def a_construct():
return join_(
pair(I, I),
pair(BOT, TOP),
pair(div, BOT),
pair(a_copy, a_join),
pair(C, C),
a_preconj(a_construct),
a_postconj(a_construct),
a_compose(a_construct, a_construct),
)
def a_construct():
return join_(
app(pair, I, I),
app(pair, BOT, TOP),
app(pair, div, BOT),
app(pair, a_copy, a_join),
app(pair, C, C),
app(a_preconj, a_construct),
app(a_postconj, a_construct),
app(a_compose, a_construct, a_construct),
)
def close(f):
"""Scott's universal closure operator V."""
return lambda x: join_(x, app(f, close(x)))
def enum_union(xs, ys):
return join_(xs, ys)
def enum(items):
assert isinstance(items, (list, set, frozenset)), items
return join_(*map(box, items))
def build_A(*part_names):
return rec(join_(*(PARTS[name] for name in part_names)))
def div_rec_call(x):
return join_(x, div_rec_call(app(x, TOP)))
def _bits_test(b0, b1, b2, b3, b4, b5, b6, b7):
bits = [b0, b1, b2, b3, b4, b5, b6, b7]
tests = map(bool_test, bits)
return app(join_(*tests), *tests)
return app(x, QUOTE(true), QUOTE(false))
@combinator
def bool_if_true(x):
x = bool_type(x)
return unit_type(app(x, ok, undefined))
@combinator
def bool_if_false(x):
x = bool_type(x)
return unit_type(app(x, undefined, ok))
enum_bool = join_(APP(CI, true), APP(CI, false))
# ----------------------------------------------------------------------------
# Maybe
none = K
@combinator
def some(arg):
return APP(K, APP(CI, arg))
@combinator
def maybe_type(x):
from pomagma.reducer.sugar import _compile, app, as_term, combinator, join_
from pomagma.reducer.syntax import NVAR, TOP
from pomagma.util.testing import for_each
f = NVAR('f')
x = NVAR('x')
y = NVAR('y')
z = NVAR('z')
TERM_EXAMPLES = [
(I, I),
(I(K), K),
(K, K),
(app(S, I, I), app(S, I, I)),
(join_(K, I), join_(K, I)),
(S(I, I), app(S, I, I)),
(K | I, join_(K, I)),
# (TOP(K | I), TOP),
]
CLOSED_FUN_EXAMPLES = [
(lambda: x, x),
(lambda: B, B),
(lambda x: x, I),
(lambda x, y: x, K),
(lambda x, y: y, KI),
(lambda x: lambda y: x, K),
(lambda x: lambda x: x, KI),
(lambda x, y, z: app(x, z, y), C),
(lambda x, y, z: app(x, app(y, z)), B),
def _bits_test(b0, b1, b2, b3, b4, b5, b6, b7):
bits = [b0, b1, b2, b3, b4, b5, b6, b7]
tests = map(bool_test, bits)
all_defined = app(*tests)
any_error = join_(*tests)
return any_error(all_defined)
from pomagma.reducer import oracle
from pomagma.reducer.code import QUOTE, QQUOTE, QAPP
from pomagma.reducer.code import TOP, BOT, I, K, B, C, NVAR
from pomagma.reducer.sugar import app, join_
from pomagma.util.testing import for_each
import pytest
F = app(K, I)
J = join_(K, F)
x = NVAR('x')
y = NVAR('y')
def box(x):
return app(C, I, x)
ORDER_EXAMPLES = [
(TOP, TOP, True, True),
(TOP, BOT, False, True),
(TOP, I, False, True),
(TOP, K, False, True),
(TOP, F, False, True),
(TOP, J, False, True),
(BOT, BOT, True, True),
(BOT, I, True, False),
(BOT, K, True, False),
(BOT, F, True, False),
(BOT, J, True, False),
(I, I, True, True),
(I, K, False, False),
# Maybe
@for_each(
[
(lib.none, lib.none),
(lib.some(undefined), lib.some(undefined)),
(lib.some(error), lib.some(error)),
(lib.some(ok), lib.some(ok)),
(lib.some(true), lib.some(true)),
(lib.some(false), lib.some(false)),
(error, error),
(undefined, undefined),
(ok, error),
(join, error),
(join_(lib.none, lib.some(undefined)), error),
(join_(lib.some(true), lib.some(false)), lib.some(join)),
]
)
def test_maybe_type(x, expected):
assert simplify(lib.maybe_type(x)) == expected
@for_each([(lib.none, ok), (lib.some(x), ok), (error, error), (undefined, undefined)])
def test_maybe_test(x, expected):
assert simplify(lib.maybe_test(x)) == expected
@for_each(
[(lib.none, quote(lib.none)), (lib.some(true), quote(lib.some(true))), (undefined, undefined), (error, error)]
)
def div(f):
return join_(f, app(div, f, TOP))
def enum_maybe(enum_item):
return join_(box(none), enum_map(some, enum_item))
def a_join(f, x, y):
return app(f, join_(x, y))
def enum_sum(enum_inl, enum_inr):
return join_(enum_map(inl, enum_inl), enum_map(inr, enum_inr))
def unit_or(x, y):
return join_(x, y)
def enum_num():
return join_(box(zero), app(enum_map, succ, enum_num))
with pytest.raises(TypeError):
_compile(arg)
@for_each(OPEN_FUN_EXAMPLES)
def test_combinator_must_be_closed(arg, expected):
with pytest.raises(SyntaxError):
combinator(arg).code
@combinator
def Y(f):
return app(lambda x: app(f, app(x, x)), lambda x: app(f, app(x, x)))
div_Y = Y(lambda f, x: join_(x, app(f, app(x, TOP))))
@combinator
def div_rec_call(x):
return join_(x, div_rec_call(app(x, TOP)))
@combinator
def div_rec_app(x):
return join_(x, app(div_rec_app, app(x, TOP)))
@for_each([(div_rec_call, div_Y), (div_rec_app, div_Y)])
def test_combinator_recursion(arg, expected):
actual = arg.code
def enum_list(enum_item):
return join_(
box(nil),
app(enum_list(enum_item), lambda t:
app(enum_item, lambda h: box(cons(h, t)))),
)
def div_rec_app(x):
return join_(x, app(div_rec_app, app(x, TOP)))
compose := (\f,f'. f\r,s. f'\r',s'. <r o r', s' o s>).
A = A | <I, I> | <copy, join> | <div, BOT> | <BOT, TOP> | <C, C>
| preconj A | postconj A | compose A A.
"""
from parsable import parsable
from pomagma.reducer.bohm import (print_tiny, sexpr_simplify, simplify,
try_compute_step)
from pomagma.reducer.lib import BOT, TOP, B, C, I, box, pair
from pomagma.reducer.sugar import app, as_term, join_, rec
from pomagma.reducer.syntax import sexpr_print
CB = app(C, B)
div = rec(lambda a: join_(I, lambda x: app(a, x, TOP)))
copy = as_term(lambda x, y: app(x, y, y))
join = as_term(lambda x, y, z: app(x, join_(y, z)))
postconj = box(lambda r, s: pair(app(B, r), app(B, s)))
preconj = box(lambda r, s: pair(app(CB, s), app(CB, r)))
compose = as_term(lambda f1, f2:
app(f1, lambda r1, s1:
app(f2, lambda r2, s2:
pair(app(B, r1, r2), app(B, s2, s1)))))
# A = A | <I, I> | <copy, join> | <div, BOT> | <BOT, TOP> | <C, C>
# | preconj A | postconj A | compose A A.
PARTS = {
'base': as_term(lambda a: pair(I, I)),
'copy': as_term(lambda a: pair(copy, join)),