = infer((pred, s2), (mul, s3), (div, s4), (nullary, (bool, s5)), dipd, branch)
|
||||
|
||||
print '-' * 40
|
||||
|
||||
for fi, fo in h:
|
||||
print doc_from_stack_effect(fi, fo)
|
||||
|
||||
The numbers at the start of the lines are the current depth of the
|
||||
Python call stack. They're followed by the current computed stack effect
|
||||
(initialized to ``ID``) then the pending expression (the inference of
|
||||
the stack effect of which is the whole object of the current example.)
|
||||
|
||||
In this example we are implementing (and inferring) ``ifte`` as
|
||||
``[nullary bool] dipd branch`` which shows off a lot of the current
|
||||
implementation in action.
|
||||
|
||||
::
|
||||
|
||||
7 (--) ∘ [pred] [mul] [div] [nullary bool] dipd branch
|
||||
8 (-- [pred ...2]) ∘ [mul] [div] [nullary bool] dipd branch
|
||||
9 (-- [pred ...2] [mul ...3]) ∘ [div] [nullary bool] dipd branch
|
||||
10 (-- [pred ...2] [mul ...3] [div ...4]) ∘ [nullary bool] dipd branch
|
||||
11 (-- [pred ...2] [mul ...3] [div ...4] [nullary bool ...5]) ∘ dipd branch
|
||||
15 (-- [pred ...5]) ∘ nullary bool [mul] [div] branch
|
||||
19 (-- [pred ...2]) ∘ [stack] dinfrirst bool [mul] [div] branch
|
||||
20 (-- [pred ...2] [stack ]) ∘ dinfrirst bool [mul] [div] branch
|
||||
22 (-- [pred ...2] [stack ]) ∘ dip infra first bool [mul] [div] branch
|
||||
26 (--) ∘ stack [pred] infra first bool [mul] [div] branch
|
||||
29 (... -- ... [...]) ∘ [pred] infra first bool [mul] [div] branch
|
||||
30 (... -- ... [...] [pred ...1]) ∘ infra first bool [mul] [div] branch
|
||||
34 (--) ∘ pred s1 swaack first bool [mul] [div] branch
|
||||
37 (n1 -- n2) ∘ [n1] swaack first bool [mul] [div] branch
|
||||
38 (... n1 -- ... n2 [n1 ...]) ∘ swaack first bool [mul] [div] branch
|
||||
41 (... n1 -- ... n1 [n2 ...]) ∘ first bool [mul] [div] branch
|
||||
44 (n1 -- n1 n2) ∘ bool [mul] [div] branch
|
||||
47 (n1 -- n1 b1) ∘ [mul] [div] branch
|
||||
48 (n1 -- n1 b1 [mul ...1]) ∘ [div] branch
|
||||
49 (n1 -- n1 b1 [mul ...1] [div ...2]) ∘ branch
|
||||
53 (n1 -- n1) ∘ div
|
||||
56 (f2 f1 -- f3) ∘
|
||||
56 (i1 f1 -- f2) ∘
|
||||
56 (f1 i1 -- f2) ∘
|
||||
56 (i2 i1 -- f1) ∘
|
||||
53 (n1 -- n1) ∘ mul
|
||||
56 (f2 f1 -- f3) ∘
|
||||
56 (i1 f1 -- f2) ∘
|
||||
56 (f1 i1 -- f2) ∘
|
||||
56 (i2 i1 -- i3) ∘
|
||||
----------------------------------------
|
||||
(f2 f1 -- f3)
|
||||
(i1 f1 -- f2)
|
||||
(f1 i1 -- f2)
|
||||
(i2 i1 -- f1)
|
||||
(i2 i1 -- i3)
|
||||
|
||||
Conclusion
|
||||
----------
|
||||
|
||||
(for now...)
|
||||
We built a simple type inferencer, and a kind of crude "compiler" for a
|
||||
subset of Joy functions. Then we built a more powerful inferencer that
|
||||
actually does some evaluation and explores branching code paths
|
||||
|
||||
Work remains to be done:
|
||||
|
||||
@@ -2900,21 +2915,18 @@ Work remains to be done:
|
||||
went off and just started writing code to see if it would work. It
|
||||
does, but now I have to come back and describe here what I did.
|
||||
|
||||
I'm starting to realize that, with the inferencer/checker/compiler
|
||||
coming along, and with the UI ready to be rewritten in Joy, I'm close to
|
||||
a time when my ephasis is going to have to shift from crunchy code stuff
|
||||
to squishy human stuff. I'm going to have to put normal people in front
|
||||
of this and see if, in fact, they *can* learn the basics of programming
|
||||
with it.
|
||||
|
||||
The rest of this stuff is junk and/or unfinished material.
|
||||
|
||||
Appendix: Joy in the Logical Paradigm
|
||||
-------------------------------------
|
||||
|
||||
For this to work the type label classes have to be modified to let
|
||||
``T >= t`` succeed, where e.g. ``T`` is ``IntJoyType`` and ``t`` is
|
||||
``int``
|
||||
For *type checking* to work the type label classes have to be modified
|
||||
to let ``T >= t`` succeed, where e.g. ``T`` is ``IntJoyType`` and ``t``
|
||||
is ``int``. If you do that you can take advantage of the *logical
|
||||
relational* 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
|
||||
``polytypes`` module. But if you're interested in all that you should
|
||||
just use Prolog!
|
||||
|
||||
Anyhow, type *checking* is a few easy steps away.
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
@@ -2926,383 +2938,3 @@ For this to work the type label classes have to be modified to let
|
||||
AnyJoyType.__ge__ = _ge
|
||||
AnyJoyType.accept = tuple, int, float, long, str, unicode, bool, Symbol
|
||||
StackJoyType.accept = tuple
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F = infer(l2s((pop, swap, rolldown, rest, rest, cons, cons)))
|
||||
|
||||
for f in F:
|
||||
print doc_from_stack_effect(*f)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
([a4 a5 .1.] a3 a2 a1 -- [a2 a3 .1.])
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
from joy.parser import text_to_expression
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F = infer(l2s((pop, pop, pop)))
|
||||
|
||||
for f in F:
|
||||
print doc_from_stack_effect(*f)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a3 a2 a1 --)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
s = text_to_expression('0 1 2')
|
||||
s
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(0, (1, (2, ())))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F[0][0]
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a1, (a2, (a3, s1)))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
L = unify(s, F[0][0])
|
||||
L
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
s = text_to_expression('0 1 2 [3 4]')
|
||||
s
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(0, (1, (2, ((3, (4, ())), ()))))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F[0][0]
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a1, (a2, (a3, s1)))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
L = unify(s, F[0][0])
|
||||
L
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
L = unify(F[0][0], s)
|
||||
L
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
()
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
F[1][0]
|
||||
|
||||
|
||||
::
|
||||
|
||||
|
||||
---------------------------------------------------------------------------
|
||||
|
||||
IndexError Traceback (most recent call last)
|
||||
|
||||
<ipython-input-133-58a8e44e9cba> in <module>()
|
||||
----> 1 F[1][0]
|
||||
|
||||
|
||||
IndexError: list index out of range
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
s[0]
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
A[1] >= 23
|
||||
|
||||
`Abstract Interpretation <https://en.wikipedia.org/wiki/Abstract_interpretation>`__
|
||||
-----------------------------------------------------------------------------------
|
||||
|
||||
I *think* this might be sorta what I'm doing above with the ``kav()``
|
||||
function... In any event "mixed-mode" interpreters that include values
|
||||
and type variables and can track constraints, etc. will be, uh,
|
||||
super-useful. And Abstract Interpretation should be a rich source of
|
||||
ideas.
|
||||
|
||||
Junk
|
||||
----
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
class SymbolJoyType(AnyJoyType): prefix = 'F'
|
||||
|
||||
W = map(SymbolJoyType, _R)
|
||||
|
||||
k = S[0], ((W[1], S[2]), S[0])
|
||||
Symbol('cons')
|
||||
print doc_from_stack_effect(*k)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
dip_a = ((W[1], S[2]), (A[1], S[0]))
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
d = relabel(S[0], dip_a)
|
||||
print doc_from_stack_effect(*d)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
s = list(unify(d[1], k[1]))[0]
|
||||
s
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
j = update(s, k)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*j)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
j
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
cons
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
for f in MC([k], [dup]):
|
||||
print doc_from_stack_effect(*f)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
l = S[0], ((cons, S[2]), (A[1], S[0]))
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*l)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
|
||||
def dip_t(F):
|
||||
(quote, (a1, sec)) = F[1]
|
||||
G = F[0], sec
|
||||
P = S[3], (a1, S[3])
|
||||
a = [P]
|
||||
while isinstance(quote, tuple):
|
||||
term, quote = quote
|
||||
a.append(term)
|
||||
a.append(G)
|
||||
return a[::-1]
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
from joy.utils.stack import iter_stack
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
a, b, c = dip_t(l)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
a
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
b
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
c
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
MC([a], [b])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
kjs = MC(MC([a], [b]), [c])
|
||||
kjs
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
print doc_from_stack_effect(*kjs[0])
|
||||
|
||||
::
|
||||
|
||||
(a0 [.0.] -- [a0 .0.] a1)
|
||||
|
||||
a0 [.0.] a1 [cons] dip
|
||||
----------------------------
|
||||
[a0 .0.] a1
|
||||
|
||||
``concat``
|
||||
~~~~~~~~~~
|
||||
|
||||
How to deal with ``concat``?
|
||||
|
||||
::
|
||||
|
||||
concat ([.0.] [.1.] -- [.0. .1.])
|
||||
|
||||
We would like to represent this in Python somehow...
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
concat = (S[0], S[1]), ((S[0], S[1]),)
|
||||
|
||||
But this is actually ``cons`` with the first argument restricted to be a
|
||||
stack:
|
||||
|
||||
::
|
||||
|
||||
([.0.] [.1.] -- [[.0.] .1.])
|
||||
|
||||
What we have implemented so far would actually only permit:
|
||||
|
||||
::
|
||||
|
||||
([.0.] [.1.] -- [.2.])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
concat = (S[0], S[1]), (S[2],)
|
||||
|
||||
Which works but can lose information. Consider ``cons concat``, this is
|
||||
how much information we *could* retain:
|
||||
|
||||
::
|
||||
|
||||
(1 [.0.] [.1.] -- [1 .0. .1.])
|
||||
|
||||
As opposed to just:
|
||||
|
||||
::
|
||||
|
||||
(1 [.0.] [.1.] -- [.2.])
|
||||
|
||||
represent ``concat``
|
||||
~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
([.0.] [.1.] -- [A*(.0.) .1.])
|
||||
|
||||
Meaning that ``A*`` on the right-hand side should all the crap from
|
||||
``.0.``.
|
||||
|
||||
::
|
||||
|
||||
([ .0.] [.1.] -- [ A* .1.])
|
||||
([a .0.] [.1.] -- [a A* .1.])
|
||||
([a b .0.] [.1.] -- [a b A* .1.])
|
||||
([a b c .0.] [.1.] -- [a b c A* .1.])
|
||||
|
||||
or...
|
||||
|
||||
::
|
||||
|
||||
([ .0.] [.1.] -- [ .1.])
|
||||
([a .0.] [.1.] -- [a .1.])
|
||||
([a b .0.] [.1.] -- [a b .1.])
|
||||
([a b c .0.] [.1.] -- [a b c .1.])
|
||||
([a A* c .0.] [.1.] -- [a A* c .1.])
|
||||
|
||||
::
|
||||
|
||||
(a, (b, S0)) . S1 = (a, (b, (A*, S1)))
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
class Astar(object):
|
||||
def __repr__(self):
|
||||
return 'A*'
|
||||
|
||||
|
||||
def concat(s0, s1):
|
||||
a = []
|
||||
while isinstance(s0, tuple):
|
||||
term, s0 = s0
|
||||
a.append(term)
|
||||
assert isinstance(s0, StackJoyType), repr(s0)
|
||||
s1 = Astar(), s1
|
||||
for term in reversed(a):
|
||||
s1 = term, s1
|
||||
return s1
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
a, b = (A[1], S[0]), (A[2], S[1])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
concat(a, b)
|
||||
|
||||
@@ -0,0 +1,141 @@
|
||||
|
||||
Type Inference of Joy Expressions
|
||||
=================================
|
||||
|
||||
Two kinds of type inference are provided, a simple inferencer that can handle functions that have a single stack effect (aka "type signature") and that can generate Python code for a limited subset of those functions, and a more complex inferencer/interpreter hybrid that can infer the stack effects of most Joy expressions, including multiple stack effects, unbounded sequences of values, and combinators (if enough information is available.)
|
||||
|
||||
|
||||
``joy.utils.types``
|
||||
-------------------
|
||||
|
||||
|
||||
Curently (asterix after name indicates a function that can be auto-compiled to Python)::
|
||||
|
||||
_Tree_add_Ee = ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) *
|
||||
_Tree_delete_R0 = ([a2 ...1] a1 -- [a2 ...1] a2 a1 a1) *
|
||||
_Tree_delete_clear_stuff = (a3 a2 [a1 ...1] -- [...1]) *
|
||||
_Tree_get_E = ([a3 a4 ...1] a2 a1 -- a4) *
|
||||
add = (n1 n2 -- n3)
|
||||
and = (b1 b2 -- b3)
|
||||
bool = (a1 -- b1)
|
||||
ccons = (a2 a1 [...1] -- [a2 a1 ...1]) *
|
||||
cons = (a1 [...0] -- [a1 ...0]) *
|
||||
div = (n1 n2 -- n3)
|
||||
divmod = (n2 n1 -- n4 n3)
|
||||
dup = (a1 -- a1 a1) *
|
||||
dupd = (a2 a1 -- a2 a2 a1) *
|
||||
dupdd = (a3 a2 a1 -- a3 a3 a2 a1) *
|
||||
eq = (n1 n2 -- b1)
|
||||
first = ([a1 ...1] -- a1) *
|
||||
first_two = ([a1 a2 ...1] -- a1 a2) *
|
||||
floordiv = (n1 n2 -- n3)
|
||||
fourth = ([a1 a2 a3 a4 ...1] -- a4) *
|
||||
ge = (n1 n2 -- b1)
|
||||
gt = (n1 n2 -- b1)
|
||||
le = (n1 n2 -- b1)
|
||||
lshift = (n1 n2 -- n3)
|
||||
lt = (n1 n2 -- b1)
|
||||
modulus = (n1 n2 -- n3)
|
||||
mul = (n1 n2 -- n3)
|
||||
ne = (n1 n2 -- b1)
|
||||
neg = (n1 -- n2)
|
||||
not = (a1 -- b1)
|
||||
over = (a2 a1 -- a2 a1 a2) *
|
||||
pm = (n2 n1 -- n4 n3)
|
||||
pop = (a1 --) *
|
||||
popd = (a2 a1 -- a1) *
|
||||
popdd = (a3 a2 a1 -- a2 a1) *
|
||||
popop = (a2 a1 --) *
|
||||
popopd = (a3 a2 a1 -- a1) *
|
||||
popopdd = (a4 a3 a2 a1 -- a2 a1) *
|
||||
pow = (n1 n2 -- n3)
|
||||
pred = (n1 -- n2)
|
||||
rest = ([a1 ...0] -- [...0]) *
|
||||
rolldown = (a1 a2 a3 -- a2 a3 a1) *
|
||||
rollup = (a1 a2 a3 -- a3 a1 a2) *
|
||||
rrest = ([a1 a2 ...1] -- [...1]) *
|
||||
rshift = (n1 n2 -- n3)
|
||||
second = ([a1 a2 ...1] -- a2) *
|
||||
sqrt = (n1 -- n2)
|
||||
stack = (... -- ... [...]) *
|
||||
stuncons = (... a1 -- ... a1 a1 [...]) *
|
||||
stununcons = (... a2 a1 -- ... a2 a1 a1 a2 [...]) *
|
||||
sub = (n1 n2 -- n3)
|
||||
succ = (n1 -- n2)
|
||||
swaack = ([...1] -- [...0]) *
|
||||
swap = (a1 a2 -- a2 a1) *
|
||||
swons = ([...1] a1 -- [a1 ...1]) *
|
||||
third = ([a1 a2 a3 ...1] -- a3) *
|
||||
truediv = (n1 n2 -- n3)
|
||||
tuck = (a2 a1 -- a1 a2 a1) *
|
||||
uncons = ([a1 ...0] -- a1 [...0]) *
|
||||
unit = (a1 -- [a1 ]) *
|
||||
unswons = ([a1 ...1] -- [...1] a1) *
|
||||
|
||||
|
||||
.. automodule:: joy.utils.types
|
||||
:members:
|
||||
|
||||
|
||||
``joy.utils.polytypes``
|
||||
-------------------------
|
||||
|
||||
Example output of the ``infer()`` function. The first number on each line is the depth of the Python stack. It goes down when the function backtracks. The next thing on each line is the currently-computed stack effect so far. It starts with the empty "identity function" and proceeds through the expression, which is the rest of each line. The function acts like an interpreter but instead of executing the terms of the expression it composes them, but for combinators it *does* execute them, using the output side of the stack effect as the stack. This seems to work fine. With proper definitions for the behavior of the combinators that can have more than one effect (like ``branch`` or ``loop``) the ``infer()`` function seems to be able to handle anything I throw at it so far.
|
||||
|
||||
::
|
||||
|
||||
7 (--) ∘ pop swap rolldown rest rest cons cons
|
||||
10 (a1 --) ∘ swap rolldown rest rest cons cons
|
||||
13 (a3 a2 a1 -- a2 a3) ∘ rolldown rest rest cons cons
|
||||
16 (a4 a3 a2 a1 -- a2 a3 a4) ∘ rest rest cons cons
|
||||
19 ([a4 ...1] a3 a2 a1 -- a2 a3 [...1]) ∘ rest cons cons
|
||||
22 ([a4 a5 ...1] a3 a2 a1 -- a2 a3 [...1]) ∘ cons cons
|
||||
25 ([a4 a5 ...1] a3 a2 a1 -- a2 [a3 ...1]) ∘ cons
|
||||
28 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
|
||||
----------------------------------------
|
||||
([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1])
|
||||
|
||||
|
||||
Here's another example (implementing ``ifte``) using some combinators::
|
||||
|
||||
7 (--) ∘ [pred] [mul] [div] [nullary bool] dipd branch
|
||||
8 (-- [pred ...2]) ∘ [mul] [div] [nullary bool] dipd branch
|
||||
9 (-- [pred ...2] [mul ...3]) ∘ [div] [nullary bool] dipd branch
|
||||
10 (-- [pred ...2] [mul ...3] [div ...4]) ∘ [nullary bool] dipd branch
|
||||
11 (-- [pred ...2] [mul ...3] [div ...4] [nullary bool ...5]) ∘ dipd branch
|
||||
15 (-- [pred ...5]) ∘ nullary bool [mul] [div] branch
|
||||
19 (-- [pred ...2]) ∘ [stack] dinfrirst bool [mul] [div] branch
|
||||
20 (-- [pred ...2] [stack ]) ∘ dinfrirst bool [mul] [div] branch
|
||||
22 (-- [pred ...2] [stack ]) ∘ dip infra first bool [mul] [div] branch
|
||||
26 (--) ∘ stack [pred] infra first bool [mul] [div] branch
|
||||
29 (... -- ... [...]) ∘ [pred] infra first bool [mul] [div] branch
|
||||
30 (... -- ... [...] [pred ...1]) ∘ infra first bool [mul] [div] branch
|
||||
34 (--) ∘ pred s1 swaack first bool [mul] [div] branch
|
||||
37 (n1 -- n2) ∘ [n1] swaack first bool [mul] [div] branch
|
||||
38 (... n1 -- ... n2 [n1 ...]) ∘ swaack first bool [mul] [div] branch
|
||||
41 (... n1 -- ... n1 [n2 ...]) ∘ first bool [mul] [div] branch
|
||||
44 (n1 -- n1 n2) ∘ bool [mul] [div] branch
|
||||
47 (n1 -- n1 b1) ∘ [mul] [div] branch
|
||||
48 (n1 -- n1 b1 [mul ...1]) ∘ [div] branch
|
||||
49 (n1 -- n1 b1 [mul ...1] [div ...2]) ∘ branch
|
||||
53 (n1 -- n1) ∘ div
|
||||
56 (f2 f1 -- f3) ∘
|
||||
56 (i1 f1 -- f2) ∘
|
||||
56 (f1 i1 -- f2) ∘
|
||||
56 (i2 i1 -- f1) ∘
|
||||
53 (n1 -- n1) ∘ mul
|
||||
56 (f2 f1 -- f3) ∘
|
||||
56 (i1 f1 -- f2) ∘
|
||||
56 (f1 i1 -- f2) ∘
|
||||
56 (i2 i1 -- i3) ∘
|
||||
----------------------------------------
|
||||
(f2 f1 -- f3)
|
||||
(i1 f1 -- f2)
|
||||
(f1 i1 -- f2)
|
||||
(i2 i1 -- f1)
|
||||
(i2 i1 -- i3)
|
||||
|
||||
.. automodule:: joy.utils.polytypes
|
||||
:members:
|
||||
|
||||
|
||||
Reference in New Issue
Block a user