This notebook presents a simple type inferencer for Joy code. It can infer the stack effect of most Joy expressions. It built largely by means of existing ideas and research (some of it may be original but I'm not able to say, as I don't fully understand the all of the source material in the depth required to make that call.) A great overview of the existing knowledge is a talk "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.
-The notebook starts with a simple inferencer based on the work of Jaanus Pöial which we then progressively elaborate to cover more Joy semantics. Along the way we write a simple "compiler" that emits Python code for what I like to call Yin functions.
-Yin functions are those that only rearrange values in stacks, as opposed to Yang functions that actually work on the values themselves. It's interesting to note that a Joy with only stacks (no other kinds of values) can be made and is Turing-complete, therefore all Yang functions are actually Yin functions, and all computation can be performed by manipulations of structures of containers, which is a restatement of the Laws of Form. (Also, this implies that every program can be put into a form such that it can be computed in a single step, although that step may be enormous or unending.)
-Although I haven't completed it yet, a Joy based on Laws of Form provides the foundation for a provably correct computing system "down to the metal". This is my original and still primary motivation for developing Joy. (I want a proven-correct Operating System for a swarm of trash-collecting recycler robots. To trust it I have to implementment it myself from first principles, and I'm not smart enough to truly grok the existing literature and software, so I had to go look for and find LoF and Joy. Now that I have the mental tools to build my robot OS I can get down to it.
-Anyhow, here's type inference...
+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" given by Rob Kleffner on or about 2017-03-10 as part of a course on the history of programming languages.)
+The notebook starts with a simple inferencer based on the work of Jaanus Pöial which we then progressively elaborate to cover more Joy semantics. Along the way we write a simple "compiler" that emits Python code for what I like to call Yin functions. (Yin functions are those that only rearrange values in stacks, as opposed to Yang functions that actually work on the values themselves.)
These are slightly tricky.
+These are slightly tricky.
rest ( [1 ...] -- [...] )
@@ -12341,18 +12338,12 @@ cons ( 1 [...] -- [1 ...] )compose() version 2¶This function has to be modified to use the new datastructures and it is no longer recursive, instead recursion happens as part of unification. Further, the first and second of Pöial's rules are now handled automatically by the unification algorithm.
+compose() version 2¶This function has to be modified to use the new datastructures and it is no longer recursive, instead recursion happens as part of unification. Further, the first and second of Pöial's rules are now handled automatically by the unification algorithm. (One easy way to see this is that now an empty stack effect comment is represented by a StackJoyType instance which is not "falsey" and so neither of the first two rules' if clauses will ever be True. Later on I change the "truthiness" of StackJoyType to false to let e.g. joy.utils.stack.concat work with our stack effect comment cons-list tuples.)
C(C(stack, uncons), uncons)
+reduce(C, (stack, uncons, uncons))
for f in MC([dup], muls):
- print doc_from_stack_effect(*f)
-for f in MC([dup], [mul]):
@@ -15560,7 +15497,40 @@ uncons = ([a1 .1.] -- a1 [.1.])
+for f in MC([dup], muls):
+ print doc_from_stack_effect(*f)
+expression = l2s([n1, n2, mul])
@@ -16630,6 +16600,171 @@ uncons = ([a1 .1.] -- a1 [.1.])
expression
+infer(expression)
+infer(expression)
+for stack_effect_comment in infer(expression):
+ print doc_from_stack_effect(*stack_effect_comment)
+expression
+class SymbolJoyType(AnyJoyType):
- prefix = 'F'
-
- def __init__(self, name, sec, number):
- self.name = name
- self.stack_effects = sec
- self.number = number
-
-class CombinatorJoyType(SymbolJoyType): prefix = 'C'
-
-def dip_t(stack, expression):
- (quote, (a1, stack)) = stack
- expression = stack_concat(quote, (a1, expression))
- return stack, expression
-
-CONS = SymbolJoyType('cons', [cons], 23)
-DIP = CombinatorJoyType('dip', [dip_t], 44)
-
-
-def kav(F, e):
- #i, stack = F
- if not e:
- return [(F, e)]
- n, e = e
- if isinstance(n, SymbolJoyType):
- Fs = []
- for sec in n.stack_effects:
- Fs.extend(MC([F], sec))
- return [kav(Fn, e) for Fn in Fs]
- if isinstance(n, CombinatorJoyType):
- res = []
- for f in n.stack_effects:
- s, e = f(F[1], e)
- new_F = F[0], s
- res.extend(kav(new_F, e))
- return res
- lit = S[0], (n, S[0])
- return [kav(Fn, e) for Fn in MC([F], [lit])]
-compare, and be amazed:
+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.
def dip_t(stack, expression):
- (quote, (a1, stack)) = stack
- expression = stack_concat(quote, (a1, expression))
- return stack, expression
-def dip(stack, expression, dictionary):
- (quote, (x, stack)) = stack
- expression = (x, expression)
- return stack, concat(quote, expression), dictionary
-And that brings us to current Work-In-Progress. I'm pretty hopeful that the mixed-mode inferencer/interpreter kav() 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.
(for now...)
+ +Work remains to be done:
+loop and genrec, etc..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.
F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
+def _ge(self, other):
+ return (issubclass(other.__class__, self.__class__)
+ or hasattr(self, 'accept')
+ and isinstance(other, self.accept))
-print doc_from_stack_effect(*F)
+AnyJoyType.__ge__ = _ge
+AnyJoyType.accept = tuple, int, float, long, str, unicode, bool, Symbol
+StackJoyType.accept = tuple
+
+
+F = infer(l2s((pop, swap, rolldown, rest, rest, cons, cons)))
+
+for f in F:
+ print doc_from_stack_effect(*f)
+from joy.parser import text_to_expression
+F = infer(l2s((pop, pop, pop)))
+
+for f in F:
+ print doc_from_stack_effect(*f)
+s = text_to_expression('0 1 2')
+s
+F[0][0]
+L = unify(s, F[0][0])
+L
+s = text_to_expression('0 1 2 [3 4]')
+s
+F[0][0]
+L = unify(s, F[0][0])
+L
+L = unify(F[0][0], s)
+L
+F[1][0]
from joy.parser import text_to_expression
-s = text_to_expression('[3 4 ...] 2 1')
-s
-L = unify(F[1], s)
-L
-F[1]
-F[1][0]
-A[1] >= 23
+This notebook presents a simple type inferencer for Joy code. It can -infer the stack effect of most Joy expressions. It built largely by -means of existing ideas and research (some of it may be original but I’m -not able to say, as I don’t fully understand the all of the source -material in the depth required to make that call.) A great overview of -the existing knowledge is a talk “Type Inference in Stack-Based -Programming +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” given by Rob Kleffner on or about 2017-03-10 as part of a course on the -history of programming languages.
+history of programming languages.)The notebook starts with a simple inferencer based on the work of Jaanus Pöial which we then progressively elaborate to cover more Joy semantics. Along the way we write a simple “compiler” that emits Python code for -what I like to call Yin functions.
-Yin functions are those that only rearrange values in stacks, as opposed -to Yang functions that actually work on the values themselves. It’s -interesting to note that a Joy with only stacks (no other kinds of -values) can be made and is Turing-complete, therefore all Yang functions -are actually Yin functions, and all computation can be performed by -manipulations of structures of containers, which is a restatement of the -Laws of Form. (Also, this implies that every program can be put into a -form such that it can be computed in a single step, although that step -may be enormous or unending.)
-Although I haven’t completed it yet, a Joy based on Laws of Form -provides the foundation for a provably correct computing system “down to -the metal”. This is my original and still primary motivation for -developing Joy. (I want a proven-correct Operating System for a swarm of -trash-collecting recycler robots. To trust it I have to implementment it -myself from first principles, and I’m not smart enough to truly grok the -existing literature and software, so I had to go look for and find LoF -and Joy. Now that I have the mental tools to build my robot OS I can get -down to it.
-Anyhow, here’s type inference…
+what I like to call Yin functions. (Yin functions are those that only +rearrange values in stacks, as opposed to Yang functions that actually +work on the values themselves.)These are slightly tricky.
rest ( [1 ...] -- [...] )
@@ -426,18 +406,12 @@ integers or tuples of type descriptors:
if s is None:
s = {}
- if u == v:
- return s
-
if isinstance(u, int):
s[u] = v
- return s
-
- if isinstance(v, int):
+ elif isinstance(v, int):
s[v] = u
- return s
- return False
+ return s
Cannot unify (1, 2) and (1001, 1002).
-unify() version 2¶The problem is that the unify() function as written doesn’t handle
@@ -607,27 +578,24 @@ deal with this recursively:
C(cons, uncons)
@@ -1122,7 +1090,7 @@ of how many labels of each domain it has “seen”.
pass
if not isinstance(f, tuple):
- seen[f] = f.__class__(c[f.prefix])
+ seen[f] = f.__class__(c[f.prefix] + 1)
c[f.prefix] += 1
return seen[f]
@@ -1132,7 +1100,7 @@ of how many labels of each domain it has “seen”.
delabel(foo)
-(((a0,), (a0, a0)), ((n0, n1), (n2,)))
+(((a1,), (a1, a1)), ((n1, n2), (n3,)))
@@ -1246,7 +1214,7 @@ of how many labels of each domain it has “seen”.
print name, '=', doc_from_stack_effect(*stack_effect_comment)
ccons = (a0 a1 [.0.] -- [a0 a1 .0.])
+ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
cons = (a1 [.1.] -- [a1 .1.])
divmod_ = (n2 n1 -- n4 n3)
dup = (a1 -- a1 a1)
@@ -1263,13 +1231,13 @@ of how many labels of each domain it has “seen”.
rest = ([a1 .1.] -- [.1.])
rolldown = (a1 a2 a3 -- a2 a3 a1)
rollup = (a1 a2 a3 -- a3 a1 a2)
-rrest = ([a0 a1 .0.] -- [.0.])
-second = ([a0 a1 .0.] -- a1)
-sqrt = (n0 -- n1)
+rrest = ([a1 a2 .1.] -- [.1.])
+second = ([a1 a2 .1.] -- a2)
+sqrt = (n1 -- n2)
succ = (n1 -- n2)
swap = (a1 a2 -- a2 a1)
-swons = ([.0.] a0 -- [a0 .0.])
-third = ([a0 a1 a2 .0.] -- a2)
+swons = ([.1.] a1 -- [a1 .1.])
+third = ([a1 a2 a3 .1.] -- a3)
tuck = (a2 a1 -- a1 a2 a1)
uncons = ([a1 .1.] -- a1 [.1.])
@@ -1283,7 +1251,7 @@ of how many labels of each domain it has “seen”.
C(dup, mul)
-((n0,), (n1,))
+((n1,), (n2,))
Revisit the F function, works fine.
@@ -1291,13 +1259,13 @@ of how many labels of each domain it has “seen”.
F
-(((a0, (a1, s0)), a2, a3, a4), ((a3, (a2, s0)),))
+(((a1, (a2, s1)), a3, a4, a5), ((a4, (a3, s1)),))
print doc_from_stack_effect(*F)
-([a0 a1 .0.] a2 a3 a4 -- [a3 a2 .0.])
+([a1 a2 .1.] a3 a4 a5 -- [a4 a3 .1.])
Some otherwise inefficient functions are no longer to be feared. We can
@@ -1310,21 +1278,21 @@ also get the effect of combinators in some limited cases.
neato(rollup, swap, rolldown)
-(a0 a1 a2 -- a1 a0 a2)
+(a1 a2 a3 -- a2 a1 a3)
# e.g. [popop] dipd
neato(popdd, rolldown, pop)
-(a0 a1 a2 a3 -- a2 a3)
+(a1 a2 a3 a4 -- a3 a4)
# Reverse the order of the top three items.
neato(rollup, swap)
-(a0 a1 a2 -- a2 a1 a0)
+(a1 a2 a3 -- a3 a2 a1)
@@ -1351,9 +1319,9 @@ the compile_()
def F(stack):
- """([a0 a1 .0.] a2 a3 a4 -- [a3 a2 .0.])"""
- (a4, (a3, (a2, ((a0, (a1, s0)), stack)))) = stack
- return ((a3, (a2, s0)), stack)
+ """([a1 a2 .1.] a3 a4 a5 -- [a4 a3 .1.])"""
+ (a5, (a4, (a3, ((a1, (a2, s1)), stack)))) = stack
+ return ((a4, (a3, s1)), stack)
But it cannot magically create new functions that involve e.g. math and
@@ -1362,9 +1330,9 @@ such. Note that this is not a def sqr(stack):
- """(n0 -- n1)"""
- (n0, stack) = stack
- return (n1, stack)
+ """(n1 -- n2)"""
+ (n1, stack) = stack
+ return (n2, stack)
(Eventually I should come back around to this becuase it’s not tooo
@@ -1392,7 +1360,7 @@ comments. We can write a function to check that:
print name, '=', doc_from_stack_effect(*stack_effect_comment)
-ccons = (a0 a1 [.0.] -- [a0 a1 .0.])
+ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
cons = (a1 [.1.] -- [a1 .1.])
dup = (a1 -- a1 a1)
dupd = (a2 a1 -- a2 a2 a1)
@@ -1405,11 +1373,11 @@ comments. We can write a function to check that:
rest = ([a1 .1.] -- [.1.])
rolldown = (a1 a2 a3 -- a2 a3 a1)
rollup = (a1 a2 a3 -- a3 a1 a2)
-rrest = ([a0 a1 .0.] -- [.0.])
-second = ([a0 a1 .0.] -- a1)
+rrest = ([a1 a2 .1.] -- [.1.])
+second = ([a1 a2 .1.] -- a2)
swap = (a1 a2 -- a2 a1)
-swons = ([.0.] a0 -- [a0 .0.])
-third = ([a0 a1 a2 .0.] -- a2)
+swons = ([.1.] a1 -- [a1 .1.])
+third = ([a1 a2 a3 .1.] -- a3)
tuck = (a2 a1 -- a1 a2 a1)
uncons = ([a1 .1.] -- a1 [.1.])
@@ -1482,7 +1450,13 @@ sequence and unify(
This function has to be modified to use the new datastructures and it is
no longer recursive, instead recursion happens as part of unification.
Further, the first and second of Pöial’s rules are now handled
-automatically by the unification algorithm.
+automatically by the unification algorithm. (One easy way to see this is
+that now an empty stack effect comment is represented by a
+StackJoyType instance which is not “falsey” and so neither of the
+first two rules’ if clauses will ever be True. Later on I change
+the “truthiness” of StackJoyType to false to let e.g.
+joy.utils.stack.concat work with our stack effect comment cons-list
+tuples.)
def compose(f, g):
(f_in, f_out), (g_in, g_out) = f, g
s = unify(g_in, f_out)
@@ -1509,13 +1483,13 @@ conversion function instead. This is programmer’s laziness.
C(stack, uncons)
-((a0, s0), (s0, (a0, (a0, s0))))
+((a1, s1), (s1, (a1, (a1, s1))))
-C(C(stack, uncons), uncons)
+reduce(C, (stack, uncons, uncons))
-((a0, (a1, s0)), (s0, (a1, (a0, (a0, (a1, s0))))))
+((a1, (a2, s1)), (s1, (a2, (a1, (a1, (a2, s1))))))
The display function should be changed too.
@@ -1575,7 +1549,7 @@ conversion function instead. This is programmer’s laziness.
print name, '=', doc_from_stack_effect(*stack_effect_comment)
-ccons = (a0 a1 [.0.] -- [a0 a1 .0.])
+ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
cons = (a1 [.1.] -- [a1 .1.])
divmod_ = (n2 n1 -- n4 n3)
dup = (a1 -- a1 a1)
@@ -1592,38 +1566,38 @@ conversion function instead. This is programmer’s laziness.
rest = ([a1 .1.] -- [.1.])
rolldown = (a1 a2 a3 -- a2 a3 a1)
rollup = (a1 a2 a3 -- a3 a1 a2)
-rrest = ([a0 a1 .0.] -- [.0.])
-second = ([a0 a1 .0.] -- a1)
-sqrt = (n0 -- n1)
+rrest = ([a1 a2 .1.] -- [.1.])
+second = ([a1 a2 .1.] -- a2)
+sqrt = (n1 -- n2)
stack = (... -- ... [...])
succ = (n1 -- n2)
swaack = ([.1.] -- [.0.])
swap = (a1 a2 -- a2 a1)
-swons = ([.0.] a0 -- [a0 .0.])
-third = ([a0 a1 a2 .0.] -- a2)
+swons = ([.1.] a1 -- [a1 .1.])
+third = ([a1 a2 a3 .1.] -- a3)
tuck = (a2 a1 -- a1 a2 a1)
uncons = ([a1 .1.] -- a1 [.1.])
print ; print doc_from_stack_effect(*stack)
print ; print doc_from_stack_effect(*C(stack, uncons))
-print ; print doc_from_stack_effect(*C(C(stack, uncons), uncons))
-print ; print doc_from_stack_effect(*C(C(stack, uncons), cons))
+print ; print doc_from_stack_effect(*reduce(C, (stack, uncons, uncons)))
+print ; print doc_from_stack_effect(*reduce(C, (stack, uncons, cons)))
(... -- ... [...])
-(... a0 -- ... a0 a0 [...])
+(... a1 -- ... a1 a1 [...])
-(... a1 a0 -- ... a1 a0 a0 a1 [...])
+(... a2 a1 -- ... a2 a1 a1 a2 [...])
-(... a0 -- ... a0 [a0 ...])
+(... a1 -- ... a1 [a1 ...])
print doc_from_stack_effect(*C(ccons, stack))
-(... a1 a0 [.0.] -- ... [a1 a0 .0.] [[a1 a0 .0.] ...])
+(... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...])
Q = C(ccons, stack)
@@ -1631,7 +1605,7 @@ conversion function instead. This is programmer’s laziness.
Q
-((s0, (a0, (a1, s1))), (((a1, (a0, s0)), s1), ((a1, (a0, s0)), s1)))
+((s1, (a1, (a2, s2))), (((a2, (a1, s1)), s2), ((a2, (a1, s1)), s2)))
@@ -1652,9 +1626,9 @@ comments are now already in the form needed for the Python code:
def Q(stack):
- """(... a1 a0 [.0.] -- ... [a1 a0 .0.] [[a1 a0 .0.] ...])"""
- (s0, (a0, (a1, s1))) = stack
- return (((a1, (a0, s0)), s1), ((a1, (a0, s0)), s1))
+ """(... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...])"""
+ (s1, (a1, (a2, s2))) = stack
+ return (((a2, (a1, s1)), s2), ((a2, (a1, s1)), s2))
unstack = (S[1], S[0]), S[1]
@@ -1676,19 +1650,19 @@ comments are now already in the form needed for the Python code:
print doc_from_stack_effect(*C(cons, unstack))
-(a0 [.0.] -- a0)
+(a1 [.1.] -- a1)
print doc_from_stack_effect(*C(cons, enstacken))
-(a0 [.0.] -- [[a0 .0.] .1.])
+(a1 [.1.] -- [[a1 .1.] .2.])
C(cons, unstack)
-((s0, (a0, s1)), (a0, s0))
+((s1, (a1, s2)), (a1, s1))
@@ -1730,8 +1704,8 @@ comments are now already in the form needed for the Python code:
print doc_from_stack_effect(*dup), doc_from_stack_effect(*f), doc_from_stack_effect(*e)
-(a1 -- a1 a1) (i1 i2 -- i3) (i0 -- i1)
-(a1 -- a1 a1) (f1 f2 -- f3) (f0 -- f1)
+(a1 -- a1 a1) (i1 i2 -- i3) (i1 -- i2)
+(a1 -- a1 a1) (f1 f2 -- f3) (f1 -- f2)
from itertools import product
@@ -1749,19 +1723,19 @@ comments are now already in the form needed for the Python code:
return sorted(set(meta_compose(F, G)))
-for f in MC([dup], muls):
- print doc_from_stack_effect(*f)
-
-
-(f0 -- f1)
-(i0 -- i1)
-
-
for f in MC([dup], [mul]):
print doc_from_stack_effect(*f)
-(n0 -- n1)
+(n1 -- n2)
+
+
+for f in MC([dup], muls):
+ print doc_from_stack_effect(*f)
+
+
+(f1 -- f2)
+(i1 -- i2)
@@ -2024,23 +1998,23 @@ disappears:
print doc_from_stack_effect(*f)
-(f0 -- f1)
-(i0 -- i1)
+(f1 -- f2)
+(i1 -- i2)
for f in MC([dup], [sum_]):
print doc_from_stack_effect(*f)
-([n0* .0.] -- [n0* .0.] n0)
+([n1* .1.] -- [n1* .1.] n1)
for f in MC([cons], [sum_]):
print doc_from_stack_effect(*f)
-(a0 [.0.] -- n0)
-(n0 [n0* .0.] -- n1)
+(a1 [.1.] -- n1)
+(n1 [n1* .1.] -- n2)
sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0]))
@@ -2051,7 +2025,7 @@ disappears:
print doc_from_stack_effect(*f)
-(a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n0 [n0* .0.] -- n1)
+(a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n1 [n1* .1.] -- n2)
a = (A[4], (As[1], (A[3], S[1])))
@@ -2241,70 +2215,77 @@ stack effect we have to “split universes” again and return both.
expression = l2s([n1, n2, mul])
+expression
+
+
+(n1, (n2, (mul, ())))
+
+
infer(expression)
-[]
+[(s1, (f1, s1)), (s1, (i1, s1))]
-class SymbolJoyType(AnyJoyType):
- prefix = 'F'
-
- def __init__(self, name, sec, number):
- self.name = name
- self.stack_effects = sec
- self.number = number
-
-class CombinatorJoyType(SymbolJoyType): prefix = 'C'
-
-def dip_t(stack, expression):
- (quote, (a1, stack)) = stack
- expression = stack_concat(quote, (a1, expression))
- return stack, expression
-
-CONS = SymbolJoyType('cons', [cons], 23)
-DIP = CombinatorJoyType('dip', [dip_t], 44)
-
-
-def kav(F, e):
- #i, stack = F
- if not e:
- return [(F, e)]
- n, e = e
- if isinstance(n, SymbolJoyType):
- Fs = []
- for sec in n.stack_effects:
- Fs.extend(MC([F], sec))
- return [kav(Fn, e) for Fn in Fs]
- if isinstance(n, CombinatorJoyType):
- res = []
- for f in n.stack_effects:
- s, e = f(F[1], e)
- new_F = F[0], s
- res.extend(kav(new_F, e))
- return res
- lit = S[0], (n, S[0])
- return [kav(Fn, e) for Fn in MC([F], [lit])]
+infer(expression)
-compare, and be amazed:
-def dip_t(stack, expression):
- (quote, (a1, stack)) = stack
- expression = stack_concat(quote, (a1, expression))
- return stack, expression
+[(s1, (f1, s1)), (s1, (i1, s1))]
-def dip(stack, expression, dictionary):
- (quote, (x, stack)) = stack
- expression = (x, expression)
- return stack, concat(quote, expression), dictionary
+for stack_effect_comment in infer(expression):
+ print doc_from_stack_effect(*stack_effect_comment)
+
+
+(-- f1)
+(-- i1)
+
+
+expression
+
+
+(n1, (n2, (mul, ())))
+
+
+infer(expression)
+
+
+[(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 kav() function along with the
-ability to specify multiple implementations for the combinators will
+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.
+
+
+Conclusion¶
+(for now…)
+Work remains to be done:
+
+- the rest of the library has to be covered
+- figure out how to deal with
loop and genrec, etc..
+- extend the types to check values (see the appendix)
+- other kinds of “higher order” type variables, OR, AND, etc..
+- maybe rewrite in Prolog for great good?
+- definitions
+- don’t permit composition of functions that don’t compose
+- auto-compile compilable functions
+- Compiling more than just the Yin functions.
+- getting better visibility (than Python debugger.)
+- DOOOOCS!!!! Lots of docs!
+- docstrings all around
+- 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.
+
+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.
@@ -2312,134 +2293,104 @@ the pace I should be able to verify that conjecture by the end of June.
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
-F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
+def _ge(self, other):
+ return (issubclass(other.__class__, self.__class__)
+ or hasattr(self, 'accept')
+ and isinstance(other, self.accept))
-print doc_from_stack_effect(*F)
+AnyJoyType.__ge__ = _ge
+AnyJoyType.accept = tuple, int, float, long, str, unicode, bool, Symbol
+StackJoyType.accept = tuple
----------------------------------------------------------------------------
+F = infer(l2s((pop, swap, rolldown, rest, rest, cons, cons)))
-TypeError Traceback (most recent call last)
-
-<ipython-input-119-7fde90b4e88f> in <module>()
- 1 F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
- 2
-----> 3 print doc_from_stack_effect(*F)
-
-
-<ipython-input-98-ddee30dbb1a6> in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
----> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
-<ipython-input-97-5eb7ac5ad2c2> in compose(f, g)
- 1 def compose(f, g):
-----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
-<ipython-input-98-ddee30dbb1a6> in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
----> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
-<ipython-input-97-5eb7ac5ad2c2> in compose(f, g)
- 1 def compose(f, g):
-----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
-<ipython-input-98-ddee30dbb1a6> in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
----> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
-<ipython-input-97-5eb7ac5ad2c2> in compose(f, g)
- 1 def compose(f, g):
-----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
-<ipython-input-98-ddee30dbb1a6> in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
----> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
-<ipython-input-97-5eb7ac5ad2c2> in compose(f, g)
- 1 def compose(f, g):
-----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
-<ipython-input-98-ddee30dbb1a6> in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
----> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
-<ipython-input-97-5eb7ac5ad2c2> in compose(f, g)
- 1 def compose(f, g):
-----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
-<ipython-input-98-ddee30dbb1a6> in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
----> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
-<ipython-input-97-5eb7ac5ad2c2> in compose(f, g)
- 1 def compose(f, g):
-----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
-TypeError: 'SymbolJoyType' object is not iterable
+for f in F:
+ print doc_from_stack_effect(*f)
+
+
+([a4 a5 .1.] a3 a2 a1 -- [a2 a3 .1.])
from joy.parser import text_to_expression
-s = text_to_expression('[3 4 ...] 2 1')
+F = infer(l2s((pop, pop, pop)))
+
+for f in F:
+ print doc_from_stack_effect(*f)
+
+
+(a3 a2 a1 --)
+
+
+s = text_to_expression('0 1 2')
s
-L = unify(F[1], s)
+(0, (1, (2, ())))
+
+
+F[0][0]
+
+
+(a1, (a2, (a3, s1)))
+
+
+L = unify(s, F[0][0])
L
-F[1]
+()
+
+
+s = text_to_expression('0 1 2 [3 4]')
+s
+
+
+(0, (1, (2, ((3, (4, ())), ()))))
+
+
+F[0][0]
+
+
+(a1, (a2, (a3, s1)))
+
+
+L = unify(s, F[0][0])
+L
+
+
+()
+
+
+L = unify(F[0][0], s)
+L
+
+
+()
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
+
+
s[0]
+A[1] >= 23
+
+
Abstract Interpretation¶
@@ -2637,7 +2588,7 @@ how much information we could retain:
pop swappop∘swap roll<Compiling pop∘swap∘roll<
-Functions on Lists
+Functions on Stacks
pop∘swap∘roll< restpop∘swap∘roll<∘rest restpop∘swap∘roll<∘rest∘rest consPart VII: Typing Combinators
+Conclusion
Appendix: Joy in the Logical Paradigm
Abstract Interpretation
Junk
diff --git a/docs/sphinx_docs/_build/html/notebooks/index.html b/docs/sphinx_docs/_build/html/notebooks/index.html
index 6176ea2..937acd7 100644
--- a/docs/sphinx_docs/_build/html/notebooks/index.html
+++ b/docs/sphinx_docs/_build/html/notebooks/index.html
@@ -126,6 +126,7 @@
- Part V: Functions that use the Stack
- Part VI: Multiple Stack Effects
- Part VII: Typing Combinators
+- Conclusion
- Appendix: Joy in the Logical Paradigm
- Abstract Interpretation
- Junk
diff --git a/docs/sphinx_docs/_build/html/searchindex.js b/docs/sphinx_docs/_build/html/searchindex.js
index 3f8d770..4cb8576 100644
--- a/docs/sphinx_docs/_build/html/searchindex.js
+++ b/docs/sphinx_docs/_build/html/searchindex.js
@@ -1 +1 @@
-Search.setIndex({docnames:["index","joy","lib","library","notebooks/Categorical","notebooks/Developing","notebooks/Generator_Programs","notebooks/Intro","notebooks/Newton-Raphson","notebooks/NoUpdates","notebooks/Ordered_Binary_Trees","notebooks/Quadratic","notebooks/Recursion_Combinators","notebooks/Replacing","notebooks/Treestep","notebooks/Types","notebooks/Zipper","notebooks/index","parser","pretty","stack"],envversion:52,filenames:["index.rst","joy.rst","lib.rst","library.rst","notebooks/Categorical.rst","notebooks/Developing.rst","notebooks/Generator_Programs.rst","notebooks/Intro.rst","notebooks/Newton-Raphson.rst","notebooks/NoUpdates.rst","notebooks/Ordered_Binary_Trees.rst","notebooks/Quadratic.rst","notebooks/Recursion_Combinators.rst","notebooks/Replacing.rst","notebooks/Treestep.rst","notebooks/Types.rst","notebooks/Zipper.rst","notebooks/index.rst","parser.rst","pretty.rst","stack.rst"],objects:{"joy.joy":{joy:[1,1,1,""],repl:[1,1,1,""],run:[1,1,1,""]},"joy.library":{"void":[3,1,1,""],BinaryBuiltinWrapper:[3,1,1,""],DefinitionWrapper:[3,2,1,""],FunctionWrapper:[3,1,1,""],SimpleFunctionWrapper:[3,1,1,""],UnaryBuiltinWrapper:[3,1,1,""],add_aliases:[3,1,1,""],app1:[3,1,1,""],app2:[3,1,1,""],app3:[3,1,1,""],b:[3,1,1,""],branch:[3,1,1,""],choice:[3,1,1,""],clear:[3,1,1,""],cmp_:[3,1,1,""],concat_:[3,1,1,""],cond:[3,1,1,""],dip:[3,1,1,""],dipd:[3,1,1,""],dipdd:[3,1,1,""],divmod_:[3,1,1,""],drop:[3,1,1,""],dupdip:[3,1,1,""],floor:[3,1,1,""],genrec:[3,1,1,""],getitem:[3,1,1,""],help_:[3,1,1,""],i:[3,1,1,""],id_:[3,1,1,""],ifte:[3,1,1,""],infra:[3,1,1,""],initialize:[3,1,1,""],inscribe:[3,1,1,""],loop:[3,1,1,""],map_:[3,1,1,""],max_:[3,1,1,""],min_:[3,1,1,""],parse:[3,1,1,""],pm:[3,1,1,""],pred:[3,1,1,""],remove:[3,1,1,""],reverse:[3,1,1,""],select:[3,1,1,""],sharing:[3,1,1,""],shunt:[3,1,1,""],sort_:[3,1,1,""],sqrt:[3,1,1,""],step:[3,1,1,""],succ:[3,1,1,""],sum_:[3,1,1,""],swaack:[3,1,1,""],take:[3,1,1,""],times:[3,1,1,""],unique:[3,1,1,""],unstack:[3,1,1,""],warranty:[3,1,1,""],words:[3,1,1,""],x:[3,1,1,""],zip_:[3,1,1,""]},"joy.library.DefinitionWrapper":{add_def:[3,3,1,""],add_definitions:[3,3,1,""],parse_definition:[3,3,1,""]},"joy.parser":{ParseError:[18,4,1,""],Symbol:[18,2,1,""],text_to_expression:[18,1,1,""]},"joy.utils":{generated_library:[3,0,0,"-"],pretty_print:[19,0,0,"-"],stack:[20,0,0,"-"]},"joy.utils.generated_library":{ccons:[3,1,1,""],cons:[3,1,1,""],dup:[3,1,1,""],dupd:[3,1,1,""],dupdd:[3,1,1,""],first:[3,1,1,""],first_two:[3,1,1,""],fourth:[3,1,1,""],over:[3,1,1,""],pop:[3,1,1,""],popd:[3,1,1,""],popdd:[3,1,1,""],popop:[3,1,1,""],popopd:[3,1,1,""],popopdd:[3,1,1,""],rest:[3,1,1,""],rolldown:[3,1,1,""],rollup:[3,1,1,""],rrest:[3,1,1,""],second:[3,1,1,""],stack:[3,1,1,""],stuncons:[3,1,1,""],stununcons:[3,1,1,""],swap:[3,1,1,""],swons:[3,1,1,""],third:[3,1,1,""],tuck:[3,1,1,""],uncons:[3,1,1,""],unswons:[3,1,1,""]},"joy.utils.pretty_print":{TracePrinter:[19,2,1,""]},"joy.utils.pretty_print.TracePrinter":{go:[19,5,1,""],viewer:[19,5,1,""]},"joy.utils.stack":{concat:[20,1,1,""],expression_to_string:[20,1,1,""],iter_stack:[20,1,1,""],list_to_stack:[20,1,1,""],pick:[20,1,1,""],stack_to_string:[20,1,1,""]},joy:{joy:[1,0,0,"-"],library:[3,0,0,"-"],parser:[18,0,0,"-"]}},objnames:{"0":["py","module","Python module"],"1":["py","function","Python function"],"2":["py","class","Python class"],"3":["py","classmethod","Python class method"],"4":["py","exception","Python exception"],"5":["py","method","Python method"]},objtypes:{"0":"py:module","1":"py:function","2":"py:class","3":"py:classmethod","4":"py:exception","5":"py:method"},terms:{"0b11100111011011":5,"23rd":15,"4b4cb6ff86e5":[],"5bkei":10,"5eb7ac5ad2c2":15,"7fde90b4e88f":15,"\u03b5":8,"abstract":[7,10,17],"boolean":[2,3,7,10],"break":[7,15],"byte":5,"case":[2,3,12,14,15,20],"class":[3,7,15,18,19,20],"default":[3,6,10,20],"export":[3,18],"final":[2,10,12],"float":[3,7,15,16,18],"function":[0,1,4,5,6,9,11,16,17,18,19,20],"g\u00e9rard":16,"import":[2,5,6,8,10,11,12,13,14,15,16],"int":[6,7,12,15,16,18,20],"long":[10,17],"new":[2,3,6,7,9,12,13,15],"p\u00f6ial":17,"p\u00f6ial06typingtool":15,"public":9,"return":[1,3,5,7,10,12,13,14,15,18,19,20],"static":[2,9],"super":15,"switch":[2,15],"throw":10,"true":[2,3,5,12,15],"try":[6,8,11,12,14,15],"void":[0,3],"while":[3,7,10,15,18,20],Adding:[7,13,17],And:[5,6,8,10,12,15,16,20],But:[0,4,5,6,7,10,13,15],CPS:7,FNs:15,For:[2,3,10,12,13,15,17,20],Has:3,Its:3,One:[2,7,15,17],TOS:[2,3],That:[5,10],The:[0,1,2,3,4,6,8,9,11,15,16,17,18,20],Then:[2,3,10,11,12,15],There:[11,12,14,15,20],These:[15,17,20],Use:[3,8,12],Using:[0,8,10,17],With:[8,12,15,17],_1000:15,__add__:15,__class__:15,__eq__:15,__ge__:15,__hash__:15,__init__:15,__main__:15,__name__:15,__radd__:15,__repr__:15,__str__:19,_names_for:15,_to_str:15,_tree_add_:10,_tree_add_e:10,_tree_add_p:10,_tree_add_r:10,_tree_add_t:10,_tree_delete_:10,_tree_delete_clear_stuff:10,_tree_delete_del:10,_tree_delete_r0:10,_tree_delete_r1:10,_tree_delete_rightmost:10,_tree_delete_w:10,_tree_get_:10,_tree_get_p:10,_tree_get_r:10,_tree_get_t:10,_tree_iter_order_curr:10,_tree_iter_order_left:10,_tree_iter_order_r:10,_tree_iter_order_right:10,_tree_t:10,_treestep_0:14,_treestep_1:14,_uniqu:15,_within_b:8,_within_p:8,_within_r:8,a10001:15,a10002:15,a10003:15,a10004:15,a1001:[],abbrevi:14,abil:15,abl:15,about:[0,7,10,15,16,20],abov:[0,5,8,10,12,15],abs:8,absolut:7,accept:[1,2,3,5,6,7,10,11,13,14,15,16],accordingli:10,accumul:5,action:[7,13,15,16],actual:[2,5,7,10,15],adapt:17,add:[3,5,6,7,13,15,19],add_alias:3,add_def:3,add_definit:[3,10,14],added:[4,10],adding:[9,15],addit:[0,2,3,5,7,12,13,14],address:17,adjust:10,after:[5,6,7,12],afterward:7,again:[2,3,5,7,10,12,15],aggreg:16,ahead:15,aka:[7,16],albrecht:0,algorithm:[7,15],alia:3,alias:[3,7],align:[7,19],all:[3,5,6,7,10,12,13,14,15,19],alloc:15,allow:[9,10],almost:10,along:[7,12,15],alphabet:3,alreadi:[8,13,15,16],also:[0,5,7,10,15,20],alter:15,altern:[4,15],although:[4,10,15],altogeth:6,alwai:[5,9,12],amaz:15,among:15,amort:10,analysi:[4,17],anamorph:[7,17],ani:[4,5,7,9,10,15,16,18],annual:7,anonym:10,anoth:[10,15,20],anyhow:15,anyjoytyp:15,anymor:15,anystarjoytyp:15,anyth:[2,3,7,15],api:9,app1:3,app2:[3,7,11,12,13],app3:3,app:7,appear:[2,4,5,10],append:15,appendix:17,appli:[2,3,5,6,10,12,15],applic:6,approach:5,approxim:17,archiv:0,aren:16,arg:[2,3],argument:[2,3,7,8,11,12,17,19,20],arithmet:2,ariti:2,around:[5,15,20],arrang:14,arriv:[6,14],articl:[0,4,6,12],ask:[4,6,15],aspect:0,assert:15,assign:20,associ:10,assum:8,astar:15,asterisk:14,asterix:15,attack:7,attempt:[0,1],attribut:3,attributeerror:15,author:15,auto:0,automat:[4,15],auxiliari:14,avail:[0,15],averag:[7,13],avoid:10,awai:10,awar:2,awkward:[10,12],azur:17,back:[10,15],backward:[9,10,11,14],bag:7,banana:12,barb:12,base:[0,2,3,9,12,14,15],basic:[1,2,3,7,10],becaus:[2,3,7,10,14,15,16,20],becom:[10,14,20],becuas:15,been:[8,9,10,15,16],befor:[6,7,10],begin:[10,14],behavior:[9,14],behaviour:[0,1,15],being:0,below:[2,3,5,6,10,15,16],bespok:7,best:0,better:[5,10,12],between:[0,5],beyond:6,biannual:7,binari:[0,6,7,17],binary_search_tre:10,binarybuiltinwrapp:3,bind:7,bingo:16,bit:[5,6,10,15],block:5,bodi:[2,7,10],body_text:3,booktitl:15,bool:12,borrow:[7,15],both:[2,5,7,11,12,13,15,20],bottom:6,bracket:[7,15,18],branch:[3,5,6,12,15],branch_fals:15,branch_tru:15,breakpoint:7,bring:[5,7,15],bruijn:15,brzozowski:15,btree:[10,14],buck:10,bug:[0,7],build:[6,7,11,12,15,16,20],built:[11,15],bundl:[2,3,12],burgeon:7,calculu:4,call:[2,7,9,10,12,15,19,20],caller:10,can:[0,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,20],cannot:15,captur:7,card:7,care:[5,20],carefulli:16,carri:[6,10],cartesian:4,catamorph:17,categor:[0,17],categori:4,ccc:4,ccon:[3,10,15],cell:[12,15],certain:[7,20],certainli:10,chain:[3,15],chang:[2,9,10,15,16],charact:16,chat:7,chatter:[0,15],check:[6,8,15],child:14,choic:[3,12],choos:9,chop:11,cinf:10,circuit:4,cite_not:10,classmethod:3,claus:[3,15],clean:15,clear:[3,5,7],clear_stuff:10,cleav:[7,11,13],close:[0,1,4],clunki:[5,15],cmp:[3,14,17],cmp_:3,code:[0,1,4,11,12,15,17],codireco:[6,8],collaps:12,collect:[4,6,7,15],combin:[0,3,5,6,7,8,11,14,16,17],combinatorjoytyp:15,combo:15,come:[7,10,15],command:[7,10,15],common:[2,5],compar:[3,4,15],comparison:[0,10],compel:4,compil:[2,4,7,10,13,17],complet:[4,15],complex:[3,15,16],complic:15,composit:15,compostit:15,compound:10,comput:[2,4,5,7,11,15],con:[3,5,6,7,8,10,11,12,14,16,20],conal:4,concat:[3,6,7,14,20],concat_:3,concaten:0,concatin:[0,3,20],conclus:17,concurr:2,cond:[3,10],condit:[3,7],confer:15,conflict:[10,15],conjectur:15,consecut:17,consid:[5,6,10,12,14,15,16],consist:[2,6,7,14],constant:10,constitu:12,constraint:15,construct:15,consum:15,contain:[0,2,3,6,7,12,15],content:15,context:2,conting:10,continu:[0,12,15,16],control:7,conveni:[4,15],convers:15,convert:[12,13,14,15,18,20],cool:10,copi:[2,3,5,10,12,14,17],copyright:7,correct:15,correspond:4,could:[2,4,5,7,9,10,15,16],count:[3,15],counter:[5,15],coupl:14,cours:[5,10,15],cover:15,crack:10,crap:15,crash:10,creat:[0,2,3,5,8,10,15],creativ:15,crude:[10,15,18],currect:[],current:[2,3,7,12,14,15,16,19],custom:9,cycl:[5,6],cython:7,dai:7,data:[2,3,12],datastructur:[0,2,12,15,17,18,20],datatyp:20,ddee30dbb1a6:15,ddididi:16,deal:[0,10],dealt:15,decid:10,declar:15,decor:3,decoupl:12,decrement:3,deduc:[5,15],deeper:0,deepli:4,def:[3,7,12,13,15,20],defaultdict:15,defi:3,defin:[2,3,4,5,6,7,8,9,11,12,13,15,16,17],definit:[2,3,5,6,7,9,10,12,14,15,17],definitionwrapp:[3,10,12,14],deleg:7,delet:17,deliber:15,demonstr:4,depend:[3,10,12],deposit:14,depth:15,dequot:12,der:10,deriv:[2,3,5,7,8,10,15,17],describ:[3,4,10,12,14,15,18],descript:[5,7],descriptor:15,design:[2,3,10,17],desir:[7,14],destruct:10,detail:[7,10,15],detect:[6,10,12,15],determin:17,develop:[0,6,7,15,17],diagram:5,dialect:1,dict:[1,3,15],dictionari:[0,1,3,7,15,17],differ:[0,4,5,8,10,11,12,20],differenti:4,difficult:15,dig:[10,16],digit:5,dinfrirst:7,dip:[3,5,6,7,8,10,11,12,13,14,15,17],dip_a:15,dip_t:15,dipd:[3,6,7,10,11,12,15,16],dipdd:[3,10,15],direco:17,direct:7,directli:[5,14,15,20],disappear:[2,15],discard:[3,6,8,10,12],disciplin:10,disenstacken:7,disk:7,displac:2,displai:15,distiguish:15,ditch:10,div:[3,7],dive:14,divis:10,divmod:3,divmod_:[3,15],doc:[2,3,7,15],document:[17,18,20],doe:[0,1,4,6,7,13,17,19],doesn:[5,9,10,14,15,20],doing:[4,5,7,15,16],domain:[4,15],don:[5,7,10,15],done:[2,5,7,9,15],door:7,dot:19,doubl:[5,7,15],down:[2,8,12,15,16],down_to_zero:7,dozen:7,draft:[4,9],dream:7,drive:[6,8],driven:5,driver:6,drop:[3,10],dudipd:7,due:15,dup:[3,5,6,7,8,10,11,12,16,20],dupd:[3,15],dupdd:3,dupdip:[3,5,10,11,12,15],duplic:[3,10,12],durat:2,dure:[2,12],each:[2,3,4,5,7,12,13,14,15,19],easi:[0,10,14,15,16],easier:[3,10],easili:4,edit:17,effect:[2,3,7,16,17],effici:[6,13,16],either:[1,2,3,10,12,15],elabor:15,eleg:[7,10,15],element:2,elif:15,elimin:15,elliott:4,els:[2,3,12,15],else_:15,embed:[4,10,16],emit:15,empti:[3,7,14,15,20],encapsul:7,enclos:7,encod:6,encount:15,end:[5,10,12,14,15,20],endless:6,enforc:[2,7],engend:7,enorm:15,enough:[7,12,15,19],enstacken:[6,7,15],enter:7,entir:20,entri:[3,16,19],enumer:15,epsilon:8,equal:[5,14,20],equat:[7,8],ergo:10,err:10,error:[7,18],essai:0,establish:15,etc:[3,14,15,16,18],euler:17,euro:15,eval:[0,15],evalu:[1,2,3,7,8,10,11,12,13,14,15],event:15,eventu:15,everi:[6,15],everyth:[3,10,11,15],evolv:9,examin:12,exampl:[0,3,5,15,17,18,20],exce:6,except:[7,10,15,18],execut:[0,1,2,3,7,12,13,14,15,16,20],exend:15,exercis:10,exist:[4,10,15],expand:10,expect:[2,3,14,15,20],experi:[7,14],explain:15,explan:7,explor:7,express:[0,1,2,3,4,10,12,13,15,16,19,20],expression_to_str:20,extend:15,extra:[5,6],extract:[10,11,17],extrem:7,extrememli:7,f1001:[],f_g:15,f_in:15,f_out:15,f_python:15,facet:0,facil:7,fact:18,factor:[2,5,7,10,15],factori:17,fail:[2,3,10,18],fairli:15,fale:[],fals:[2,3,5,12,15],far:[8,10,12,15],fascin:0,fear:[10,15],few:[5,7,8,11],fewer:[3,7],fg_in:15,fg_out:15,fib:6,fib_gen:6,fibonacci:17,figur:[2,3,10,12],filter:10,fin:5,find:[2,3,5,6,14,15,17],finder:8,fine:[0,5,10,15],first:[3,6,7,8,10,11,12,13,14,16,17],first_two:[3,10],fit:[5,7],five:[5,7,17],fix:[2,3,12,15],fixm:[],flag:15,flatten:[7,14,15],flexibl:17,floatjoytyp:15,floatstarjoytyp:15,floor:3,floordiv:5,flow:7,follow:[0,2,3,7,9,12,14,15,16],foo:[7,9,10,15],foo_ii:9,form:[2,3,4,5,6,12,14,15,20],forman:7,format:[15,17,19],formula:[0,5,17],forth:[7,15],forum:0,forward:15,found:7,foundat:15,four:[2,3,5,6,7,10,17],fourteen:5,fourth:[2,3,10,12],fractal:7,fraction0:7,fraction:[2,7],frame:12,framework:7,free:[4,7,10],freeli:2,from:[0,1,2,3,5,6,7,8,10,11,12,13,14,15,16,17,20],from_iter:15,front:[2,3,12],full:5,fulli:15,fun:17,func:15,functionjoytyp:15,functionwrapp:3,funtion:10,further:[8,15,17],g_in:15,g_out:15,garbag:7,gari:10,gcd:7,gener:[0,2,4,12,15,17,20],generated_librari:3,genrec:[3,7,10,12,14],geometr:5,get:[2,4,5,6,7,11,12,15,17],getitem:3,getrecursionlimit:20,getsourc:7,ghc:4,give:[4,5,10,12,14,15,20],given:[2,3,5,6,8,10,12,15,16,17],global:15,glue:7,going:[10,11,14,15,16],good:[5,10],grab:[3,15],grammar:18,grand:7,great:[0,7,15,17],greater:20,grok:15,group:0,gsra:8,guard:10,had:[5,15,16],haiku:7,half:[5,15,16],hand:[7,13,15,17],handi:[8,15],handl:[10,15,20],happen:[7,15],hard:[15,16],hardwar:4,has:[0,2,6,7,8,9,10,12,15,16,20],hash:15,haskel:4,have:[2,3,5,6,7,8,9,12,13,15,16,17,20],haven:15,head:20,help:[7,10,12,15],help_:3,helper:3,herd:7,here:[5,6,10,14,15,16],hide:10,hierarchi:15,higher:[7,10],highli:7,histori:[15,19],hmm:10,hoist:3,hold:[5,15],hood:10,hope:[0,5,7,15,17],hopefulli:12,host:17,how:[0,4,8,10,12,15,16,17],howev:[12,13,15],html:[2,3,6,11,12,17],http:10,huet:16,huge:10,hugh:[8,14],human:7,hybrid:15,hylomorph:17,hypothet:2,id_:3,idea:[4,5,7,15],ident:[3,12,15],if_not_empti:10,ift:[3,10,12,14,15],ignor:[3,10,15],iii:17,illustr:12,imagin:16,imap:15,imit:14,immedi:12,immut:[7,10],imper:12,implement:[0,1,2,3,4,7,9,10,12,13,17],impli:15,implicit:7,includ:[4,10,14,15],inclus:5,incom:20,incompat:9,incorpor:11,increas:5,increment:[3,4,5,9],index:[0,7,15,20],indexerror:20,indic:[14,15],ineffici:15,infer:[0,17],inform:[3,15],infra:[3,6,7,10,11,13,14,15,17],infrastructur:3,initi:[2,3,7,8,10],inlin:10,inner:15,inproceed:15,input:[1,8,15],inscrib:3,insert:15,insight:12,inspect:7,instal:0,instanti:[4,19],instead:[5,6,10,12,15,16,20],integ:[2,3,7,12,14,15],integr:3,intend:[0,7],interact:[7,17],interest:[0,5,10,15,17],interlud:17,intermedi:12,intern:[0,15,19,20],interpret:[0,4,9,13,17,18,19],interrupt:7,interv:[4,5],intjoytyp:15,introduc:9,introduct:0,intstarjoytyp:15,intuit:15,invari:3,invent:15,involv:15,ipf:7,ipython:15,isinst:15,isn:[10,16],issubclass:15,item:[2,3,7,10,12,14,15,17,20],iter:[1,3,7,12,14,15,17,20],iter_stack:[13,15,20],iteritem:15,itertool:15,its:[0,2,3,4,5,7,10,12,14,15,20],itself:[0,2,7,10,15],j05cmp:[2,3,12],jaanu:15,job:17,john:[8,14],joi:[2,4,9,10,11,13],join:15,joypi:[7,16],june:15,junk:17,jupyt:17,just:[0,2,3,6,7,9,10,12,14,15,16],kav:15,keep:[10,11,15,16],kei:[14,17],kevin:0,key_n:10,keyerror:[10,15],kind:[2,4,7,10,12,14,15],kinda:15,kjs:15,kleen:[14,15],kleenestar:15,kleffner:15,know:[5,10,15],knowledg:15,known:4,l2s:15,l_kei:10,l_left:10,l_right:10,l_valu:10,label:15,lambda:[4,15],languag:[4,7,9,10,13,15],larg:15,larger:20,largest:3,last:[5,10,12,15],lastli:6,later:[7,14,15],law:[2,15],lazi:15,lazili:8,lcm:5,lead:[7,15],leaf:10,lean:7,learn:0,least:[2,5,12,15,20],least_fract:7,leav:5,left:[7,11,12,14,15,16,19,20],leftov:12,len:15,length:[3,5,20],lens:12,less:[5,6,7,12,15,20],let:[6,8,10,11,12,14,15,16],letter:15,level:[4,10],librari:[0,13],like:[2,3,5,7,14,15,17,18],limit:15,line:[3,7,10,11,19],linear:20,link:0,linux:0,list:[0,3,5,7,8,10,12,14,16,19],list_to_stack:[15,20],lit:15,liter:[1,10,14,15,16,18],literatur:15,littl:[6,10,15,17],live:17,lkei:14,load:[5,7],local:15,locat:2,locu:19,lof:15,log_2:10,logic:[0,5,17],longer:[10,15],look:[6,7,8,10,11,15],lookup:7,loop:[0,1,3,5],lose:15,lot:[7,10,16],love:5,low:4,lower:5,lowercas:15,lowest:10,machin:0,machineri:[10,15],macro:7,made:[0,7,15,16],magic:15,mai:[2,12,15],mail:0,main:[0,3,7,11,15,16],mainloop:9,maintain:16,major:9,make:[2,3,4,5,7,10,12,13,14,15,16,17],make_gener:8,manfr:[0,2,3,4,12],mani:[0,7,15],manipul:15,manner:11,map:[1,3,5,7,9,12,14,15],map_:3,marker:7,mask:[5,6],match:[0,1],materi:[0,15],math:[0,7,8,10,11,15],mathemat:7,matter:[5,8,10,14],max_:3,maximum:3,mayb:10,mean:[4,5,7,8,10,12,14,15,20],meant:[7,10,12,14],member:[2,3,12],mental:[7,15],mention:2,mercuri:0,mess:15,meta:[7,10,13],meta_compos:15,metal:15,method:[0,3,7,15,17,19],midpoint:5,might:[4,6,10,15],mike:10,million:6,min_:3,mind:15,minimum:3,minor:10,minu:3,mirror:0,miscellan:0,mix:[7,15],mod:3,mode:15,model:[4,7,15],modern:0,modif:6,modifi:[7,10,16],modul:[0,1,3,7,15,18],modulu:7,moment:15,month:7,more:[0,3,4,5,6,7,8,12,13,14,15,18,20],most:15,mostli:0,motiv:15,move:10,movement:2,much:[5,6,10,12,15],muck:10,mul:[7,11,16,19],multi:3,multipl:17,must:[2,3,5,9,12,14,15],myself:15,n10001:15,n10002:15,n10003:15,n1001:15,n1002:15,n1003:15,name:[1,3,7,9,10,12,15,16,17,18,20],natur:[5,6,10],navig:16,nearli:15,neat:10,neato:15,necessarili:15,need:[2,3,5,6,8,9,10,12,15],neg:[3,11],nest:[3,7,10,16],network:7,never:[9,12],new_def:15,new_f:15,new_fo:15,new_kei:10,new_valu:10,newton:[0,17],next:[5,14,15],nice:[0,12,20],niether:2,node:[14,17],node_kei:10,node_valu:10,non:[14,15],none:[1,3,15],nope:14,notat:[7,10],note:[2,5,8,10,12,15,20],notebook:[5,6,7,15,16,17],notebook_preambl:[2,5,6,8,10,11,12,13,14,15,16],noth:[2,10],notic:5,now:[5,6,7,12,13,14,15,17],nth:[3,20],nullari:[7,10],number:[1,2,3,5,6,8,20],numberjoytyp:15,numberstarjoytyp:15,numer:15,object:[15,18],observ:5,obviou:6,obvious:15,occur:10,odd:[5,6],off:[2,3,5,6,11,16],okai:[],old:[2,13],old_k:10,old_kei:10,old_valu:10,omit:[12,15],onc:[3,9,10],one:[2,3,5,6,10,12,14,15,19,20],ones:[6,15],onli:[2,3,5,10,12,15,16,20],onto:[1,2,3,7,12,20],open:[7,15],oper:[3,7,10,12,15,20],oppos:15,optim:10,option:[1,7,10,20],order:[0,2,3,7,12,15,17,20],org:[0,10],origin:[0,1,2,3,10,15,16],other:[0,2,3,4,7,10,12,14,15,20],otherwis:[3,5,6,10,14,15],our:[5,6,7,8,12,14,15],out:[2,3,4,5,6,7,8,10,11,12,15,16],outcom:14,output:[8,12,15],outsid:4,over:[3,4,5,6,7,8,10,11,14,15,17],overhaul:15,overview:15,own:[10,15],pace:15,pack:20,packag:[0,7],page:[0,10,15,20],pair:[2,3,5,6,10,15],palidrom:5,palindrom:5,pam:7,paper:[4,7,12,16],paradigm:17,parallel:2,paramet:[1,2,3,12,13,18,19,20],parameter:17,paramorph:12,parenthes:[10,20],pariti:6,pars:[0,3,7],parse_definit:3,parseerror:18,parser:[0,15],part:[2,3,8,12,14,17],partial:15,particular:16,pass:[0,10,15,19],path:17,pattern:[5,14,17],pe1:[5,6],pe2:6,pearl:16,pend:[3,7,12,16,19],peopl:17,per:[7,14],perform:15,perhap:6,period:7,permit:[15,20],permut:15,persist:10,phase:2,pick:[5,6,20],pickl:7,pictur:10,piec:12,pip:0,place:[3,5,7,15],plai:0,plu:3,plug:[6,12,14],point:[4,7,10,12],pointless:2,pop:[3,5,6,7,10,12,13,14,20],popd:[3,7,8,10,13,15],popdd:[3,6,11,15],popop:[3,5,6,7,8,10,14,15],popopd:3,popopdd:3,posit:[3,5,7,12],possibilit:10,possibl:[10,14,15,17],post:7,poswrd:15,power:7,pragmat:5,preambl:8,precis:[0,1],pred:[3,15],predic:[2,3,6,12],prefix:[15,19],present:15,preserv:[4,14],pretti:[8,10,11,14,15,19,20],pretty_print:0,previou:7,primari:15,prime:8,primit:[2,3,15,17],primrec:[3,6,7,8,12],principl:15,print:[0,1,2,3,15,19,20],probabl:[6,7,10,15],problem:[7,15,17],proc_curr:10,proc_left:10,proc_right:10,proce:5,process:[7,14,15,19],produc:[5,10,12,14,15],product:[6,7,15],program:[0,2,3,6,7,8,10,12,15,16],programm:15,progress:15,project:17,prompt:7,proper:[2,3,12],properti:0,provabl:15,proven:15,provid:[0,3,4,7,15],pun:[0,7],punctuat:15,pure:0,puriti:7,purpos:7,push:[2,3,7,12,16,20],pushback:7,put:[1,2,6,7,15,17,20],pypi:0,python:[0,2,3,10,12,16,17,18,20],quadrat:[0,17],queri:[10,14],query_kei:14,queu:12,quit:[0,1,14],quot:[0,3,6,7,10,11,12,14,15,16,19],quotat:[2,3,12],quotient:3,r_kei:10,r_left:10,r_right:10,r_valu:10,rais:[10,15,18,20],rang:[7,15],range_revers:12,range_to_zero:7,ranger:12,ranger_revers:12,raphson:8,rather:[5,7,12,14],ratio:7,reach:[5,6,12],read:[0,1,5,6,10,15,16],readabl:13,reader:10,readi:15,real:10,realiz:[4,10],rearrang:[2,10,15],reason:[5,7,15],rebuild:[14,16],rec1:[2,3,12],rec2:[2,3,12],recent:15,recogn:18,record:[7,19],recur:[12,15],recurs:[0,2,3,6,7,8,15,17,20],recus:7,recycl:15,redefin:17,redistribut:[3,7],reduc:[2,15],redund:20,refactor:[7,9],refer:[0,2],regist:2,regular:[15,18],reimplement:17,relat:15,releas:9,remain:[2,7,9],remaind:[3,8],remind:15,remov:[3,10,15,20],render:17,repeat:5,repeatedli:5,repl:[0,1],replac:[0,2,3,6,11,12,14,15,16,17,20],repositori:0,repr:15,repres:[2,7,10,18,19],represent:20,reprod:6,repurpos:15,requir:[15,20],res:15,research:15,resembl:7,respect:5,rest:[3,5,6,7,10,12,16,17,20],rest_two:10,restat:15,restor:2,restrict:15,result:[1,2,3,5,10,11,12,14,15,16],resum:7,retain:15,retir:2,retri:7,reus:[10,15],revers:[3,5,6,12,15,16,20],revisit:15,rewrit:[3,7,15],rewritten:7,rich:15,rid:10,right:[6,7,11,14,15,17,19,20],rightest:10,rightmost:5,rkei:14,rob:15,robot:15,roll:[3,8,10,14],roll_dn:15,roll_down:[],roll_up:[],rolldown:[3,15],rollup:[3,15],root:[3,8,11],round:15,rrest:[3,15],rule:17,run:[0,1,3,5,7,8,10,11,12,14,16],runtimeerror:20,s1000:[],s1002:[],s23:[],sai:[6,10,11,14,15],same:[2,4,5,10,15,20],sandwich:[2,3,12],save:[2,5,7],scan:3,scanner:[7,18],scenario:16,scope:[6,10],search:[0,10],sec:15,second:[3,7,10,12,14,20],section:12,see:[0,6,7,8,9,11,12,13,15,16,19],seem:[0,5,7,14,15],seen:[15,16],select:3,self:15,semant:[2,3,7,9,10,15],semi:7,send:7,sens:[0,2,5,15,16],separ:[7,15],seq:15,sequenc:[0,1,2,3,5,7,10,12,13,16,17,18],sequence_to_stack:15,seri:[5,6,10,16],ses:15,set:[2,3,12,15,17],seven:[5,6],sever:[0,4,7,12],share:[3,7],shelf:2,shift:[5,6],shorter:17,shorthand:10,should:[2,3,5,10,12,15],shouldn:7,show:[4,16],shunt:[3,16],side:[10,15],signifi:[7,10],similar:[10,14,15],simon:7,simpl:[7,12,15,20],simplefunctionwrapp:[3,13,15],simpler:14,simplest:[15,17],simpli:4,simplifi:[5,10,16],sinc:[2,5,10,15],singl:[3,6,7,13,15,18],situ:10,situat:10,six:[5,6,7],sixti:[5,6],size:[7,17],skeptic:7,skip:15,slight:8,slightli:[10,12,15],smallest:3,smart:[10,15],softwar:[7,15],solei:2,solut:[5,6],solvabl:7,some:[2,3,6,7,10,12,14,15,17,20],somehow:[10,15],someth:[2,9,10,15],sometim:10,somewher:[10,17],sort:[3,10,15],sort_:3,sorta:15,sourc:[0,1,3,15,17,18,19,20],space:[5,19],span:5,spawn:15,special:[6,10,15,17],specif:[0,4],specifi:[10,15],speed:13,spell:14,sphinx:[17,20],spirit:[0,1,14],split:15,sqr:[7,8,11,16],sqrt:[3,8,15],squar:[3,8,15,18],stack:[0,1,3,5,6,8,10,11,12,13,14,16,17,18,19],stack_concat:15,stack_effect:15,stack_effect_com:15,stack_to_str:20,stacki:15,stackjoytyp:15,stackstarjoytyp:15,stage:14,stai:[0,1],stand:4,standard:[7,10],star:[14,15],stare:10,start:[5,6,7,8,10,12,14,15],state:7,statement:3,step:[3,5,7,10,13,15,16,17],still:[10,15],stop:10,storag:[5,10],store:[5,12],stori:12,str:[1,15,18,19,20],straightforward:[1,6,8,15,17],stream:5,stretch:10,string:[1,2,3,7,15,16,18,19,20],strip:15,structur:[7,14,15,16,17,20],stuff:[10,15],stuncon:3,stununcon:3,style:[0,4,15],sub:9,subclass:7,subject:16,subset:15,substitut:[10,15],subtract:5,subtyp:17,succ:[3,15],succe:15,success:8,suffic:15,suffici:10,suffix:15,suggest:[4,10],suitabl:[3,4,5],sum:[3,6,7,11,12,13,14,15],sum_:[3,15],summand:5,sumtre:14,suppli:[10,18],support:[7,15,19,20],suspect:2,swaack:[3,11,13,15,16],swap:[3,5,6,7,8,10,12,13,14,16],swarm:15,swon:[3,6,7,12,14,15,16],swoncat:[6,7,8,12,14],swuncon:12,symbol:[2,3,15,16,17,18],symboljoytyp:15,symmetr:[5,10],syntact:7,syntax:[7,20],sys:20,system:[7,10,15],tabl:15,tag:15,tail:[10,15,17,20],take:[3,5,7,8,10,12,15,20],talk:[7,10,15,20],target:16,tast:4,tbd:7,tear:12,technic:2,techniqu:[4,16],technolog:2,temporari:16,ten:5,term:[1,2,7,8,12,15,17,18,20],termin:[2,3,12],ternari:7,test:[2,3,12],text:[0,1,3,15],text_to_express:[7,15,18],textual:7,than:[0,3,5,6,7,8,12,14,15,20],thei:[2,5,6,7,10,12,15,16,18,20],them:[2,3,5,6,10,12,15,16,17],themselv:15,theori:[2,3,12],therefor:[6,15],thi:[0,1,2,3,4,5,6,7,8,11,12,14,15,16,17,18,19,20],thing:[2,6,10,12,15,16,18,20],think:[2,5,7,10,12,14,15],third:[3,6,7,10],thirti:5,those:[2,3,10,12,15,17],though:5,thought:7,thousand:5,thread:2,three:[2,3,5,7,10,11,14,15,17],through:[1,5,7,14,15,16,20],thun:[2,3,4,9,12],thunder:7,time:[3,5,7,8,10,12,15,16],titl:15,to_set:10,todai:7,todo:[7,18],togeth:[6,7,15,17],token:18,toler:17,too:[12,15],tool:[7,15],tooo:15,top:[2,3,7,12,15,19,20],total:5,tower:15,trace:[0,7,11,12,16,17,20],traceback:15,traceprint:19,track:[11,15,16],tracker:0,transform:4,translat:[4,11,15],trash:15,travers:[0,17],treasur:0,treat:[0,2,3,12,15,17],treatment:6,tree:[0,7,17],treegrind:17,treestep:[0,17],tri:5,triangular_numb:12,trick:[5,15],tricki:15,trobe:0,trove:0,truli:15,trust:15,truthi:[3,7],tuck:[3,7,15],tupl:[3,7,15,20],ture:15,turn:[2,3,15],twice:[10,12],two:[2,3,5,7,8,10,11,12,14,15,16,17,20],type:[0,1,4,7,10,12,17,18,19,20],typeerror:15,typeless:15,typic:[2,3,11,12],unari:7,unarybuiltinwrapp:3,unbalanc:[10,18],unchang:10,uncompil:15,uncon:[3,6,7,10,12,14,16],under:[2,3,7,10],underli:15,underscor:15,understand:[0,10,15],undistinguish:10,undocu:7,unend:15,unfinish:15,unfortun:20,unif:15,uniqu:[3,10,15],unit:[7,12],univers:[0,7,15],unnecessari:17,unnecesssari:15,unpack:[2,3,10,20],unpair:5,unquot:[7,14],unstack:[3,15],unswon:3,untangl:12,until:6,unus:5,unusu:10,updat:[0,17],usag:7,use:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,20],used:[3,4,7,10,12,16,18,20],useful:[0,15],user:14,uses:[2,5,12],using:[3,6,10,11,12,14,16],usual:[0,2,12],util:[0,3,13,15],valid:15,valu:[0,2,3,5,7,8,11,12,13,14,15,17,20],value_n:10,valueerror:[15,20],variabl:[15,17],variant:10,variat:[12,17],varieti:[4,7],variou:0,vener:20,verbos:4,veri:[0,1,4,7,10,20],verifi:15,versa:[2,15],version:[0,1,2,6,9,14,16,17],via:7,vice:[2,15],view:[10,17],viewer:[1,7,9,19],vii:17,von:[0,2,3,4,12],wai:[0,2,3,4,5,7,12,13,15],wait:[],want:[2,5,6,8,10,12,15],warranti:[3,7],wash:7,wast:7,web:20,websit:[0,5],welcom:7,well:[0,4,7,8,10,15,18],were:[7,15,16],what:[2,3,4,7,10,12,14,15,19],whatev:[2,3,12,14,20],when:[5,6,7,10,12,15,16,18,20],where:[2,3,7,10,12,15,17,20],whether:12,which:[0,1,3,5,7,8,10,12,14,15,16,20],whole:[2,3,5,12,14,15],whose:6,why:[8,14],wiki:10,wikipedia:[0,10,16],wildli:7,wind:7,wire:12,within:[7,10,13,17],without:[2,7,10,11,15],won:[10,15,20],word:[0,3,5,7,12,16],work:[0,3,5,6,7,8,10,11,12,14,15,16,20],worth:5,would:[2,5,6,7,8,10,12,15,16,20],wrap:[3,7],wrapper:15,write:[4,8,10,12,14,15,16,17,20],written:[0,1,8,10,13,15,20],wrong:2,wrote:15,xrang:15,yang:15,year:[7,15],yet:[10,15,16],yield:[2,3,12,15,20],yin:17,you:[0,2,3,5,6,7,9,10,11,12,13,14,15,16,19,20],your:[2,3,7,12,15],yourself:[7,10],zero:[3,10,12,14,15,18,20],zip:[5,15],zip_:3,zipper:[0,17],zstr:16},titles:["Thun 0.2.0 Documentation","Joy Interpreter","Functions Grouped by, er, Function with Examples","Function Reference","Categorical Programming","Developing a Program in Joy","Using x to Generate Values","Thun: Joy in Python","Newton\u2019s method","No Updates","Treating Trees I: Ordered Binary Trees","Quadratic formula","Recursive Combinators","Replacing Functions in the Dictionary","Treating Trees II: treestep","Type Inference","Traversing Datastructures with Zippers","Essays about Programming in Joy","Parsing Text into Joy Expressions","Tracing Joy Execution","Stack or Quote or Sequence or List\u2026"],titleterms:{"abstract":15,"case":[8,10],"function":[2,3,7,8,10,12,13,14,15],"long":13,"new":10,"p\u00f6ial":15,"void":2,"while":2,Adding:10,One:[6,10],The:[5,7,10,12,14],There:7,Using:6,With:14,about:17,add:[2,10],adding:10,address:16,altern:14,ana:12,analysi:5,anamorph:[2,12],app1:2,app2:2,app3:2,appendix:[10,12,15],approxim:8,argument:15,auto:3,averag:2,base:[8,10],binari:[2,10,14],both:10,branch:[2,10],can:10,cata:12,catamorph:12,categor:4,chatter:2,child:10,choic:2,clear:2,cleav:2,cmp:10,code:[7,10],combin:[2,10,12,15],comment:15,compar:10,comparison:2,compil:[6,15],compile_:15,compos:15,comput:8,con:[2,15],concat:[2,15],conclus:12,consecut:8,continu:7,current:10,datastructur:[7,10,16],deal:15,defin:[10,14],definit:11,delabel:15,delet:10,deriv:[11,12,14],design:12,determin:16,develop:5,dialect:0,dictionari:13,dip:[2,16],dipd:2,dipdd:2,direco:6,disenstacken:2,distinguish:15,div:2,doc_from_stack_effect:15,document:0,doe:10,down_to_zero:2,drop:2,dup:[2,15],dupd:2,dupdip:2,effect:15,els:10,empti:10,enstacken:2,equal:10,essai:17,euler:[5,6],eval:7,even:6,exampl:[2,7,10,12,14],execut:19,express:[7,18],extract:14,factori:12,fibonacci:6,filter:5,find:[8,10,12],first:[2,5,15],five:6,flatten:2,flexibl:14,floordiv:2,formula:11,found:10,four:12,fun:12,further:5,gcd:2,gener:[3,5,6,8],genrec:2,get:[10,14],getitem:2,given:14,greater:10,group:2,have:[10,14],help:2,highest:10,host:0,how:[5,6],hylo:12,hylomorph:12,identifi:15,ift:2,iii:15,implement:15,indic:0,infer:15,inferenc:15,inform:0,infra:[2,16],integ:5,interest:6,interlud:10,intern:18,interpret:[1,7,15],item:16,iter:[5,10],joi:[0,1,3,5,7,12,15,16,17,18,19,20],junk:15,just:5,kei:10,languag:0,least_fract:2,left:10,less:10,let:5,librari:[3,7,15],like:10,list:[2,15,20],literari:7,littl:5,logic:[2,15],loop:[2,7],lower:10,lshift:2,make:[6,8],mani:5,map:2,math:2,method:8,min:2,miscellan:2,mod:2,modifi:15,modulu:2,more:10,most:10,mul:[2,15],multipl:[5,6,15],must:10,name:11,neg:2,newton:8,next:8,node:10,non:10,now:10,nullari:2,number:[12,15],one:7,onli:7,order:[10,14],osdn:0,our:10,over:2,pack:5,pam:2,para:12,paradigm:15,parameter:[10,14],pars:[2,18],parser:[7,18],part:15,pass:7,path:16,pattern:12,per:10,pop:[2,15],popd:2,popop:2,pow:2,power:6,pred:2,predic:[5,8,10,14],pretty_print:19,primit:12,primrec:2,print:7,problem:[5,6],process:10,product:2,program:[4,5,11,14,17],project:[0,5,6],pure:7,put:[10,11,14],python:[7,13,15],quadrat:11,quick:0,quot:[2,20],rang:[2,5,12],range_to_zero:2,read:7,recur:[8,10],recurs:[10,12,14],redefin:[10,14],refactor:[5,10],refer:3,regular:7,reimplement:14,relabel:15,rem:2,remaind:2,remov:2,render:5,repl:7,replac:[10,13],repres:15,reset:6,rest:[2,15],revers:2,right:[10,16],rightmost:10,roll:[2,15],rolldown:2,rollup:2,rshift:2,rule:15,run:[2,6],second:[2,15],select:2,sequenc:[6,15,20],set:[8,10],shorter:13,should:7,shunt:2,simplest:5,size:[2,13],someth:[],sourc:10,special:12,sqr:[2,15],sqrt:[2,11],stack:[2,7,15,20],start:0,step:[2,12,14],straightforward:11,structur:10,style:7,sub:[2,10],subtyp:15,succ:2,sum:[2,5],swaack:2,swap:[2,15],swon:2,swoncat:2,symbol:[7,12],tabl:0,tail:12,take:2,term:[5,6,14],ternari:2,text:18,than:10,them:11,thi:10,third:[2,15],three:6,thun:[0,7],time:[2,6],togeth:[10,11,14],token:7,toler:8,trace:[13,19],traceprint:7,travers:[10,14,16],treat:[10,14],tree:[10,14,16],treegrind:14,treestep:14,triangular:12,truediv:2,truthi:2,tuck:2,two:6,type:15,unari:2,unbound:15,uncon:[2,15],unifi:15,unit:2,unnecessari:5,unquot:2,unstack:2,updat:[9,15],use:15,util:[19,20],valu:[6,10],variabl:11,variat:6,version:[5,10,13,15],view:7,vii:15,within:8,word:2,write:11,xor:2,yin:15,zero:6,zip:2,zipper:16}})
\ No newline at end of file
+Search.setIndex({docnames:["index","joy","lib","library","notebooks/Categorical","notebooks/Developing","notebooks/Generator_Programs","notebooks/Intro","notebooks/Newton-Raphson","notebooks/NoUpdates","notebooks/Ordered_Binary_Trees","notebooks/Quadratic","notebooks/Recursion_Combinators","notebooks/Replacing","notebooks/Treestep","notebooks/Types","notebooks/Zipper","notebooks/index","parser","pretty","stack"],envversion:52,filenames:["index.rst","joy.rst","lib.rst","library.rst","notebooks/Categorical.rst","notebooks/Developing.rst","notebooks/Generator_Programs.rst","notebooks/Intro.rst","notebooks/Newton-Raphson.rst","notebooks/NoUpdates.rst","notebooks/Ordered_Binary_Trees.rst","notebooks/Quadratic.rst","notebooks/Recursion_Combinators.rst","notebooks/Replacing.rst","notebooks/Treestep.rst","notebooks/Types.rst","notebooks/Zipper.rst","notebooks/index.rst","parser.rst","pretty.rst","stack.rst"],objects:{"joy.joy":{joy:[1,1,1,""],repl:[1,1,1,""],run:[1,1,1,""]},"joy.library":{"void":[3,1,1,""],BinaryBuiltinWrapper:[3,1,1,""],DefinitionWrapper:[3,2,1,""],FunctionWrapper:[3,1,1,""],SimpleFunctionWrapper:[3,1,1,""],UnaryBuiltinWrapper:[3,1,1,""],add_aliases:[3,1,1,""],app1:[3,1,1,""],app2:[3,1,1,""],app3:[3,1,1,""],b:[3,1,1,""],branch:[3,1,1,""],choice:[3,1,1,""],clear:[3,1,1,""],cmp_:[3,1,1,""],concat_:[3,1,1,""],cond:[3,1,1,""],dip:[3,1,1,""],dipd:[3,1,1,""],dipdd:[3,1,1,""],divmod_:[3,1,1,""],drop:[3,1,1,""],dupdip:[3,1,1,""],floor:[3,1,1,""],genrec:[3,1,1,""],getitem:[3,1,1,""],help_:[3,1,1,""],i:[3,1,1,""],id_:[3,1,1,""],ifte:[3,1,1,""],infra:[3,1,1,""],initialize:[3,1,1,""],inscribe:[3,1,1,""],loop:[3,1,1,""],map_:[3,1,1,""],max_:[3,1,1,""],min_:[3,1,1,""],parse:[3,1,1,""],pm:[3,1,1,""],pred:[3,1,1,""],remove:[3,1,1,""],reverse:[3,1,1,""],select:[3,1,1,""],sharing:[3,1,1,""],shunt:[3,1,1,""],sort_:[3,1,1,""],sqrt:[3,1,1,""],step:[3,1,1,""],succ:[3,1,1,""],sum_:[3,1,1,""],swaack:[3,1,1,""],take:[3,1,1,""],times:[3,1,1,""],unique:[3,1,1,""],unstack:[3,1,1,""],warranty:[3,1,1,""],words:[3,1,1,""],x:[3,1,1,""],zip_:[3,1,1,""]},"joy.library.DefinitionWrapper":{add_def:[3,3,1,""],add_definitions:[3,3,1,""],parse_definition:[3,3,1,""]},"joy.parser":{ParseError:[18,4,1,""],Symbol:[18,2,1,""],text_to_expression:[18,1,1,""]},"joy.utils":{generated_library:[3,0,0,"-"],pretty_print:[19,0,0,"-"],stack:[20,0,0,"-"]},"joy.utils.generated_library":{ccons:[3,1,1,""],cons:[3,1,1,""],dup:[3,1,1,""],dupd:[3,1,1,""],dupdd:[3,1,1,""],first:[3,1,1,""],first_two:[3,1,1,""],fourth:[3,1,1,""],over:[3,1,1,""],pop:[3,1,1,""],popd:[3,1,1,""],popdd:[3,1,1,""],popop:[3,1,1,""],popopd:[3,1,1,""],popopdd:[3,1,1,""],rest:[3,1,1,""],rolldown:[3,1,1,""],rollup:[3,1,1,""],rrest:[3,1,1,""],second:[3,1,1,""],stack:[3,1,1,""],stuncons:[3,1,1,""],stununcons:[3,1,1,""],swap:[3,1,1,""],swons:[3,1,1,""],third:[3,1,1,""],tuck:[3,1,1,""],uncons:[3,1,1,""],unswons:[3,1,1,""]},"joy.utils.pretty_print":{TracePrinter:[19,2,1,""]},"joy.utils.pretty_print.TracePrinter":{go:[19,5,1,""],viewer:[19,5,1,""]},"joy.utils.stack":{concat:[20,1,1,""],expression_to_string:[20,1,1,""],iter_stack:[20,1,1,""],list_to_stack:[20,1,1,""],pick:[20,1,1,""],stack_to_string:[20,1,1,""]},joy:{joy:[1,0,0,"-"],library:[3,0,0,"-"],parser:[18,0,0,"-"]}},objnames:{"0":["py","module","Python module"],"1":["py","function","Python function"],"2":["py","class","Python class"],"3":["py","classmethod","Python class method"],"4":["py","exception","Python exception"],"5":["py","method","Python method"]},objtypes:{"0":"py:module","1":"py:function","2":"py:class","3":"py:classmethod","4":"py:exception","5":"py:method"},terms:{"0b11100111011011":5,"23rd":15,"4b4cb6ff86e5":[],"58a8e44e9cba":15,"5bkei":10,"5eb7ac5ad2c2":[],"7fde90b4e88f":[],"\u03b5":8,"abstract":[7,10,17],"boolean":[2,3,7,10],"break":[7,15],"byte":5,"case":[2,3,12,14,15,20],"class":[3,7,15,18,19,20],"default":[3,6,10,20],"export":[3,18],"final":[2,10,12],"float":[3,7,15,16,18],"function":[0,1,4,5,6,9,11,16,17,18,19,20],"g\u00e9rard":16,"import":[2,5,6,8,10,11,12,13,14,15,16],"int":[6,7,12,15,16,18,20],"long":[10,15,17],"new":[2,3,6,7,9,12,13,15],"p\u00f6ial":17,"p\u00f6ial06typingtool":15,"public":9,"return":[1,3,5,7,10,12,13,14,15,18,19,20],"static":[2,9],"super":15,"switch":[2,15],"throw":10,"true":[2,3,5,12,15],"try":[6,8,11,12,14,15],"void":[0,3],"while":[3,7,10,15,18,20],AND:15,Adding:[7,13,17],And:[5,6,8,10,12,15,16,20],But:[0,4,5,6,7,10,13,15],CPS:7,FNs:15,For:[2,3,10,12,13,15,17,20],Has:3,Its:3,Not:15,One:[2,7,15,17],TOS:[2,3],That:[5,10],The:[0,1,2,3,4,6,8,9,11,15,16,17,18,20],Then:[2,3,10,11,12,15],There:[11,12,14,15,20],These:[15,17,20],Use:[3,8,12],Using:[0,8,10,17],With:[8,12,15,17],_1000:15,__add__:15,__class__:15,__eq__:15,__ge__:15,__hash__:15,__init__:15,__main__:15,__name__:15,__radd__:15,__repr__:15,__str__:19,_ge:15,_names_for:15,_to_str:15,_tree_add_:10,_tree_add_e:10,_tree_add_p:10,_tree_add_r:10,_tree_add_t:10,_tree_delete_:10,_tree_delete_clear_stuff:10,_tree_delete_del:10,_tree_delete_r0:10,_tree_delete_r1:10,_tree_delete_rightmost:10,_tree_delete_w:10,_tree_get_:10,_tree_get_p:10,_tree_get_r:10,_tree_get_t:10,_tree_iter_order_curr:10,_tree_iter_order_left:10,_tree_iter_order_r:10,_tree_iter_order_right:10,_tree_t:10,_treestep_0:14,_treestep_1:14,_uniqu:15,_within_b:8,_within_p:8,_within_r:8,a10001:15,a10002:15,a10003:15,a10004:15,a1001:[],abbrevi:14,abil:15,abl:15,about:[0,7,10,15,16,20],abov:[0,5,8,10,12,15],abs:8,absolut:7,accept:[1,2,3,5,6,7,10,11,13,14,15,16],accordingli:10,accumul:5,action:[7,13,15,16],actual:[2,5,7,10,15],adapt:17,add:[3,5,6,7,13,15,19],add_alias:3,add_def:3,add_definit:[3,10,14],added:[4,10],adding:[9,15],addit:[0,2,3,5,7,12,13,14],address:17,adjust:10,after:[5,6,7,12],afterward:7,again:[2,3,5,7,10,12,15],aggreg:16,ahead:15,aka:[7,16],albrecht:0,algorithm:[7,15],alia:3,alias:[3,7],align:[7,19],all:[3,5,6,7,10,12,13,14,15,19],alloc:15,allow:[9,10],almost:10,along:[7,12,15],alphabet:3,alreadi:[8,13,15,16],also:[0,5,7,10,15,20],alter:15,altern:[4,15],although:[4,10],altogeth:6,alwai:[5,9,12],amaz:[],among:15,amort:10,analysi:[4,17],anamorph:[7,17],ani:[4,5,7,9,10,15,16,18],annual:7,anonym:10,anoth:[10,15,20],anyhow:[],anyjoytyp:15,anymor:15,anystarjoytyp:15,anyth:[2,3,7,15],apart:15,api:9,app1:3,app2:[3,7,11,12,13],app3:3,app:7,appear:[2,4,5,10],append:15,appendix:17,appli:[2,3,5,6,10,12,15],applic:6,approach:5,approxim:17,archiv:0,aren:16,arg:[2,3],argument:[2,3,7,8,11,12,17,19,20],arithmet:2,ariti:2,around:[5,15,20],arrang:14,arriv:[6,14],articl:[0,4,6,12],ask:[4,6,15],aspect:0,assert:15,assign:20,associ:10,assum:8,astar:15,asterisk:14,asterix:15,attack:7,attempt:[0,1],attribut:3,attributeerror:15,author:15,auto:[0,15],automat:[4,15],auxiliari:14,avail:[0,15],averag:[7,13],avoid:10,awai:10,awar:2,awkward:[10,12],azur:17,back:[10,15],backward:[9,10,11,14],bad:15,bag:7,banana:12,barb:12,base:[0,2,3,9,12,14,15],basic:[1,2,3,7,10,15],becaus:[2,3,7,10,14,15,16,20],becom:[10,14,20],becuas:15,been:[8,9,10,15,16],befor:[6,7,10],begin:[10,14],behavior:[9,14],behaviour:[0,1,15],being:0,below:[2,3,5,6,10,15,16],bespok:7,best:0,better:[5,10,12,15],between:[0,5],beyond:6,biannual:7,binari:[0,6,7,17],binary_search_tre:10,binarybuiltinwrapp:3,bind:7,bingo:16,bit:[5,6,10,15],block:5,bodi:[2,7,10],body_text:3,booktitl:15,bool:[12,15],borrow:[7,15],both:[2,5,7,11,12,13,15,20],bottom:6,bracket:[7,15,18],branch:[3,5,6,12,15],branch_fals:15,branch_tru:15,breakpoint:7,bring:[5,7,15],bruijn:15,brzozowski:15,btree:[10,14],buck:10,bug:[0,7],build:[6,7,11,12,16,20],built:[11,15],bundl:[2,3,12],burgeon:7,calculu:4,call:[2,7,9,10,12,15,19,20],caller:[10,15],can:[0,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,20],cannot:15,captur:7,card:7,care:[5,20],carefulli:16,carri:[6,10],cartesian:4,catamorph:17,categor:[0,17],categori:4,ccc:4,ccon:[3,10,15],cell:[12,15],certain:[7,20],certainli:10,chain:[3,15],chang:[2,9,10,15,16],charact:16,chat:7,chatter:[0,15],check:[6,8,15],checker:15,child:14,choic:[3,12],choos:9,chop:11,cinf:10,circuit:4,cite_not:10,classmethod:3,claus:[3,15],clean:15,clear:[3,5,7],clear_stuff:10,cleav:[7,11,13],close:[0,1,4,15],clunki:[5,15],cmp:[3,14,17],cmp_:3,code:[0,1,4,11,12,15,17],codireco:[6,8],collaps:12,collect:[4,6,7,15],combin:[0,3,5,6,7,8,11,14,16,17],combinatorjoytyp:15,combo:15,come:[7,10,15],command:[7,10,15],common:[2,5],compar:[3,4,15],comparison:[0,10],compel:4,compil:[2,4,7,10,13,17],complet:4,complex:[3,15,16],complic:15,composit:15,compostit:15,compound:10,comput:[2,4,5,7,11,15],con:[3,5,6,7,8,10,11,12,14,16,20],conal:4,concat:[3,6,7,14,20],concat_:3,concaten:0,concatin:[0,3,20],conclus:17,concurr:2,cond:[3,10],condit:[3,7],confer:15,conflict:[10,15],conjectur:15,consecut:17,consid:[5,6,10,12,14,15,16],consist:[2,6,7,14],constant:10,constitu:12,constraint:15,construct:15,consum:15,contain:[0,2,3,6,7,12],content:15,context:2,conting:10,continu:[0,12,15,16],control:7,conveni:[4,15],convers:15,convert:[12,13,14,15,18,20],cool:10,copi:[2,3,5,10,12,14,17],copyright:7,correct:[],correspond:4,could:[2,4,5,7,9,10,15,16],count:[3,15],counter:[5,15],coupl:14,cours:[5,10,15],cover:15,crack:10,crap:15,crash:10,creat:[0,2,3,5,8,10,15],creativ:15,crude:[10,15,18],crunchi:15,currect:[],current:[2,3,7,12,14,15,16,19],custom:9,cycl:[5,6],cython:7,dai:7,data:[2,3,12],datastructur:[0,2,12,15,17,18,20],datatyp:20,ddee30dbb1a6:[],ddididi:16,deal:[0,10],dealt:15,debugg:15,decid:10,declar:15,decor:3,decoupl:12,decrement:3,deduc:[5,15],deeper:0,deepli:4,def:[3,7,12,13,15,20],defaultdict:15,defi:3,defin:[2,3,4,5,6,7,8,9,11,12,13,15,16,17],definit:[2,3,5,6,7,9,10,12,14,15,17],definitionwrapp:[3,10,12,14],deleg:7,delet:17,deliber:15,demonstr:4,depend:[3,10,12],deposit:14,depth:[],dequot:12,der:10,deriv:[2,3,5,7,8,10,15,17],describ:[3,4,10,12,14,15,18],descript:[5,7],descriptor:15,design:[2,3,10,17],desir:[7,14],destruct:10,detail:[7,10,15],detect:[6,10,12,15],determin:17,develop:[0,6,7,15,17],diagram:5,dialect:1,dict:[1,3,15],dictionari:[0,1,3,7,15,17],did:15,differ:[0,4,5,8,10,11,12,20],differenti:4,difficult:15,dig:[10,16],digit:5,dinfrirst:7,dip:[3,5,6,7,8,10,11,12,13,14,15,17],dip_a:15,dip_t:15,dipd:[3,6,7,10,11,12,15,16],dipdd:[3,10,15],direco:17,direct:7,directli:[5,14,15,20],disappear:[2,15],discard:[3,6,8,10,12],disciplin:10,disenstacken:7,disk:7,displac:2,displai:15,distiguish:15,ditch:10,div:[3,7],dive:14,divis:10,divmod:3,divmod_:[3,15],doc:[2,3,7,15],docstr:15,document:[17,18,20],doe:[0,1,4,6,7,13,15,17,19],doesn:[5,9,10,14,15,20],doing:[4,5,7,15,16],domain:[4,15],don:[5,7,10,15],done:[2,5,7,9,15],dooooc:15,door:7,dot:19,doubl:[5,7,15],down:[2,8,12,16],down_to_zero:7,dozen:7,draft:[4,9],dream:7,drive:[6,8],driven:5,driver:6,drop:[3,10],dudipd:7,due:15,dup:[3,5,6,7,8,10,11,12,16,20],dupd:[3,15],dupdd:3,dupdip:[3,5,10,11,12,15],duplic:[3,10,12],durat:2,dure:[2,12],each:[2,3,4,5,7,12,13,14,15,19],easi:[0,10,14,15,16],easier:[3,10],easili:4,edit:17,effect:[2,3,7,16,17],effici:[6,13,16],either:[1,2,3,10,12,15],elabor:15,eleg:[7,10,15],element:2,elif:15,elimin:15,elliott:4,els:[2,3,12,15],else_:15,embed:[4,10,16],emit:15,empti:[3,7,14,15,20],encapsul:7,enclos:7,encod:6,encount:15,end:[5,10,12,14,15,20],endless:6,enforc:[2,7],engend:7,enorm:[],enough:[7,12,19],enstacken:[6,7,15],enter:7,entir:20,entri:[3,16,19],enumer:15,ephasi:15,epsilon:8,equal:[5,14,20],equat:[7,8],ergo:10,err:10,error:[7,15,18],essai:0,establish:15,etc:[3,14,15,16,18],euler:17,euro:15,eval:[0,15],evalu:[1,2,3,7,8,10,11,12,13,14,15],event:15,eventu:15,ever:15,everi:6,everyth:[3,10,11,15],evolv:9,examin:12,exampl:[0,3,5,15,17,18,20],exce:6,except:[7,10,15,18],execut:[0,1,2,3,7,12,13,14,15,16,20],exend:15,exercis:10,exist:[4,10,15],expand:10,expect:[2,3,14,15,20],experi:[7,14],explain:15,explan:7,explor:7,express:[0,1,2,3,4,10,12,13,15,16,19,20],expression_to_str:20,extend:15,extra:[5,6],extract:[10,11,17],extrem:7,extrememli:7,f1001:[],f_g:15,f_in:15,f_out:15,f_python:15,facet:0,facil:7,fact:[15,18],factor:[2,5,7,10,15],factori:17,fail:[2,3,10,18],fairli:15,fale:[],fall:15,fals:[2,3,5,12,15],falsei:15,far:[8,10,12,15],fascin:0,fear:[10,15],few:[5,7,8,11],fewer:[3,7],fg_in:15,fg_out:15,fib:6,fib_gen:6,fibonacci:17,figur:[2,3,10,12,15],filter:10,fin:5,find:[2,3,5,6,14,15,17],finder:8,fine:[0,5,10,15],first:[3,6,7,8,10,11,12,13,14,16,17],first_two:[3,10],fit:[5,7],five:[5,7,17],fix:[2,3,12,15],fixm:15,flag:15,flatten:[7,14,15],flexibl:17,floatjoytyp:15,floatstarjoytyp:15,floor:3,floordiv:5,flow:7,follow:[0,2,3,7,9,12,14,15,16],foo:[7,9,10,15],foo_ii:9,form:[2,3,4,5,6,12,14,15,20],forman:7,format:[15,17,19],formula:[0,5,17],forth:[7,15],forum:0,forward:15,found:7,foundat:[],four:[2,3,5,6,7,10,17],fourteen:5,fourth:[2,3,10,12],fractal:7,fraction0:7,fraction:[2,7],frame:12,framework:7,free:[4,7,10],freeli:2,from:[0,1,2,3,5,6,7,8,10,11,12,13,14,15,16,17,20],from_iter:15,front:[2,3,12,15],full:5,fulli:[],fun:17,func:15,functionjoytyp:15,functionwrapp:3,funtion:10,further:[8,15,17],g_in:15,g_out:15,garbag:7,gari:10,gcd:7,gener:[0,2,4,12,15,17,20],generated_librari:3,genrec:[3,7,10,12,14,15],geometr:5,get:[2,4,5,6,7,11,12,15,17],getitem:3,getrecursionlimit:20,getsourc:7,ghc:4,give:[4,5,10,12,14,15,20],given:[2,3,5,6,8,10,12,15,16,17],global:15,glue:7,going:[10,11,14,15,16],good:[5,10,15],grab:[3,15],grammar:18,grand:7,great:[0,7,15,17],greater:20,grok:[],group:0,gsra:8,guard:10,had:[5,16],haiku:7,half:[5,15,16],hand:[7,13,15,17],handi:[8,15],handl:[10,15,20],happen:[7,15],hard:[15,16],hardwar:4,has:[0,2,6,7,8,9,10,12,15,16,20],hasattr:15,hash:15,haskel:4,have:[2,3,5,6,7,8,9,12,13,15,16,17,20],haven:[],head:20,help:[7,10,12,15],help_:3,helper:3,herd:7,here:[5,6,10,14,15,16],hide:10,hierarchi:15,higher:[7,10,15],highli:7,histori:[15,19],hmm:10,hoist:3,hold:[5,15],hood:10,hope:[0,5,7,15,17],hopefulli:12,host:17,how:[0,4,8,10,12,15,16,17],howev:[12,13,15],html:[2,3,6,11,12,17],http:10,huet:16,huge:10,hugh:[8,14],human:[7,15],hybrid:15,hylomorph:17,hypothet:2,id_:3,idea:[4,5,7,15],ident:[3,12,15],if_not_empti:10,ift:[3,10,12,14,15],ignor:[3,10,15],iii:17,illustr:12,imagin:16,imap:15,imit:14,immedi:12,immut:[7,10],imper:12,implement:[0,1,2,3,4,7,9,10,12,13,17],impli:[],implicit:7,improv:15,includ:[4,10,14,15],inclus:5,incom:20,incompat:9,incorpor:11,increas:5,increment:[3,4,5,9],index:[0,7,15,20],indexerror:[15,20],indic:[14,15],ineffici:15,infer:[0,17],inform:[3,15],infra:[3,6,7,10,11,13,14,15,17],infrastructur:3,initi:[2,3,7,8,10],inlin:10,inner:15,inproceed:15,input:[1,8,15],inscrib:3,insert:15,insight:12,inspect:7,instal:0,instanc:15,instanti:[4,19],instead:[5,6,10,12,15,16,20],integ:[2,3,7,12,14,15],integr:3,intend:[0,7],interact:[7,17],interest:[0,5,10,15,17],interlud:17,intermedi:12,intern:[0,15,19,20],interpret:[0,4,9,13,17,18,19],interrupt:7,interv:[4,5],intjoytyp:15,introduc:9,introduct:0,intstarjoytyp:15,intuit:15,invari:3,invent:15,involv:15,ipf:7,ipython:15,isinst:15,isn:[10,16],issubclass:15,item:[2,3,7,10,12,14,15,17,20],iter:[1,3,7,12,14,15,17,20],iter_stack:[13,15,20],iteritem:15,itertool:15,its:[0,2,3,4,5,7,10,12,14,15,20],itself:[0,2,7,10,15],j05cmp:[2,3,12],jaanu:15,job:17,john:[8,14],joi:[2,4,9,10,11,13],join:15,joypi:[7,16],june:15,junk:17,jupyt:17,just:[0,2,3,6,7,9,10,12,14,15,16],kav:15,keep:[10,11,15,16],kei:[14,17],kevin:0,key_n:10,keyerror:[10,15],kind:[2,4,7,10,12,14,15],kinda:15,kjs:15,kleen:[14,15],kleenestar:15,kleffner:15,know:[5,10,15],knowledg:15,known:4,l2s:15,l_kei:10,l_left:10,l_right:10,l_valu:10,label:15,lambda:[4,15],languag:[4,7,9,10,13,15],larg:15,larger:20,largest:3,last:[5,10,12,15],lastli:6,later:[7,14,15],law:2,lazi:15,lazili:8,lcm:5,lead:[7,15],leaf:10,lean:7,learn:[0,15],least:[2,5,12,15,20],least_fract:7,leav:5,left:[7,11,12,14,15,16,19,20],leftov:12,len:15,length:[3,5,20],lens:12,less:[5,6,7,12,15,20],let:[6,8,10,11,12,14,15,16],letter:15,level:[4,10],librari:[0,13],like:[2,3,5,7,14,15,17,18],limit:15,line:[3,7,10,11,19],linear:20,link:0,linux:0,list:[0,3,5,7,8,10,12,14,15,16,19],list_to_stack:[15,20],lit:15,liter:[1,10,14,15,16,18],literatur:15,littl:[6,10,15,17],live:17,lkei:14,load:[5,7],local:15,locat:2,locu:19,lof:[],log_2:10,logic:[0,5,17],longer:[10,15],look:[6,7,8,10,11,15],lookup:7,loop:[0,1,3,5,15],lose:15,lot:[7,10,15,16],love:5,low:4,lower:5,lowercas:15,lowest:10,machin:0,machineri:[10,15],macro:7,made:[0,7,15,16],magic:15,mai:[2,12],mail:0,main:[0,3,7,11,15,16],mainloop:9,maintain:16,major:9,make:[2,3,4,5,7,10,12,13,14,15,16,17],make_gener:8,manfr:[0,2,3,4,12],mani:[0,7,15],manipul:15,manner:11,map:[1,3,5,7,9,12,14,15],map_:3,marker:7,mask:[5,6],match:[0,1],materi:[0,15],math:[0,7,8,10,11,15],mathemat:7,matter:[5,8,10,14],max_:3,maximum:3,mayb:[10,15],mean:[4,5,7,8,10,12,14,15,20],meant:[7,10,12,14],member:[2,3,12],mental:7,mention:2,mercuri:0,mess:15,messag:15,meta:[7,10,13],meta_compos:15,metal:[],method:[0,3,7,15,17,19],midpoint:5,might:[4,6,10,15],mike:10,million:6,min_:3,mind:15,minimum:3,minor:10,minu:3,mirror:0,miscellan:0,mix:[7,15],mod:3,mode:15,model:[4,7,15],modern:0,modif:6,modifi:[7,10,16],modul:[0,1,3,7,15,18],modulu:7,moment:15,month:7,more:[0,3,4,5,6,7,8,12,13,14,15,18,20],most:15,mostli:0,motiv:[],move:10,movement:2,much:[5,6,10,12,15],muck:10,mul:[7,11,16,19],multi:3,multipl:17,must:[2,3,5,9,12,14,15],myself:15,n10001:15,n10002:15,n10003:15,n1001:15,n1002:15,n1003:15,name:[1,3,7,9,10,12,15,16,17,18,20],narr:15,natur:[5,6,10],navig:16,nearli:15,neat:10,neato:15,necessarili:15,need:[2,3,5,6,8,9,10,12,15],neg:[3,11],neither:15,nest:[3,7,10,16],network:7,never:[9,12],new_def:15,new_f:15,new_fo:15,new_kei:10,new_valu:10,newton:[0,17],next:[5,14,15],nice:[0,12,20],niether:2,node:[14,17],node_kei:10,node_valu:10,non:[14,15],none:[1,3,15],nope:14,normal:15,notat:[7,10],note:[2,5,8,10,12,15,20],notebook:[5,6,7,15,16,17],notebook_preambl:[2,5,6,8,10,11,12,13,14,15,16],noth:[2,10],notic:5,now:[5,6,7,12,13,14,15,17],nth:[3,20],nullari:[7,10],number:[1,2,3,5,6,8,20],numberjoytyp:15,numberstarjoytyp:15,numer:15,object:[15,18],observ:5,obviou:6,obvious:15,occur:10,odd:[5,6],off:[2,3,5,6,11,15,16],okai:[],old:[2,13],old_k:10,old_kei:10,old_valu:10,omit:[12,15],onc:[3,9,10],one:[2,3,5,6,10,12,14,15,19,20],ones:[6,15],onli:[2,3,5,10,12,15,16,20],onto:[1,2,3,7,12,20],open:[7,15],oper:[3,7,10,12,20],oppos:15,optim:10,option:[1,7,10,20],order:[0,2,3,7,12,15,17,20],org:[0,10],origin:[0,1,2,3,10,16],other:[0,2,3,4,7,10,12,14,15,20],otherwis:[3,5,6,10,14,15],our:[5,6,7,8,12,14,15],out:[2,3,4,5,6,7,8,10,11,12,15,16],outcom:14,output:[8,12,15],outsid:4,over:[3,4,5,6,7,8,10,11,14,15,17],overhaul:15,overview:15,own:[10,15],pace:15,pack:20,packag:[0,7],page:[0,10,15,20],pair:[2,3,5,6,10,15],palidrom:5,palindrom:5,pam:7,paper:[4,7,12,16],paradigm:17,parallel:2,paramet:[1,2,3,12,13,18,19,20],parameter:17,paramorph:12,parenthes:[10,20],pariti:6,pars:[0,3,7],parse_definit:3,parseerror:18,parser:[0,15],part:[2,3,8,12,14,17],partial:15,particular:16,pass:[0,10,15,19],path:17,pattern:[5,14,17],pe1:[5,6],pe2:6,pearl:16,pend:[3,7,12,16,19],peopl:[15,17],per:[7,14],perform:15,perhap:6,period:7,permit:[15,20],permut:15,persist:10,phase:2,pick:[5,6,20],pickl:7,pictur:10,piec:12,pip:0,place:[3,5,7,15],plai:0,plu:3,plug:[6,12,14],point:[4,7,10,12],pointless:2,pop:[3,5,6,7,10,12,13,14,20],popd:[3,7,8,10,13,15],popdd:[3,6,11,15],popop:[3,5,6,7,8,10,14,15],popopd:3,popopdd:3,posit:[3,5,7,12],possibilit:10,possibl:[10,14,15,17],post:7,poswrd:15,power:7,pragmat:5,preambl:8,precis:[0,1],pred:[3,15],predic:[2,3,6,12],prefix:[15,19],present:15,preserv:[4,14],pretti:[8,10,11,14,15,19,20],pretty_print:0,previou:7,primari:[],prime:8,primit:[2,3,15,17],primrec:[3,6,7,8,12],principl:[],print:[0,1,2,3,15,19,20],probabl:[6,7,10,15],problem:[7,15,17],proc_curr:10,proc_left:10,proc_right:10,proce:5,process:[7,14,15,19],produc:[5,10,12,14,15],product:[6,7,15],program:[0,2,3,6,7,8,10,12,15,16],programm:15,progress:15,project:17,prolog:15,prompt:7,proper:[2,3,12],properti:0,provabl:[],proven:[],provid:[0,3,4,7],pun:[0,7],punctuat:15,pure:0,puriti:7,purpos:7,push:[2,3,7,12,16,20],pushback:7,put:[1,2,6,7,15,17,20],pypi:0,python:[0,2,3,10,12,16,17,18,20],quadrat:[0,17],queri:[10,14],query_kei:14,queu:12,quit:[0,1,14],quot:[0,3,6,7,10,11,12,14,15,16,19],quotat:[2,3,12],quotient:3,r_kei:10,r_left:10,r_right:10,r_valu:10,rais:[10,15,18,20],rang:[7,15],range_revers:12,range_to_zero:7,ranger:12,ranger_revers:12,raphson:8,rather:[5,7,12,14],ratio:7,reach:[5,6,12],read:[0,1,5,6,10,15,16],readabl:13,reader:10,readi:15,real:10,realiz:[4,10,15],rearrang:[2,10,15],reason:[5,7,15],rebuild:[14,16],rec1:[2,3,12],rec2:[2,3,12],recent:15,recogn:18,record:[7,19],recur:[12,15],recurs:[0,2,3,6,7,8,15,17,20],recus:7,recycl:[],redefin:17,redistribut:[3,7],reduc:[2,15],redund:20,refactor:[7,9],refer:[0,2],regist:2,regular:[15,18],reimplement:17,relat:15,releas:9,remain:[2,7,9,15],remaind:[3,8],remind:15,remov:[3,10,15,20],render:17,repeat:5,repeatedli:5,repl:[0,1],replac:[0,2,3,6,11,12,14,15,16,17,20],repositori:0,repr:15,repres:[2,7,10,18,19],represent:20,reprod:6,repurpos:15,requir:[15,20],res:15,research:15,resembl:7,respect:5,rest:[3,5,6,7,10,12,16,17,20],rest_two:10,restat:[],restor:2,restrict:15,result:[1,2,3,5,10,11,12,14,15,16],resum:7,retain:15,retir:2,retri:7,reus:[10,15],revers:[3,5,6,12,15,16,20],revisit:15,rewrit:[3,7,15],rewritten:[7,15],rich:15,rid:10,right:[6,7,11,14,15,17,19,20],rightest:10,rightmost:5,rkei:14,rob:15,robot:[],roll:[3,8,10,14],roll_dn:15,roll_down:[],roll_up:[],rolldown:[3,15],rollup:[3,15],root:[3,8,11],round:15,rrest:[3,15],rule:17,run:[0,1,3,5,7,8,10,11,12,14,16],runtimeerror:20,s1000:[],s1002:[],s23:[],sai:[6,10,11,14,15],same:[2,4,5,10,15,20],sandwich:[2,3,12],save:[2,5,7],scan:3,scanner:[7,18],scenario:16,scope:[6,10],search:[0,10],sec:15,second:[3,7,10,12,14,20],section:12,see:[0,6,7,8,9,11,12,13,15,16,19],seem:[0,5,7,14,15],seen:[15,16],select:3,self:15,semant:[2,3,7,9,10,15],semi:7,send:7,sens:[0,2,5,15,16],separ:[7,15],seq:15,sequenc:[0,1,2,3,5,7,10,12,13,16,17,18],sequence_to_stack:15,seri:[5,6,10,16],ses:15,set:[2,3,12,15,17],seven:[5,6],sever:[0,4,7,12],share:[3,7],shelf:2,shift:[5,6,15],shorter:17,shorthand:10,should:[2,3,5,10,12,15],shouldn:7,show:[4,16],shunt:[3,16],side:[10,15],signifi:[7,10],similar:[10,14,15],simon:7,simpl:[7,12,15,20],simplefunctionwrapp:[3,13,15],simpler:14,simplest:[15,17],simpli:4,simplifi:[5,10,16],sinc:[2,5,10,15],singl:[3,6,7,13,15,18],situ:10,situat:10,six:[5,6,7],sixti:[5,6],size:[7,17],skeptic:7,skip:15,slight:8,slightli:[10,12,15],smallest:3,smart:10,softwar:7,solei:2,solut:[5,6],solvabl:7,some:[2,3,6,7,10,12,14,15,17,20],somehow:[10,15],someth:[2,9,10,15],sometim:10,somewher:[10,17],sort:[3,10,15],sort_:3,sorta:15,sourc:[0,1,3,15,17,18,19,20],space:[5,19],span:5,spawn:15,special:[6,10,15,17],specif:[0,4],specifi:[10,15],speed:13,spell:14,sphinx:[17,20],spirit:[0,1,14],split:15,sqr:[7,8,11,16],sqrt:[3,8,15],squar:[3,8,15,18],squishi:15,stack:[0,1,3,5,6,8,10,11,12,13,14,16,17,18,19],stack_concat:[],stack_effect:15,stack_effect_com:15,stack_to_str:20,stacki:15,stackjoytyp:15,stackstarjoytyp:15,stage:14,stai:[0,1],stand:4,standard:[7,10],star:[14,15],stare:10,start:[5,6,7,8,10,12,14,15],state:7,statement:3,step:[3,5,7,10,13,15,16,17],still:[10,15],stop:10,storag:[5,10],store:[5,12],stori:12,str:[1,15,18,19,20],straightforward:[1,6,8,15,17],stream:5,stretch:10,string:[1,2,3,7,15,16,18,19,20],strip:15,structur:[7,14,15,16,17,20],stuff:[10,15],stuncon:3,stununcon:3,style:[0,4,15],sub:9,subclass:7,subject:16,subset:15,substitut:[10,15],subtract:5,subtyp:17,succ:[3,15],succe:15,success:8,suck:15,suffic:15,suffici:10,suffix:15,suggest:[4,10],suitabl:[3,4,5],sum:[3,6,7,11,12,13,14,15],sum_:[3,15],summand:5,sumtre:14,suppli:[10,18],support:[7,15,19,20],suspect:2,swaack:[3,11,13,15,16],swap:[3,5,6,7,8,10,12,13,14,16],swarm:[],swon:[3,6,7,12,14,15,16],swoncat:[6,7,8,12,14],swuncon:12,symbol:[2,3,15,16,17,18],symboljoytyp:15,symmetr:[5,10],syntact:7,syntax:[7,20],sys:20,system:[7,10],tabl:15,tag:15,tail:[10,15,17,20],take:[3,5,7,8,10,12,15,20],talk:[7,10,15,20],target:16,tast:4,tbd:7,tear:12,technic:2,techniqu:[4,16],technolog:2,temporari:16,ten:5,term:[1,2,7,8,12,15,17,18,20],termin:[2,3,12],ternari:7,test:[2,3,12],text:[0,1,3,15],text_to_express:[7,15,18],textual:7,than:[0,3,5,6,7,8,12,14,15,20],thei:[2,5,6,7,10,12,15,16,18,20],them:[2,3,5,6,10,12,15,16,17],themselv:15,theori:[2,3,12],therefor:6,thi:[0,1,2,3,4,5,6,7,8,11,12,14,15,16,17,18,19,20],thing:[2,6,10,12,15,16,18,20],think:[2,5,7,10,12,14,15],third:[3,6,7,10],thirti:5,those:[2,3,10,12,15,17],though:5,thought:7,thousand:5,thread:2,three:[2,3,5,7,10,11,14,15,17],through:[1,5,7,14,15,16,20],thun:[2,3,4,9,12],thunder:7,time:[3,5,7,8,10,12,15,16],titl:15,to_set:10,todai:7,todo:[7,18],togeth:[6,7,15,17],token:18,toler:17,too:[12,15],tool:[7,15],tooo:15,top:[2,3,7,12,15,19,20],total:5,tower:15,trace:[0,7,11,12,16,17,20],traceback:15,traceprint:19,track:[11,15,16],tracker:0,transform:4,translat:[4,11,15],trash:[],travers:[0,17],treasur:0,treat:[0,2,3,12,15,17],treatment:6,tree:[0,7,17],treegrind:17,treestep:[0,17],tri:5,triangular_numb:12,trick:[5,15],tricki:15,trobe:0,trove:0,truli:[],trust:[],truthi:[3,7,15],tuck:[3,7,15],tupl:[3,7,15,20],ture:[],turn:[2,3,15],twice:[10,12],two:[2,3,5,7,8,10,11,12,14,15,16,17,20],type:[0,1,4,7,10,12,17,18,19,20],typeerror:15,typeless:15,typic:[2,3,11,12],unari:7,unarybuiltinwrapp:3,unbalanc:[10,18],unchang:10,uncompil:15,uncon:[3,6,7,10,12,14,16],under:[2,3,7,10],underli:15,underscor:15,understand:[0,10],undistinguish:10,undocu:7,unend:[],unfinish:15,unfortun:20,unicod:15,unif:15,uniqu:[3,10,15],unit:[7,12],univers:[0,7,15],unnecessari:17,unnecesssari:15,unpack:[2,3,10,20],unpair:5,unquot:[7,14],unstack:[3,15],unswon:3,untangl:12,until:6,unus:5,unusu:10,updat:[0,17],usag:7,use:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,20],used:[3,4,7,10,12,16,18,20],useful:[0,15],user:14,uses:[2,5,12],using:[3,6,10,11,12,14,16],usual:[0,2,12],util:[0,3,13,15],valid:15,valu:[0,2,3,5,7,8,11,12,13,14,15,17,20],value_n:10,valueerror:[15,20],variabl:[15,17],variant:10,variat:[12,17],varieti:[4,7],variou:0,vener:20,verbos:4,veri:[0,1,4,7,10,20],verifi:15,versa:[2,15],version:[0,1,2,6,9,14,16,17],via:7,vice:[2,15],view:[10,17],viewer:[1,7,9,19],vii:17,visibl:15,von:[0,2,3,4,12],wai:[0,2,3,4,5,7,12,13,15],wait:[],want:[2,5,6,8,10,12,15],warranti:[3,7],wash:7,wast:7,web:20,websit:[0,5],welcom:7,well:[0,4,7,8,10,15,18],went:15,were:[7,15,16],what:[2,3,4,7,10,12,14,15,19],whatev:[2,3,12,14,20],when:[5,6,7,10,12,15,16,18,20],where:[2,3,7,10,12,15,17,20],whether:12,which:[0,1,3,5,7,8,10,12,14,15,16,20],whole:[2,3,5,12,14,15],whose:6,why:[8,14],wiki:10,wikipedia:[0,10,16],wildli:7,wind:7,wire:12,within:[7,10,13,17],without:[2,7,10,11,15],won:[10,15,20],word:[0,3,5,7,12,16],work:[0,3,5,6,7,8,10,11,12,14,15,16,20],worth:5,would:[2,5,6,7,8,10,12,15,16,20],wrap:[3,7],wrapper:15,write:[4,8,10,12,14,15,16,17,20],written:[0,1,8,10,13,15,20],wrong:2,wrote:15,xrang:15,yang:15,year:[7,15],yet:[10,15,16],yield:[2,3,12,15,20],yin:17,you:[0,2,3,5,6,7,9,10,11,12,13,14,15,16,19,20],your:[2,3,7,12,15],yourself:[7,10],zero:[3,10,12,14,15,18,20],zip:[5,15],zip_:3,zipper:[0,17],zstr:16},titles:["Thun 0.2.0 Documentation","Joy Interpreter","Functions Grouped by, er, Function with Examples","Function Reference","Categorical Programming","Developing a Program in Joy","Using x to Generate Values","Thun: Joy in Python","Newton\u2019s method","No Updates","Treating Trees I: Ordered Binary Trees","Quadratic formula","Recursive Combinators","Replacing Functions in the Dictionary","Treating Trees II: treestep","Type Inference","Traversing Datastructures with Zippers","Essays about Programming in Joy","Parsing Text into Joy Expressions","Tracing Joy Execution","Stack or Quote or Sequence or List\u2026"],titleterms:{"abstract":15,"case":[8,10],"function":[2,3,7,8,10,12,13,14,15],"long":13,"new":10,"p\u00f6ial":15,"void":2,"while":2,Adding:10,One:[6,10],The:[5,7,10,12,14],There:7,Using:6,With:14,about:17,add:[2,10],adding:10,address:16,altern:14,ana:12,analysi:5,anamorph:[2,12],app1:2,app2:2,app3:2,appendix:[10,12,15],approxim:8,argument:15,auto:3,averag:2,base:[8,10],binari:[2,10,14],both:10,branch:[2,10],can:10,cata:12,catamorph:12,categor:4,chatter:2,child:10,choic:2,clear:2,cleav:2,cmp:10,code:[7,10],combin:[2,10,12,15],comment:15,compar:10,comparison:2,compil:[6,15],compile_:15,compos:15,comput:8,con:[2,15],concat:[2,15],conclus:[12,15],consecut:8,continu:7,current:10,datastructur:[7,10,16],deal:15,defin:[10,14],definit:11,delabel:15,delet:10,deriv:[11,12,14],design:12,determin:16,develop:5,dialect:0,dictionari:13,dip:[2,16],dipd:2,dipdd:2,direco:6,disenstacken:2,distinguish:15,div:2,doc_from_stack_effect:15,document:0,doe:10,down_to_zero:2,drop:2,dup:[2,15],dupd:2,dupdip:2,effect:15,els:10,empti:10,enstacken:2,equal:10,essai:17,euler:[5,6],eval:7,even:6,exampl:[2,7,10,12,14],execut:19,express:[7,18],extract:14,factori:12,fibonacci:6,filter:5,find:[8,10,12],first:[2,5,15],five:6,flatten:2,flexibl:14,floordiv:2,formula:11,found:10,four:12,fun:12,further:5,gcd:2,gener:[3,5,6,8],genrec:2,get:[10,14],getitem:2,given:14,greater:10,group:2,have:[10,14],help:2,highest:10,host:0,how:[5,6],hylo:12,hylomorph:12,identifi:15,ift:2,iii:15,implement:15,indic:0,infer:15,inferenc:15,inform:0,infra:[2,16],integ:5,interest:6,interlud:10,intern:18,interpret:[1,7,15],item:16,iter:[5,10],joi:[0,1,3,5,7,12,15,16,17,18,19,20],junk:15,just:5,kei:10,languag:0,least_fract:2,left:10,less:10,let:5,librari:[3,7,15],like:10,list:[2,20],literari:7,littl:5,logic:[2,15],loop:[2,7],lower:10,lshift:2,make:[6,8],mani:5,map:2,math:2,method:8,min:2,miscellan:2,mod:2,modifi:15,modulu:2,more:10,most:10,mul:[2,15],multipl:[5,6,15],must:10,name:11,neg:2,newton:8,next:8,node:10,non:10,now:10,nullari:2,number:[12,15],one:7,onli:7,order:[10,14],osdn:0,our:10,over:2,pack:5,pam:2,para:12,paradigm:15,parameter:[10,14],pars:[2,18],parser:[7,18],part:15,pass:7,path:16,pattern:12,per:10,pop:[2,15],popd:2,popop:2,pow:2,power:6,pred:2,predic:[5,8,10,14],pretty_print:19,primit:12,primrec:2,print:7,problem:[5,6],process:10,product:2,program:[4,5,11,14,17],project:[0,5,6],pure:7,put:[10,11,14],python:[7,13,15],quadrat:11,quick:0,quot:[2,20],rang:[2,5,12],range_to_zero:2,read:7,recur:[8,10],recurs:[10,12,14],redefin:[10,14],refactor:[5,10],refer:3,regular:7,reimplement:14,relabel:15,rem:2,remaind:2,remov:2,render:5,repl:7,replac:[10,13],repres:15,reset:6,rest:[2,15],revers:2,right:[10,16],rightmost:10,roll:[2,15],rolldown:2,rollup:2,rshift:2,rule:15,run:[2,6],second:[2,15],select:2,sequenc:[6,15,20],set:[8,10],shorter:13,should:7,shunt:2,simplest:5,size:[2,13],someth:[],sourc:10,special:12,sqr:[2,15],sqrt:[2,11],stack:[2,7,15,20],start:0,step:[2,12,14],straightforward:11,structur:10,style:7,sub:[2,10],subtyp:15,succ:2,sum:[2,5],swaack:2,swap:[2,15],swon:2,swoncat:2,symbol:[7,12],tabl:0,tail:12,take:2,term:[5,6,14],ternari:2,text:18,than:10,them:11,thi:10,third:[2,15],three:6,thun:[0,7],time:[2,6],togeth:[10,11,14],token:7,toler:8,trace:[13,19],traceprint:7,travers:[10,14,16],treat:[10,14],tree:[10,14,16],treegrind:14,treestep:14,triangular:12,truediv:2,truthi:2,tuck:2,two:6,type:15,unari:2,unbound:15,uncon:[2,15],unifi:15,unit:2,unnecessari:5,unquot:2,unstack:2,updat:[9,15],use:15,util:[19,20],valu:[6,10],variabl:11,variat:6,version:[5,10,13,15],view:7,vii:15,within:8,word:2,write:11,xor:2,yin:15,zero:6,zip:2,zipper:16}})
\ No newline at end of file
diff --git a/docs/sphinx_docs/notebooks/Types.rst b/docs/sphinx_docs/notebooks/Types.rst
index 216ce90..a8084de 100644
--- a/docs/sphinx_docs/notebooks/Types.rst
+++ b/docs/sphinx_docs/notebooks/Types.rst
@@ -3,42 +3,19 @@ Type Inference
==============
This notebook presents a simple type inferencer for Joy code. It can
-infer the stack effect of most Joy expressions. It built largely by
-means of existing ideas and research (some of it may be original but I'm
-not able to say, as I don't fully understand the all of the source
-material in the depth required to make that call.) A great overview of
-the existing knowledge is a talk `"Type Inference in Stack-Based
-Programming
+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" in ()
- 1 F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
- 2
- ----> 3 print doc_from_stack_effect(*F)
+ F = infer(l2s((pop, swap, rolldown, rest, rest, cons, cons)))
-
- in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
- ---> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
+ for f in F:
+ print doc_from_stack_effect(*f)
- in compose(f, g)
- 1 def compose(f, g):
- ----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
+.. parsed-literal::
-
- in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
- ---> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
- in compose(f, g)
- 1 def compose(f, g):
- ----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
- in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
- ---> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
- in compose(f, g)
- 1 def compose(f, g):
- ----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
- in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
- ---> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
- in compose(f, g)
- 1 def compose(f, g):
- ----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
- in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
- ---> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
- in compose(f, g)
- 1 def compose(f, g):
- ----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
- in C(f, g)
- 10 def C(f, g):
- 11 f, g = relabel(f, g)
- ---> 12 for fg in compose(f, g):
- 13 yield delabel(fg)
-
-
- in compose(f, g)
- 1 def compose(f, g):
- ----> 2 (f_in, f_out), (g_in, g_out) = f, g
- 3 s = unify(g_in, f_out)
- 4 if not s:
- 5 raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-
-
- TypeError: 'SymbolJoyType' object is not iterable
+ ([a4 a5 .1.] a3 a2 a1 -- [a2 a3 .1.])
.. code:: ipython2
@@ -3031,26 +2946,140 @@ For this to work the type label classes have to be modified to let
.. code:: ipython2
- s = text_to_expression('[3 4 ...] 2 1')
+ 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
- L = unify(F[1], s)
+ F[0][0]
+
+
+
+
+.. parsed-literal::
+
+ (a1, (a2, (a3, s1)))
+
+
+
+.. code:: ipython2
+
+ L = unify(s, F[0][0])
L
+
+
+
+.. parsed-literal::
+
+ ()
+
+
+
.. code:: ipython2
- F[1]
+ 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)
+
+ in ()
+ ----> 1 F[1][0]
+
+
+ IndexError: list index out of range
+
+
.. code:: ipython2
s[0]
+.. code:: ipython2
+
+ A[1] >= 23
+
`Abstract Interpretation `__
-----------------------------------------------------------------------------------
diff --git a/test/test_type_inference.py b/test/test_type_inference.py
index 194c0c6..a1d3435 100644
--- a/test/test_type_inference.py
+++ b/test/test_type_inference.py
@@ -53,18 +53,17 @@ class TestCombinators(TestMixin, unittest.TestCase):
]
self.assertEqualTypeStructure(infr(expression), f)
- def test_cons_dip(self):
- expression = (cons, s0), dip # [cons] dip
- # (a2 [...1] a1 -- [a2 ...1] a3)
- f = (a1, (s1, (a2, s2))), (a1, ((a2, s1), s2))
- # shouldn't a3 be a1?
- self.assertEqualTypeStructure(infr(expression), [f])
-
def test_dip(self):
expression = dip,
f = ((s1, (a1, s2)), (a2, s2)) # (a1 [...1] -- a2)
self.assertEqualTypeStructure(infr(expression), [f])
+ def test_cons_dip(self):
+ expression = (cons, s0), dip # [cons] dip
+ # (a2 [...1] a1 -- [a2 ...1] a1)
+ f = (a1, (s1, (a2, s2))), (a1, ((a2, s1), s2))
+ self.assertEqualTypeStructure(infr(expression), [f])
+
def test_cons_dipd(self):
expression = a1, a3, (cons, s0), dipd
f = ((s0, (a0, s1)), (a1, (a2, ((a0, s0), s1))))
@@ -169,4 +168,4 @@ class TestYin(TestMixin, unittest.TestCase):
if __name__ == '__main__':
- unittest.main(defaultTest='TestCombinators.test_cons_dip')
+ unittest.main()