Source code for joy.library

# -*- coding: utf-8 -*-
#
#    Copyright © 2014, 2015, 2017, 2018 Simon Forman
#
#    This file is part of Thun
#
#    Thun is free software: you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation, either version 3 of the License, or
#    (at your option) any later version.
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#    Thun is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.
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#    You should have received a copy of the GNU General Public License
#    along with Thun.  If not see <http://www.gnu.org/licenses/>. 
#
'''
This module contains the Joy function infrastructure and a library of
functions.  Its main export is a Python function initialize() that
returns a dictionary of Joy functions suitable for use with the joy()
function.
'''
from inspect import getdoc
from functools import wraps
from inspect import getmembers, isfunction
import operator, math

from .parser import text_to_expression, Symbol
from .utils.stack import list_to_stack, iter_stack, pick, concat
from .utils.brutal_hackery import rename_code_object

from .utils import generated_library as genlib


_dictionary = {}


[docs]def inscribe(function): '''A decorator to inscribe functions into the default dictionary.''' _dictionary[function.name] = function return function
[docs]def initialize(): '''Return a dictionary of Joy functions for use with joy().''' return _dictionary.copy()
ALIASES = ( ('add', ['+']), ('and', ['&']), ('bool', ['truthy']), ('mul', ['*']), ('truediv', ['/']), ('mod', ['%', 'rem', 'remainder', 'modulus']), ('eq', ['=']), ('ge', ['>=']), ('getitem', ['pick', 'at']), ('gt', ['>']), ('le', ['<=']), ('lshift', ['<<']), ('lt', ['<']), ('ne', ['<>', '!=']), ('rshift', ['>>']), ('sub', ['-']), ('xor', ['^']), ('succ', ['++']), ('pred', ['--']), ('rolldown', ['roll<']), ('rollup', ['roll>']), ('id', [u'•']), )
[docs]def add_aliases(D, A): ''' Given a dict and a iterable of (name, [alias, ...]) pairs, create additional entries in the dict mapping each alias to the named function if it's in the dict. Aliases for functions not in the dict are ignored. ''' for name, aliases in A: try: F = D[name] except KeyError: continue for alias in aliases: D[alias] = F
definitions = ('''\ of == swap at product == 1 swap [*] step flatten == [] swap [concat] step quoted == [unit] dip unquoted == [i] dip enstacken == stack [clear] dip disenstacken == ? [uncons ?] loop pop ? == dup truthy dinfrirst == dip infra first nullary == [stack] dinfrirst unary == nullary popd binary == nullary [popop] dip ternary == unary [popop] dip pam == [i] map run == [] swap infra sqr == dup mul size == 0 swap [pop ++] step fork == [i] app2 cleave == fork [popd] dip average == [sum 1.0 *] [size] cleave / gcd == 1 [tuck modulus dup 0 >] loop pop least_fraction == dup [gcd] infra [div] concat map *fraction == [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons *fraction0 == concat [[swap] dip * [*] dip] infra down_to_zero == [0 >] [dup --] while range_to_zero == unit [down_to_zero] infra anamorphism == [pop []] swap [dip swons] genrec range == [0 <=] [1 - dup] anamorphism while == swap [nullary] cons dup dipd concat loop dupdipd == dup dipd primrec == [i] genrec step_zero == 0 roll> step codireco == cons dip rest cons make_generator == [codireco] ccons ifte == [nullary not] dipd branch ''' # # ifte == [nullary] dipd swap branch # genrec == [[genrec] cons cons cons cons] nullary swons concat ifte # Another definition for while. FWIW # while == over [[i] dip nullary] ccons [nullary] dip loop ##ccons == cons cons ##unit == [] cons ##second == rest first ##third == rest rest first ##swons == swap cons ##swoncat == swap concat ##Zipper ##z-down == [] swap uncons swap ##z-up == swons swap shunt ##z-right == [swons] cons dip uncons swap ##z-left == swons [uncons swap] dip swap ##Quadratic Formula ##divisor == popop 2 * ##minusb == pop neg ##radical == swap dup * rollup * 4 * - sqrt ##root1 == + swap / ##root2 == - swap / ##q0 == [[divisor] [minusb] [radical]] pam ##q1 == [[root1] [root2]] pam ##quadratic == [q0] ternary i [q1] ternary # Project Euler ##'''\ ##PE1.1 == + dup [+] dip ##PE1.2 == dup [3 & PE1.1] dip 2 >> ##PE1.3 == 14811 swap [PE1.2] times pop ##PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop ##''' #PE1.2 == [PE1.1] step #PE1 == 0 0 66 [[3 2 1 3 1 2 3] PE1.2] times [3 2 1 3] PE1.2 pop )
[docs]def FunctionWrapper(f): '''Set name attribute.''' if not f.__doc__: raise ValueError('Function %s must have doc string.' % f.__name__) f.name = f.__name__.rstrip('_') # Don't shadow builtins. return f
[docs]def SimpleFunctionWrapper(f): ''' Wrap functions that take and return just a stack. ''' @FunctionWrapper @wraps(f) @rename_code_object(f.__name__) def inner(stack, expression, dictionary): return f(stack), expression, dictionary return inner
[docs]def BinaryBuiltinWrapper(f): ''' Wrap functions that take two arguments and return a single result. ''' @FunctionWrapper @wraps(f) @rename_code_object(f.__name__) def inner(stack, expression, dictionary): (a, (b, stack)) = stack result = f(b, a) return (result, stack), expression, dictionary return inner
[docs]def UnaryBuiltinWrapper(f): ''' Wrap functions that take one argument and return a single result. ''' @FunctionWrapper @wraps(f) @rename_code_object(f.__name__) def inner(stack, expression, dictionary): (a, stack) = stack result = f(a) return (result, stack), expression, dictionary return inner
[docs]class DefinitionWrapper(object): ''' Provide implementation of defined functions, and some helper methods. ''' def __init__(self, name, body_text, doc=None): self.name = self.__name__ = name self.body = text_to_expression(body_text) self._body = tuple(iter_stack(self.body)) self.__doc__ = doc or body_text self._compiled = None def __call__(self, stack, expression, dictionary): if self._compiled: return self._compiled(stack, expression, dictionary) expression = list_to_stack(self._body, expression) return stack, expression, dictionary
[docs] @classmethod def parse_definition(class_, defi): ''' Given some text describing a Joy function definition parse it and return a DefinitionWrapper. ''' name, proper, body_text = (n.strip() for n in defi.partition('==')) if not proper: raise ValueError('Definition %r failed' % (defi,)) return class_(name, body_text)
[docs] @classmethod def add_definitions(class_, defs, dictionary): ''' Scan multi-line string defs for definitions and add them to the dictionary. ''' for definition in _text_to_defs(defs): class_.add_def(definition, dictionary)
[docs] @classmethod def add_def(class_, definition, dictionary): ''' Add the definition to the dictionary. ''' F = class_.parse_definition(definition) dictionary[F.name] = F
def _text_to_defs(text): return (line.strip() for line in text.splitlines() if '==' in line) # # Functions # # Load the auto-generated primitives into the dictionary. for name, primitive in getmembers(genlib, isfunction): inscribe(SimpleFunctionWrapper(primitive))
[docs]@inscribe @SimpleFunctionWrapper def parse(stack): '''Parse the string on the stack to a Joy expression.''' text, stack = stack expression = text_to_expression(text) return expression, stack
[docs]@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
[docs]@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
[docs]@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
[docs]@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 Currently Python semantics are used to evaluate the "truthiness" of the Boolean value (so empty string, zero, etc. are counted as false, etc.) ''' (if_, (then, (else_, stack))) = stack return then if if_ else else_, stack
[docs]@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
[docs]@inscribe @SimpleFunctionWrapper def max_(S): '''Given a list find the maximum.''' tos, stack = S return max(iter_stack(tos)), stack
[docs]@inscribe @SimpleFunctionWrapper def min_(S): '''Given a list find the minimum.''' tos, stack = S return min(iter_stack(tos)), stack
[docs]@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
[docs]@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. :: [1 2 3 1] 1 remove ------------------------ [2 3 1] ''' (tos, (second, stack)) = S l = list(iter_stack(second)) l.remove(tos) return list_to_stack(l), stack
[docs]@inscribe @SimpleFunctionWrapper def unique(S): '''Given a list remove duplicate items.''' tos, stack = S I = list(iter_stack(tos)) list_to_stack(sorted(set(I), key=I.index)) return list_to_stack(sorted(set(I), key=I.index)), stack
[docs]@inscribe @SimpleFunctionWrapper def sort_(S): '''Given a list return it sorted.''' tos, stack = S return list_to_stack(sorted(iter_stack(tos))), stack
[docs]@inscribe @SimpleFunctionWrapper def clear(stack): '''Clear everything from the stack. :: clear == stack [pop stack] loop ... clear --------------- ''' return ()
[docs]@inscribe @SimpleFunctionWrapper def unstack(stack): ''' The unstack operator expects a list on top of the stack and makes that the stack discarding the rest of the stack. ''' return stack[0]
[docs]@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
[docs]@inscribe @SimpleFunctionWrapper def concat_(S): '''Concatinate the two lists on the top of the stack. :: [a b c] [d e f] concat ---------------------------- [a b c d e f] ''' (tos, (second, stack)) = S return concat(second, tos), stack
[docs]@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
[docs]@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
[docs]@inscribe @SimpleFunctionWrapper def succ(S): '''Increment TOS.''' (tos, stack) = S return tos + 1, stack
[docs]@inscribe @SimpleFunctionWrapper def pred(S): '''Decrement TOS.''' (tos, stack) = S return tos - 1, stack
[docs]@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)
[docs]def floor(n): return int(math.floor(n))
floor.__doc__ = math.floor.__doc__
[docs]@inscribe @SimpleFunctionWrapper def divmod_(S): ''' divmod(x, y) -> (quotient, remainder) Return the tuple (x//y, x%y). Invariant: div*y + mod == x. ''' a, (b, stack) = S d, m = divmod(a, b) return d, (m, stack)
[docs]def sqrt(a): ''' Return the square root of the number a. Negative numbers return complex roots. ''' try: r = math.sqrt(a) except ValueError: assert a < 0, repr(a) r = math.sqrt(-a) * 1j return r
#def execute(S): # (text, stack) = S # if isinstance(text, str): # return run(text, stack) # return stack
[docs]@inscribe @SimpleFunctionWrapper def id_(stack): '''The identity function.''' return stack
[docs]@inscribe @SimpleFunctionWrapper def void(stack): '''True if the form on TOS is void otherwise False.''' form, stack = stack return _void(form), stack
def _void(form): return any(not _void(i) for i in iter_stack(form)) ## transpose ## sign ## take
[docs]@inscribe @FunctionWrapper def words(stack, expression, dictionary): '''Print all the words in alphabetical order.''' print(' '.join(sorted(dictionary))) return stack, expression, dictionary
[docs]@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
[docs]@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
# def simple_manual(stack): # ''' # Print words and help for each word. # ''' # for name, f in sorted(FUNCTIONS.items()): # d = getdoc(f) # boxline = '+%s+' % ('-' * (len(name) + 2)) # print('\n'.join(( # boxline, # '| %s |' % (name,), # boxline, # d if d else ' ...', # '', # '--' * 40, # '', # ))) # return stack
[docs]@inscribe @FunctionWrapper def help_(S, expression, dictionary): '''Accepts a quoted symbol on the top of the stack and prints its docs.''' ((symbol, _), stack) = S word = dictionary[symbol] print(getdoc(word)) return stack, expression, dictionary
# # § Combinators # # Several combinators depend on other words in their definitions, # we use symbols to prevent hard-coding these, so in theory, you # could change the word in the dictionary to use different semantics. S_choice = Symbol('choice') S_first = Symbol('first') S_getitem = Symbol('getitem') S_genrec = Symbol('genrec') S_loop = Symbol('loop') S_i = Symbol('i') S_ifte = Symbol('ifte') S_infra = Symbol('infra') S_step = Symbol('step') S_times = Symbol('times') S_swaack = Symbol('swaack') S_truthy = Symbol('truthy')
[docs]@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 ''' quote, stack = stack return stack, concat(quote, expression), dictionary
[docs]@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
[docs]@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
[docs]@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
[docs]@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. :: ... [a b c] [Q] . infra ----------------------------- c b a . Q [...] swaack ''' (quote, (aggregate, stack)) = stack return aggregate, concat(quote, (stack, (S_swaack, expression))), dictionary
[docs]@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] primrec == [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
[docs]@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
#def cleave(S, expression, dictionary): # ''' # The cleave combinator expects two quotations, and below that an item X. # It first executes [P], with X on top, and saves the top result element. # Then it executes [Q], again with X, and saves the top result. # Finally it restores the stack to what it was below X and pushes the two # results P(X) and Q(X). # ''' # (Q, (P, (x, stack))) = S # p = joy((x, stack), P, dictionary)[0][0] # q = joy((x, stack), Q, dictionary)[0][0] # return (q, (p, stack)), expression, dictionary
[docs]@inscribe @FunctionWrapper def branch(stack, expression, dictionary): ''' Use a Boolean value to select one of two quoted programs to run. :: branch == roll< choice i :: False [F] [T] branch -------------------------- F True [F] [T] branch ------------------------- T ''' (then, (else_, (flag, stack))) = stack return stack, concat(then if flag else else_, expression), dictionary
##@inscribe ##@FunctionWrapper ##def ifte(stack, expression, dictionary): ## ''' ## If-Then-Else Combinator ## :: ## ## ... [if] [then] [else] ifte ## --------------------------------------------------- ## ... [[else] [then]] [...] [if] infra select i ## ## ## ## ## ... [if] [then] [else] ifte ## ------------------------------------------------------- ## ... [else] [then] [...] [if] infra first choice i ## ## ## Has the effect of grabbing a copy of the stack on which to run the ## if-part using infra. ## ''' ## (else_, (then, (if_, stack))) = stack ## expression = (S_infra, (S_first, (S_choice, (S_i, expression)))) ## stack = (if_, (stack, (then, (else_, stack)))) ## return stack, expression, dictionary
[docs]@inscribe @FunctionWrapper def cond(stack, expression, dictionary): ''' This combinator works like a case statement. It expects a single quote on the stack that must contain zero or more condition quotes and a default quote. Each condition clause should contain a quoted predicate followed by the function expression to run if that predicate returns true. If no predicates return true the default function runs. It works by rewriting into a chain of nested `ifte` expressions, e.g.:: [[[B0] T0] [[B1] T1] [D]] cond ----------------------------------------- [B0] [T0] [[B1] [T1] [D] ifte] ifte ''' conditions, stack = stack if conditions: expression = _cond(conditions, expression) try: # Attempt to preload the args to first ifte. (P, (T, (E, expression))) = expression except ValueError: # If, for any reason, the argument to cond should happen to contain # only the default clause then this optimization will fail. pass else: stack = (E, (T, (P, stack))) return stack, expression, dictionary
def _cond(conditions, expression): (clause, rest) = conditions if not rest: # clause is [D] return clause P, T = clause return (P, (T, (_cond(rest, ()), (S_ifte, expression))))
[docs]@inscribe @FunctionWrapper def dip(stack, expression, dictionary): ''' The dip combinator expects a quoted program on the stack and below it some item, it hoists the item into the expression and runs the program on the rest of the stack. :: ... x [Q] dip ------------------- ... Q x ''' (quote, (x, stack)) = stack expression = (x, expression) return stack, concat(quote, expression), dictionary
[docs]@inscribe @FunctionWrapper def dipd(S, expression, dictionary): ''' Like dip but expects two items. :: ... y x [Q] dip --------------------- ... Q y x ''' (quote, (x, (y, stack))) = S expression = (y, (x, expression)) return stack, concat(quote, expression), dictionary
[docs]@inscribe @FunctionWrapper def dipdd(S, expression, dictionary): ''' Like dip but expects three items. :: ... z y x [Q] dip ----------------------- ... Q z y x ''' (quote, (x, (y, (z, stack)))) = S expression = (z, (y, (x, expression))) return stack, concat(quote, expression), dictionary
[docs]@inscribe @FunctionWrapper def app1(S, expression, dictionary): ''' Given a quoted program on TOS and anything as the second stack item run the program and replace the two args with the first result of the program. :: ... x [Q] . app1 ----------------------------------- ... [x ...] [Q] . infra first ''' (quote, (x, stack)) = S stack = (quote, ((x, stack), stack)) expression = (S_infra, (S_first, expression)) return stack, expression, dictionary
[docs]@inscribe @FunctionWrapper def app2(S, expression, dictionary): '''Like app1 with two items. :: ... y x [Q] . app2 ----------------------------------- ... [y ...] [Q] . infra first [x ...] [Q] infra first ''' (quote, (x, (y, stack))) = S expression = (S_infra, (S_first, ((x, stack), (quote, (S_infra, (S_first, expression)))))) stack = (quote, ((y, stack), stack)) return stack, expression, dictionary
[docs]@inscribe @FunctionWrapper def app3(S, expression, dictionary): '''Like app1 with three items. :: ... z y x [Q] . app3 ----------------------------------- ... [z ...] [Q] . infra first [y ...] [Q] infra first [x ...] [Q] infra first ''' (quote, (x, (y, (z, stack)))) = S expression = (S_infra, (S_first, ((y, stack), (quote, (S_infra, (S_first, ((x, stack), (quote, (S_infra, (S_first, expression)))))))))) stack = (quote, ((z, stack), stack)) return stack, expression, dictionary
[docs]@inscribe @FunctionWrapper def step(S, expression, dictionary): ''' Run a quoted program on each item in a sequence. :: ... [] [Q] . step ----------------------- ... . ... [a] [Q] . step ------------------------ ... a . Q ... [a b c] [Q] . step ---------------------------------------- ... a . Q [b c] [Q] step The step combinator executes the quotation on each member of the list on top of the stack. ''' (quote, (aggregate, stack)) = S if not aggregate: return stack, expression, dictionary head, tail = aggregate stack = quote, (head, stack) if tail: expression = tail, (quote, (S_step, expression)) expression = S_i, expression return stack, expression, dictionary
[docs]@inscribe @FunctionWrapper def times(stack, expression, dictionary): ''' times == [-- dip] cons [swap] infra [0 >] swap while pop :: ... n [Q] . times --------------------- w/ n <= 0 ... . ... 1 [Q] . times --------------------------------- ... . Q ... n [Q] . times --------------------------------- w/ n > 1 ... . Q (n - 1) [Q] times ''' # times == [-- dip] cons [swap] infra [0 >] swap while pop (quote, (n, stack)) = stack if n <= 0: return stack, expression, dictionary n -= 1 if n: expression = n, (quote, (S_times, expression)) expression = concat(quote, expression) return stack, expression, dictionary
# The current definition above works like this: # [P] [Q] while # -------------------------------------- # [P] nullary [Q [P] nullary] loop # while == [pop i not] [popop] [dudipd] primrec #def while_(S, expression, dictionary): # '''[if] [body] while''' # (body, (if_, stack)) = S # while joy(stack, if_, dictionary)[0][0]: # stack = joy(stack, body, dictionary)[0] # return stack, expression, dictionary
[docs]@inscribe @FunctionWrapper def loop(stack, expression, dictionary): ''' Basic loop combinator. :: ... True [Q] loop ----------------------- ... Q [Q] loop ... False [Q] loop ------------------------ ... ''' quote, (flag, stack) = stack if flag: expression = concat(quote, (quote, (S_loop, expression))) return stack, expression, dictionary
[docs]@inscribe @FunctionWrapper def cmp_(stack, expression, dictionary): ''' cmp takes two values and three quoted programs on the stack and runs one of the three depending on the results of comparing the two values: :: a b [G] [E] [L] cmp ------------------------- a > b G a b [G] [E] [L] cmp ------------------------- a = b E a b [G] [E] [L] cmp ------------------------- a < b L ''' L, (E, (G, (b, (a, stack)))) = stack expression = concat(G if a > b else L if a < b else E, expression) return stack, expression, dictionary
# FunctionWrapper(cleave), # FunctionWrapper(while_), for F in ( BinaryBuiltinWrapper(operator.add), BinaryBuiltinWrapper(operator.and_), BinaryBuiltinWrapper(operator.div), BinaryBuiltinWrapper(operator.eq), BinaryBuiltinWrapper(operator.floordiv), BinaryBuiltinWrapper(operator.ge), BinaryBuiltinWrapper(operator.gt), BinaryBuiltinWrapper(operator.le), BinaryBuiltinWrapper(operator.lshift), BinaryBuiltinWrapper(operator.lt), BinaryBuiltinWrapper(operator.mod), BinaryBuiltinWrapper(operator.mul), BinaryBuiltinWrapper(operator.ne), BinaryBuiltinWrapper(operator.or_), BinaryBuiltinWrapper(operator.pow), BinaryBuiltinWrapper(operator.rshift), BinaryBuiltinWrapper(operator.sub), BinaryBuiltinWrapper(operator.truediv), BinaryBuiltinWrapper(operator.xor), UnaryBuiltinWrapper(abs), UnaryBuiltinWrapper(bool), UnaryBuiltinWrapper(floor), UnaryBuiltinWrapper(operator.neg), UnaryBuiltinWrapper(operator.not_), UnaryBuiltinWrapper(sqrt), ): inscribe(F) del F # Otherwise Sphinx autodoc will pick it up. add_aliases(_dictionary, ALIASES) DefinitionWrapper.add_definitions(definitions, _dictionary)