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Bringing over some of the "upgrades".

This commit is contained in:
Simon Forman 2022-09-11 13:57:19 -07:00
parent cb553a1a65
commit 4bd32f2c0b
3 changed files with 690 additions and 538 deletions
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14
implementations/Python/align_trace.py Normal file
View File

@ -0,0 +1,14 @@
import sys
SEP = '•'
lines = sys.stdin.readlines()
indicies = [line.index(SEP) for line in lines if SEP in line]
MAX = max(indicies)
prefix_counts = [MAX - i for i in indicies]
for count, line in zip(prefix_counts, lines):
print(' ' * count, line, sep='', end = '')

534
implementations/Python/joy/library.py
View File

@ -7,322 +7,6 @@ ALIASES = (
('id', [u'•']), ('id', [u'•']),
) )
@inscribe
@FunctionWrapper
def inscribe_(stack, expression, dictionary):
'''
Create a new Joy function definition in the Joy dictionary. A
definition is given as a quote with a name followed by a Joy
expression. for example:
[sqr dup mul] inscribe
'''
(name, body), stack = stack
inscribe(Def(name, body), dictionary)
return stack, expression, dictionary
@inscribe
@SimpleFunctionWrapper
def getitem(stack):
'''
::
getitem == drop first
Expects an integer and a quote on the stack and returns the item at the
nth position in the quote counting from 0.
::
[a b c d] 0 getitem
-------------------------
a
'''
n, (Q, stack) = stack
return pick(Q, n), stack
@inscribe
@SimpleFunctionWrapper
def drop(stack):
'''
::
drop == [rest] times
Expects an integer and a quote on the stack and returns the quote with
n items removed off the top.
::
[a b c d] 2 drop
----------------------
[c d]
'''
n, (Q, stack) = stack
while n > 0:
try:
_, Q = Q
except ValueError:
raise IndexError
n -= 1
return Q, stack
@inscribe
@SimpleFunctionWrapper
def take(stack):
'''
Expects an integer and a quote on the stack and returns the quote with
just the top n items in reverse order (because that's easier and you can
use reverse if needed.)
::
[a b c d] 2 take
----------------------
[b a]
'''
n, (Q, stack) = stack
x = ()
while n > 0:
try:
item, Q = Q
except ValueError:
raise IndexError
x = item, x
n -= 1
return x, stack
@inscribe
@FunctionWrapper
def gcd2(stack, expression, dictionary):
'''Compiled GCD function.'''
(v1, (v2, stack)) = stack
tos = True
while tos:
v3 = v2 % v1
tos = v3 > 0
(v1, (v2, stack)) = (v3, (v1, stack))
return (v2, stack), expression, dictionary
@inscribe
@SimpleFunctionWrapper
def choice(stack):
'''
Use a Boolean value to select one of two items.
::
A B false choice
----------------------
A
A B true choice
---------------------
B
'''
(if_, (then, (else_, stack))) = stack
assert isinstance(if_, bool), repr(if_)
return then if if_ else else_, stack
@inscribe
@SimpleFunctionWrapper
def select(stack):
'''
Use a Boolean value to select one of two items from a sequence.
::
[A B] false select
------------------------
A
[A B] true select
-----------------------
B
The sequence can contain more than two items but not fewer.
Currently Python semantics are used to evaluate the "truthiness" of the
Boolean value (so empty string, zero, etc. are counted as false, etc.)
'''
(flag, (choices, stack)) = stack
(else_, (then, _)) = choices
return then if flag else else_, stack
@inscribe
@SimpleFunctionWrapper
def max_(S):
'''Given a list find the maximum.'''
tos, stack = S
return max(iter_stack(tos)), stack
@inscribe
@SimpleFunctionWrapper
def min_(S):
'''Given a list find the minimum.'''
tos, stack = S
return min(iter_stack(tos)), stack
@inscribe
@SimpleFunctionWrapper
def sum_(S):
'''
Given a quoted sequence of numbers return the sum.
::
sum == 0 swap [+] step
'''
tos, stack = S
return sum(iter_stack(tos)), stack
@inscribe
@SimpleFunctionWrapper
def remove(S):
'''
Expects an item on the stack and a quote under it and removes that item
from the the quote. The item is only removed once. If the list is
empty or the item isn't in the list then the list is unchanged.
::
[1 2 3 1] 1 remove
------------------------
[2 3 1]
'''
(item, (quote, stack)) = S
return _remove(item, quote), stack
def _remove(item, quote):
try: head, tail = quote
except ValueError: return quote
return tail if head == item else (head, _remove(item, tail))
@inscribe
@SimpleFunctionWrapper
def unique(S):
'''Given a list remove duplicate items.'''
tos, stack = S
I = list(iter_stack(tos))
return list_to_stack(sorted(set(I), key=I.index)), stack
@inscribe
@SimpleFunctionWrapper
def sort_(S):
'''Given a list return it sorted.'''
tos, stack = S
return list_to_stack(sorted(iter_stack(tos))), stack
@inscribe
@SimpleFunctionWrapper
def disenstacken(stack):
'''
The disenstacken operator expects a list on top of the stack and makes that
the stack discarding the rest of the stack.
'''
return stack[0]
@inscribe
@SimpleFunctionWrapper
def reverse(S):
'''
Reverse the list on the top of the stack.
::
reverse == [] swap shunt
'''
(tos, stack) = S
res = ()
for term in iter_stack(tos):
res = term, res
return res, stack
@inscribe
@SimpleFunctionWrapper
def shunt(stack):
'''
Like concat but reverses the top list into the second.
::
shunt == [swons] step == reverse swap concat
[a b c] [d e f] shunt
---------------------------
[f e d a b c]
'''
(tos, (second, stack)) = stack
while tos:
term, tos = tos
second = term, second
return second, stack
@inscribe
@SimpleFunctionWrapper
def zip_(S):
'''
Replace the two lists on the top of the stack with a list of the pairs
from each list. The smallest list sets the length of the result list.
'''
(tos, (second, stack)) = S
accumulator = [
(a, (b, ()))
for a, b in zip(iter_stack(tos), iter_stack(second))
]
return list_to_stack(accumulator), stack
@inscribe
@SimpleFunctionWrapper
def succ(S):
'''Increment TOS.'''
(tos, stack) = S
return tos + 1, stack
@inscribe
@SimpleFunctionWrapper
def pred(S):
'''Decrement TOS.'''
(tos, stack) = S
return tos - 1, stack
@inscribe
@SimpleFunctionWrapper
def pm(stack):
'''
Plus or minus
::
a b pm
-------------
a+b a-b
'''
a, (b, stack) = stack
p, m, = b + a, b - a
return m, (p, stack)
def floor(n): def floor(n):
return int(math.floor(n)) return int(math.floor(n))
@ -350,39 +34,6 @@ def id_(stack):
@inscribe
@FunctionWrapper
def sharing(stack, expression, dictionary):
'''Print redistribution information.'''
print("You may convey verbatim copies of the Program's source code as"
' you receive it, in any medium, provided that you conspicuously'
' and appropriately publish on each copy an appropriate copyright'
' notice; keep intact all notices stating that this License and'
' any non-permissive terms added in accord with section 7 apply'
' to the code; keep intact all notices of the absence of any'
' warranty; and give all recipients a copy of this License along'
' with the Program.'
' You should have received a copy of the GNU General Public License'
' along with Thun. If not see <http://www.gnu.org/licenses/>.')
return stack, expression, dictionary
@inscribe
@FunctionWrapper
def warranty(stack, expression, dictionary):
'''Print warranty information.'''
print('THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY'
' APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE'
' COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM'
' "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR'
' IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES'
' OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE'
' ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS'
' WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE'
' COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.')
return stack, expression, dictionary
# #
# § Combinators # § Combinators
# #
@ -406,194 +57,9 @@ S_swaack = Symbol('swaack')
S_times = Symbol('times') S_times = Symbol('times')
@inscribe
@FunctionWrapper
def i(stack, expression, dictionary):
'''
The i combinator expects a quoted program on the stack and unpacks it
onto the pending expression for evaluation.
::
[Q] i
-----------
Q
'''
try:
quote, stack = stack
except ValueError:
raise StackUnderflowError('Not enough values on stack.')
return stack, concat(quote, expression), dictionary
@inscribe
@FunctionWrapper
def x(stack, expression, dictionary):
'''
::
x == dup i
... [Q] x = ... [Q] dup i
... [Q] x = ... [Q] [Q] i
... [Q] x = ... [Q] Q
'''
quote, _ = stack
return stack, concat(quote, expression), dictionary
@inscribe
@FunctionWrapper
def b(stack, expression, dictionary):
'''
::
b == [i] dip i
... [P] [Q] b == ... [P] i [Q] i
... [P] [Q] b == ... P Q
'''
q, (p, (stack)) = stack
return stack, concat(p, concat(q, expression)), dictionary
@inscribe
@FunctionWrapper
def ii(stack, expression, dictionary):
'''
::
... a [Q] ii
------------------
... Q a Q
'''
quote, (a, stack) = stack
expression = concat(quote, (a, concat(quote, expression)))
return stack, expression, dictionary
@inscribe
@FunctionWrapper
def dupdip(stack, expression, dictionary):
'''
::
[F] dupdip == dup [F] dip
... a [F] dupdip
... a dup [F] dip
... a a [F] dip
... a F a
'''
F, stack = stack
a = stack[0]
return stack, concat(F, (a, expression)), dictionary
@inscribe
@FunctionWrapper
def infra(stack, expression, dictionary):
'''
Accept a quoted program and a list on the stack and run the program
with the list as its stack. Does not affect the rest of the stack.
::
... [a b c] [Q] . infra
-----------------------------
c b a . Q [...] swaack
'''
(quote, (aggregate, stack)) = stack
return aggregate, concat(quote, (stack, (S_swaack, expression))), dictionary
@inscribe
@FunctionWrapper
def genrec(stack, expression, dictionary):
'''
General Recursion Combinator.
::
[if] [then] [rec1] [rec2] genrec
---------------------------------------------------------------------
[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte
From "Recursion Theory and Joy" (j05cmp.html) by Manfred von Thun:
"The genrec combinator takes four program parameters in addition to
whatever data parameters it needs. Fourth from the top is an if-part,
followed by a then-part. If the if-part yields true, then the then-part
is executed and the combinator terminates. The other two parameters are
the rec1-part and the rec2-part. If the if-part yields false, the
rec1-part is executed. Following that the four program parameters and
the combinator are again pushed onto the stack bundled up in a quoted
form. Then the rec2-part is executed, where it will find the bundled
form. Typically it will then execute the bundled form, either with i or
with app2, or some other combinator."
The way to design one of these is to fix your base case [then] and the
test [if], and then treat rec1 and rec2 as an else-part "sandwiching"
a quotation of the whole function.
For example, given a (general recursive) function 'F':
::
F == [I] [T] [R1] [R2] genrec
If the [I] if-part fails you must derive R1 and R2 from:
::
... R1 [F] R2
Just set the stack arguments in front, and figure out what R1 and R2
have to do to apply the quoted [F] in the proper way. In effect, the
genrec combinator turns into an ifte combinator with a quoted copy of
the original definition in the else-part:
::
F == [I] [T] [R1] [R2] genrec
== [I] [T] [R1 [F] R2] ifte
Primitive recursive functions are those where R2 == i.
::
P == [I] [T] [R] tailrec
== [I] [T] [R [P] i] ifte
== [I] [T] [R P] ifte
'''
(rec2, (rec1, stack)) = stack
(then, (if_, _)) = stack
F = (if_, (then, (rec1, (rec2, (S_genrec, ())))))
else_ = concat(rec1, (F, rec2))
return (else_, stack), (S_ifte, expression), dictionary
@inscribe
@FunctionWrapper
def map_(S, expression, dictionary):
'''
Run the quoted program on TOS on the items in the list under it, push a
new list with the results in place of the program and original list.
'''
# (quote, (aggregate, stack)) = S
# results = list_to_stack([
# joy((term, stack), quote, dictionary)[0][0]
# for term in iter_stack(aggregate)
# ])
# return (results, stack), expression, dictionary
(quote, (aggregate, stack)) = S
if not aggregate:
return (aggregate, stack), expression, dictionary
batch = ()
for term in iter_stack(aggregate):
s = term, stack
batch = (s, (quote, (S_infra, (S_first, batch))))
stack = (batch, ((), stack))
return stack, (S_infra, expression), dictionary
@inscribe @inscribe

680
implementations/Python/simplejoy.py
View File

@ -307,6 +307,9 @@ def joy(stack, expression, dictionary):
''' '''
expr = push_quote(expression) # We keep a stack-of-stacks, see below. expr = push_quote(expression) # We keep a stack-of-stacks, see below.
while expr: while expr:
print(
f'{stack_to_string(stack)} • {expr_to_string(expr)}'
)
term, expr = next_term(expr) term, expr = next_term(expr)
if isinstance(term, Symbol): if isinstance(term, Symbol):
try: try:
@ -625,6 +628,13 @@ def expression_to_string(expression):
return _stack_to_string(expression, iter_stack) return _stack_to_string(expression, iter_stack)
def expr_to_string(expr):
'''
Return a "pretty print" string for a stack-of-stacks expression.
'''
return ' '.join(map(expression_to_string, iter_stack(expr)))
def _stack_to_string(stack, iterator): def _stack_to_string(stack, iterator):
isnt_stack(stack) isnt_stack(stack)
if not stack: # shortcut if not stack: # shortcut
@ -1329,13 +1339,675 @@ inscribe(UnaryWrapper(isnt_bool))
inscribe(UnaryWrapper(isnt_stack)) inscribe(UnaryWrapper(isnt_stack))
'''
███████╗██╗ ██╗████████╗██████╗ █████╗
██╔════╝╚██╗██╔╝╚══██╔══╝██╔══██╗██╔══██╗
█████╗ ╚███╔╝ ██║ ██████╔╝███████║
██╔══╝ ██╔██╗ ██║ ██╔══██╗██╔══██║
███████╗██╔╝ ██╗ ██║ ██║ ██║██║ ██║
╚══════╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝╚═╝ ╚═╝
'''
def dnd(stack, from_index, to_index):
'''
Given a stack and two indices return a rearranged stack.
First remove the item at from_index and then insert it at to_index,
the second index is relative to the stack after removal of the item
at from_index.
This function reuses all of the items and as much of the stack as it
can. It's meant to be used by remote clients to support drag-n-drop
rearranging of the stack from e.g. the StackListbox.
'''
assert 0 <= from_index
assert 0 <= to_index
if from_index == to_index:
return stack
head, n = [], from_index
while True:
item, stack = stack
n -= 1
if n < 0:
break
head.append(item)
assert len(head) == from_index
# now we have two cases:
diff = from_index - to_index
if diff < 0:
# from < to
# so the destination index is still in the stack
while diff:
h, stack = stack
head.append(h)
diff += 1
else:
# from > to
# so the destination is in the head list
while diff:
stack = head.pop(), stack
diff -= 1
stack = item, stack
while head:
stack = head.pop(), stack
return stack
def pick(stack, n):
'''
Return the nth item on the stack.
:param stack stack: A stack.
:param int n: An index into the stack.
:raises ValueError: if ``n`` is less than zero.
:raises IndexError: if ``n`` is equal to or greater than the length of ``stack``.
:rtype: whatever
'''
if n < 0:
raise ValueError
while True:
try:
item, stack = stack
except ValueError:
raise IndexError
n -= 1
if n < 0:
break
return item
@inscribe
def inscribe_(stack, expression, dictionary):
'''
Create a new Joy function definition in the Joy dictionary. A
definition is given as a quote with a name followed by a Joy
expression. for example:
[sqr dup mul] inscribe
'''
(name, body), stack = stack
inscribe(Def(name, body), dictionary)
return stack, expression, dictionary
@inscribe
@SimpleFunctionWrapper
def getitem(stack):
'''
::
getitem == drop first
Expects an integer and a quote on the stack and returns the item at the
nth position in the quote counting from 0.
::
[a b c d] 0 getitem
-------------------------
a
'''
n, (Q, stack) = stack
return pick(Q, n), stack
@inscribe
@SimpleFunctionWrapper
def drop(stack):
'''
::
drop == [rest] times
Expects an integer and a quote on the stack and returns the quote with
n items removed off the top.
::
[a b c d] 2 drop
----------------------
[c d]
'''
n, (Q, stack) = stack
while n > 0:
try:
_, Q = Q
except ValueError:
raise StackUnderflowError
n -= 1
return Q, stack
@inscribe
@SimpleFunctionWrapper
def take(stack):
'''
Expects an integer and a quote on the stack and returns the quote with
just the top n items in reverse order (because that's easier and you can
use reverse if needed.)
::
[a b c d] 2 take
----------------------
[b a]
'''
n, (Q, stack) = stack
x = ()
while n > 0:
try:
item, Q = Q
except ValueError:
raise StackUnderflowError
x = item, x
n -= 1
return x, stack
@inscribe
def gcd2(stack, expression, dictionary):
'''Compiled GCD function.'''
(v1, (v2, stack)) = stack
tos = True
while tos:
v3 = v2 % v1
tos = v3 > 0
(v1, (v2, stack)) = (v3, (v1, stack))
return (v2, stack), expression, dictionary
@inscribe
@SimpleFunctionWrapper
def choice(stack):
'''
Use a Boolean value to select one of two items.
::
A B false choice
----------------------
A
A B true choice
---------------------
B
'''
(if_, (then, (else_, stack))) = stack
assert isinstance(if_, bool), repr(if_)
return then if if_ else else_, stack
@inscribe
@SimpleFunctionWrapper
def select(stack):
'''
Use a Boolean value to select one of two items from a sequence.
::
[A B] false select
------------------------
A
[A B] true select
-----------------------
B
The sequence can contain more than two items but not fewer.
Currently Python semantics are used to evaluate the "truthiness" of the
Boolean value (so empty string, zero, etc. are counted as false, etc.)
'''
(flag, (choices, stack)) = stack
(else_, (then, _)) = choices
return then if flag else else_, stack
@inscribe
@SimpleFunctionWrapper
def max_(S):
'''Given a list find the maximum.'''
tos, stack = S
return max(iter_stack(tos)), stack
@inscribe
@SimpleFunctionWrapper
def min_(S):
'''Given a list find the minimum.'''
tos, stack = S
return min(iter_stack(tos)), stack
@inscribe
@SimpleFunctionWrapper
def sum_(S):
'''
Given a quoted sequence of numbers return the sum.
::
sum == 0 swap [+] step
'''
tos, stack = S
return sum(iter_stack(tos)), stack
@inscribe
@SimpleFunctionWrapper
def remove(S):
'''
Expects an item on the stack and a quote under it and removes that item
from the the quote. The item is only removed once. If the list is
empty or the item isn't in the list then the list is unchanged.
::
[1 2 3 1] 1 remove
------------------------
[2 3 1]
'''
(item, (quote, stack)) = S
return _remove(item, quote), stack
def _remove(item, quote):
try: head, tail = quote
except ValueError: return quote
return tail if head == item else (head, _remove(item, tail))
@inscribe
@SimpleFunctionWrapper
def unique(S):
'''Given a list remove duplicate items.'''
tos, stack = S
I = list(iter_stack(tos))
return list_to_stack(sorted(set(I), key=I.index)), stack
@inscribe
@SimpleFunctionWrapper
def sort_(S):
'''Given a list return it sorted.'''
tos, stack = S
return list_to_stack(sorted(iter_stack(tos))), stack
@inscribe
@SimpleFunctionWrapper
def disenstacken(stack):
'''
The disenstacken operator expects a list on top of the stack and makes that
the stack discarding the rest of the stack.
'''
return stack[0]
@inscribe
@SimpleFunctionWrapper
def reverse(S):
'''
Reverse the list on the top of the stack.
::
reverse == [] swap shunt
'''
(tos, stack) = S
res = ()
for term in iter_stack(tos):
res = term, res
return res, stack
@inscribe
@SimpleFunctionWrapper
def shunt(stack):
'''
Like concat but reverses the top list into the second.
::
shunt == [swons] step == reverse swap concat
[a b c] [d e f] shunt
---------------------------
[f e d a b c]
'''
(tos, (second, stack)) = stack
while tos:
term, tos = tos
second = term, second
return second, stack
@inscribe
@SimpleFunctionWrapper
def zip_(S):
'''
Replace the two lists on the top of the stack with a list of the pairs
from each list. The smallest list sets the length of the result list.
'''
(tos, (second, stack)) = S
accumulator = [
(a, (b, ()))
for a, b in zip(iter_stack(tos), iter_stack(second))
]
return list_to_stack(accumulator), stack
@inscribe
@SimpleFunctionWrapper
def succ(S):
'''Increment TOS.'''
(tos, stack) = S
return tos + 1, stack
@inscribe
@SimpleFunctionWrapper
def pred(S):
'''Decrement TOS.'''
(tos, stack) = S
return tos - 1, stack
@inscribe
@SimpleFunctionWrapper
def pm(stack):
'''
Plus or minus
::
a b pm
-------------
a+b a-b
'''
a, (b, stack) = stack
p, m, = b + a, b - a
return m, (p, stack)
@inscribe
def sharing(stack, expression, dictionary):
'''Print redistribution information.'''
print("You may convey verbatim copies of the Program's source code as"
' you receive it, in any medium, provided that you conspicuously'
' and appropriately publish on each copy an appropriate copyright'
' notice; keep intact all notices stating that this License and'
' any non-permissive terms added in accord with section 7 apply'
' to the code; keep intact all notices of the absence of any'
' warranty; and give all recipients a copy of this License along'
' with the Program.'
' You should have received a copy of the GNU General Public License'
' along with Thun. If not see <http://www.gnu.org/licenses/>.')
return stack, expression, dictionary
@inscribe
def warranty(stack, expression, dictionary):
'''Print warranty information.'''
print('THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY'
' APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE'
' COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM'
' "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR'
' IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES'
' OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE'
' ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS'
' WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE'
' COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.')
return stack, expression, dictionary
@inscribe
def x(stack, expr, dictionary):
'''
::
x == dup i
... [Q] x = ... [Q] dup i
... [Q] x = ... [Q] [Q] i
... [Q] x = ... [Q] Q
'''
quote, _ = stack
isnt_stack(quote)
return stack, push_quote(quote, expr), dictionary
@inscribe
def b(stack, expr, dictionary):
'''
::
b == [i] dip i
... [P] [Q] b == ... [P] i [Q] i
... [P] [Q] b == ... P Q
'''
q, (p, (stack)) = stack
isnt_stack(q)
isnt_stack(p)
expr = push_quote(q, expr)
expr = push_quote(p, expr)
return stack, expr, dictionary
@inscribe
def ii(stack, expr, dictionary):
'''
::
... a [Q] ii
------------------
... Q a Q
'''
quote, (a, stack) = stack
isnt_stack(quote)
expr = push_quote((a, quote), expr)
expr = push_quote(quote, expr)
return stack, expr, dictionary
@inscribe
def dupdip(stack, expr, dictionary):
'''
::
[F] dupdip == dup [F] dip
... a [F] dupdip
... a dup [F] dip
... a a [F] dip
... a F a
'''
quote, stack = stack
isnt_stack(quote)
a = stack[0]
expr = push_quote((a, ()), expr)
expr = push_quote(quote, expr)
return stack, expr, dictionary
S_swaack = Symbol('swaack')
@inscribe
def infra(stack, expr, dictionary):
'''
Accept a quoted program and a list on the stack and run the program
with the list as its stack. Does not affect the rest of the stack.
::
... [a b c] [Q] . infra
-----------------------------
c b a . Q [...] swaack
'''
quote, aggregate, stack = get_n_items(2, stack)
isnt_stack(quote)
isnt_stack(aggregate)
expr = push_quote((stack, (S_swaack, ())), expr)
expr = push_quote(quote, expr)
return aggregate, expr, dictionary
S_genrec = Symbol('genrec')
S_ifte = Symbol('ifte')
@inscribe
def genrec(stack, expr, dictionary):
'''
General Recursion Combinator.
::
[if] [then] [rec1] [rec2] genrec
---------------------------------------------------------------------
[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte
From "Recursion Theory and Joy" (j05cmp.html) by Manfred von Thun:
"The genrec combinator takes four program parameters in addition to
whatever data parameters it needs. Fourth from the top is an if-part,
followed by a then-part. If the if-part yields true, then the then-part
is executed and the combinator terminates. The other two parameters are
the rec1-part and the rec2-part. If the if-part yields false, the
rec1-part is executed. Following that the four program parameters and
the combinator are again pushed onto the stack bundled up in a quoted
form. Then the rec2-part is executed, where it will find the bundled
form. Typically it will then execute the bundled form, either with i or
with app2, or some other combinator."
The way to design one of these is to fix your base case [then] and the
test [if], and then treat rec1 and rec2 as an else-part "sandwiching"
a quotation of the whole function.
For example, given a (general recursive) function 'F':
::
F == [I] [T] [R1] [R2] genrec
If the [I] if-part fails you must derive R1 and R2 from:
::
... R1 [F] R2
Just set the stack arguments in front, and figure out what R1 and R2
have to do to apply the quoted [F] in the proper way. In effect, the
genrec combinator turns into an ifte combinator with a quoted copy of
the original definition in the else-part:
::
F == [I] [T] [R1] [R2] genrec
== [I] [T] [R1 [F] R2] ifte
Primitive recursive functions are those where R2 == i.
::
P == [I] [T] [R] tailrec
== [I] [T] [R [P] i] ifte
== [I] [T] [R P] ifte
'''
rec2, rec1, then, if_, stack = get_n_items(4, stack)
isnt_stack(if_)
isnt_stack(then)
isnt_stack(rec1)
isnt_stack(rec2)
F = (if_, (then, (rec1, (rec2, (S_genrec, ())))))
else_ = concat(rec1, (F, rec2))
stack = (else_, (then, (if_, stack)))
expr = push_quote((S_ifte, ()), expr)
return stack, expr, dictionary
S_infra = Symbol('infra')
S_first = Symbol('first')
@inscribe
def map_(stack, expr, dictionary):
'''
Run the quoted program on TOS on the items in the list under it, push a
new list with the results in place of the program and original list.
'''
quote, aggregate, stack = get_n_items(2, stack)
isnt_stack(quote)
isnt_stack(aggregate)
if not aggregate:
return (aggregate, stack), expr, dictionary
batch = ()
for term in iter_stack(aggregate):
s = term, stack
batch = (s, (quote, (S_infra, (S_first, batch))))
stack = (batch, ((), stack))
expr = push_quote((S_infra, ()), expr)
return stack, expr, dictionary
S_primrec = Symbol('primrec')
@inscribe
def primrec(stack, expr, dictionary):
'''
From the "Overview of the language JOY":
> The primrec combinator expects two quoted programs in addition to a
data parameter. For an integer data parameter it works like this: If
the data parameter is zero, then the first quotation has to produce
the value to be returned. If the data parameter is positive then the
second has to combine the data parameter with the result of applying
the function to its predecessor.::
5 [1] [*] primrec
> Then primrec tests whether the top element on the stack (initially
the 5) is equal to zero. If it is, it pops it off and executes one of
the quotations, the [1] which leaves 1 on the stack as the result.
Otherwise it pushes a decremented copy of the top element and
recurses. On the way back from the recursion it uses the other
quotation, [*], to multiply what is now a factorial on top of the
stack by the second element on the stack.::
n [Base] [Recur] primrec
0 [Base] [Recur] primrec
------------------------------
Base
n [Base] [Recur] primrec
------------------------------------------ n > 0
n (n-1) [Base] [Recur] primrec Recur
'''
recur, base, n, stack = get_n_items(3, stack)
isnt_stack(recur)
isnt_stack(base)
if n <= 0:
expr = push_quote(base, expr)
else:
expr = push_quote(recur, expr)
expr = push_quote((S_primrec, ()), expr)
stack = recur, (base, (n - 1, (n, stack)))
return stack, expr, dictionary
if __name__ == '__main__': if __name__ == '__main__':
import sys import sys
J = interp if '-q' in sys.argv else repl J = interp if '-q' in sys.argv else repl
dictionary = initialize() dictionary = initialize()
Def.load_definitions(__doc__.splitlines(), dictionary) Def.load_definitions(__doc__.splitlines(), dictionary)
try: ## try:
stack = J(dictionary=dictionary) ## stack = J(dictionary=dictionary)
except SystemExit: ## except SystemExit:
pass ## pass
stack, _ = run("5 [1] [*] primrec", (), dictionary)
print(stack_to_string(stack), '•')