Thun/joy/library.py

# -*- coding: utf-8 -*-
#
#    Copyright © 2014, 2015, 2017, 2018 Simon Forman
#
#    This file is part of Joypy
#
#    Joypy 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.
#
#    Joypy 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.
#
#    You should have received a copy of the GNU General Public License
#    along with Joypy.  If not see <http://www.gnu.org/licenses/>.
#
'''
This module contains the Joy function infrastructure and a library of
functions.  It's 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
import operator, math

from .parser import text_to_expression, Symbol
from .utils.stack import list_to_stack, iter_stack, pick, pushback


_dictionary = {}


def inscribe(function):
  '''A decorator to inscribe functions in to the default dictionary.'''
  _dictionary[function.name] = function
  return function


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', ['•']),
  )


def add_aliases(D, A=ALIASES):
  '''
  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 = ('''\
second == rest first
third == rest rest first
of == swap at
product == 1 swap [*] step
swons == swap cons
swoncat == swap concat
flatten == [] swap [concat] step
unit == [] cons
quoted == [unit] dip
unquoted == [i] dip
enstacken == stack [clear] dip
disenstacken == ? [uncons ?] loop pop
? == dup truthy
dinfrirst == dip infra first
nullary == [stack] dinfrirst
unary == [stack [pop] dip] dinfrirst
binary == [stack [popop] dip] dinfrirst
ternary == [stack [popop pop] dip] dinfrirst
pam == [i] map
run == [] swap infra
sqr == dup mul
size == 0 swap [pop ++] step
cleave == [i] app2 [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
dudipd == dup dipd
primrec == [i] genrec
step_zero == 0 roll> step
'''

##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
)


class FunctionWrapper(object):
  '''
  Allow functions to have a nice repr().

  At some point it's likely this class and its subclasses would gain
  machinery to support type checking and inference.
  '''

  def __init__(self, f):
    self.f = f
    self.name = f.__name__.rstrip('_')  # Don't shadow builtins.
    self.__doc__ = f.__doc__ or str(f)

  def __call__(self, stack, expression, dictionary):
    '''
    Functions in general receive and return all three.
    '''
    return self.f(stack, expression, dictionary)

  def __repr__(self):
    return self.name


class SimpleFunctionWrapper(FunctionWrapper):
  '''
  Wrap functions that take and return just a stack.
  '''

  def __call__(self, stack, expression, dictionary):
    return self.f(stack), expression, dictionary


class BinaryBuiltinWrapper(FunctionWrapper):
  '''
  Wrap functions that take two arguments and return a single result.
  '''

  def __call__(self, stack, expression, dictionary):
    (a, (b, stack)) = stack
    result = self.f(b, a)
    return (result, stack), expression, dictionary


class UnaryBuiltinWrapper(FunctionWrapper):
  '''
  Wrap functions that take one argument and return a single result.
  '''

  def __call__(self, stack, expression, dictionary):
    (a, stack) = stack
    result = self.f(a)
    return (result, stack), expression, dictionary


class DefinitionWrapper(FunctionWrapper):
  '''
  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

  def __call__(self, stack, expression, dictionary):
    expression = list_to_stack(self._body, expression)
    return stack, expression, dictionary

  @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)

  @classmethod
  def add_definitions(class_, defs, dictionary):
    for definition in _text_to_defs(defs):
      class_.add_def(definition, dictionary)

  @classmethod
  def add_def(class_, definition, dictionary):
    F = class_.parse_definition(definition)
    dictionary[F.name] = F


def _text_to_defs(text):
  return filter(None, (line.strip() for line in text.splitlines()))


#
# Functions
#


@inscribe
@SimpleFunctionWrapper
def parse((text, stack)):
  '''Parse the string on the stack to a Joy expression.'''
  expression = text_to_expression(text)
  return expression, stack


@inscribe
@SimpleFunctionWrapper
def first(((head, tail), stack)):
  '''first == uncons pop'''
  return head, stack


@inscribe
@SimpleFunctionWrapper
def rest(((head, tail), stack)):
  '''rest == uncons popd'''
  return tail, stack


@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
@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


@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.

     [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


@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


@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 cons(S):
  '''
  The cons operator expects a list on top of the stack and the potential
  member below. The effect is to add the potential member into the
  aggregate.
  '''
  (tos, (second, stack)) = S
  return (second, tos), stack


@inscribe
@SimpleFunctionWrapper
def uncons(S):
  '''
  Inverse of cons, removes an item from the top of the list on the stack
  and places it under the remaining list.
  '''
  (tos, stack) = S
  item, tos = tos
  return tos, (item, stack)


@inscribe
@SimpleFunctionWrapper
def clear(stack):
  '''Clear everything from the stack.

     ... clear
  ---------------

  '''
  return ()


@inscribe
@SimpleFunctionWrapper
def dup(S):
  '''Duplicate the top item on the stack.'''
  (tos, stack) = S
  return tos, (tos, stack)


@inscribe
@SimpleFunctionWrapper
def over(S):
  '''
  Copy the second item down on the stack to the top of the stack.

     a b over
  --------------
      a b a

  '''
  second = S[1][0]
  return second, S


@inscribe
@SimpleFunctionWrapper
def tuck(S):
  '''
  Copy the item at TOS under the second item of the stack.

     a b tuck
  --------------
      b a b

  '''
  (tos, (second, stack)) = S
  return tos, (second, (tos, stack))


@inscribe
@SimpleFunctionWrapper
def swap(S):
  '''Swap the top two items on stack.'''
  (tos, (second, stack)) = S
  return second, (tos, stack)


@inscribe
@SimpleFunctionWrapper
def swaack(stack):
  '''swap stack'''
  old_stack, stack = stack
  return stack, old_stack


@inscribe
@SimpleFunctionWrapper
def stack_(stack):
  '''
  The stack operator pushes onto the stack a list containing all the
  elements of the stack.
  '''
  return stack, stack


@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]


@inscribe
@SimpleFunctionWrapper
def pop(stack):
  '''Pop and discard the top item from the stack.'''
  return stack[1]


@inscribe
@SimpleFunctionWrapper
def popd(stack):
  '''Pop and discard the second item from the stack.'''
  (tos, (_, stack)) = stack
  return tos, stack


@inscribe
@SimpleFunctionWrapper
def popdd(stack):
  '''Pop and discard the third item from the stack.'''
  (tos, (second, (_, stack))) = stack
  return tos, (second, stack)


@inscribe
@SimpleFunctionWrapper
def popop(stack):
  '''Pop and discard the first and second items from the stack.'''
  return stack[1][1]


@inscribe
@SimpleFunctionWrapper
def dupd(S):
  '''Duplicate the second item on the stack.'''
  (tos, (second, stack)) = S
  return tos, (second, (second, stack))


@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 concat(S):
  '''Concatinate the two lists on the top of the stack.'''
  (tos, (second, stack)) = S
  for term in reversed(list(iter_stack(second))):
    tos = term, tos
  return tos, stack


@inscribe
@SimpleFunctionWrapper
def shunt((tos, (second, stack))):
  '''
  shunt == [swons] step

  Like concat but reverses the top list into the second.
  '''
  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):
  return int(math.floor(n))

floor.__doc__ = math.floor.__doc__


@inscribe
@SimpleFunctionWrapper
def divmod_(S):
  a, (b, stack) = S
  d, m = divmod(a, b)
  return d, (m, stack)

divmod_.__doc__ = divmod.__doc__


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


@inscribe
@SimpleFunctionWrapper
def rollup(S):
  '''a b c -> b c a'''
  (a, (b, (c, stack))) = S
  return b, (c, (a, stack))


@inscribe
@SimpleFunctionWrapper
def rolldown(S):
  '''a b c -> c a b'''
  (a, (b, (c, stack))) = S
  return c, (a, (b, stack))


#def execute(S):
#  (text, stack) = S
#  if isinstance(text, str):
#    return run(text, stack)
#  return stack


@inscribe
@SimpleFunctionWrapper
def id_(stack):
  return stack


@inscribe
@SimpleFunctionWrapper
def void(stack):
  form, stack = stack
  return _void(form), stack


def _void(form):
  return any(not _void(i) for i in iter_stack(form))



##  transpose
##  sign
##  take


@inscribe
@FunctionWrapper
def words(stack, expression, dictionary):
  '''Print all the words in alphabetical order.'''
  print(' '.join(sorted(dictionary)))
  return stack, expression, dictionary


@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 Joypy.  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


# 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


@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')


@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, pushback(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, pushback(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, pushback(p, pushback(q, 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, pushback(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.

     ... [a b c] [Q] . infra
  -----------------------------
     c b a . Q [...] swaack

  '''
  (quote, (aggregate, stack)) = stack
  return aggregate, pushback(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] 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_ = pushback(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


#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


@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, pushback(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


@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, pushback(quote, expression), dictionary


@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, pushback(quote, expression), dictionary


@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, pushback(quote, expression), dictionary


@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


@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


@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


@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


@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 = pushback(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


@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 = pushback(quote, (quote, (S_loop, expression)))
  return stack, expression, dictionary


#def nullary(S, expression, dictionary):
#  '''
#  Run the program on TOS and return its first result without consuming
#  any of the stack (except the program on TOS.)
#  '''
#  (quote, stack) = S
#  result = joy(stack, quote, dictionary)
#  return (result[0][0], stack), expression, dictionary
#
#
#def unary(S, expression, dictionary):
#  (quote, stack) = S
#  _, return_stack = stack
#  result = joy(stack, quote, dictionary)[0]
#  return (result[0], return_stack), expression, dictionary
#
#
#def binary(S, expression, dictionary):
#  (quote, stack) = S
#  _, (_, return_stack) = stack
#  result = joy(stack, quote, dictionary)[0]
#  return (result[0], return_stack), expression, dictionary
#
#
#def ternary(S, expression, dictionary):
#  (quote, stack) = S
#  _, (_, (_, return_stack)) = stack
#  result = joy(stack, quote, dictionary)[0]
#  return (result[0], return_stack), expression, dictionary


#  FunctionWrapper(binary),
#  FunctionWrapper(cleave),
#  FunctionWrapper(nullary),
#  FunctionWrapper(ternary),
#  FunctionWrapper(unary),
#  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)


add_aliases(_dictionary)


DefinitionWrapper.add_definitions(definitions, _dictionary)