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"""Logic expressions handling
NOTE
----
at present this is mainly needed for facts.py, feel free however to improve
this stuff for general purpose.
"""
from __future__ import annotations
from typing import Optional
# Type of a fuzzy bool
FuzzyBool = Optional[bool]
def _torf(args):
"""Return True if all args are True, False if they
are all False, else None.
>>> from sympy.core.logic import _torf
>>> _torf((True, True))
True
>>> _torf((False, False))
False
>>> _torf((True, False))
"""
sawT = sawF = False
for a in args:
if a is True:
if sawF:
return
sawT = True
elif a is False:
if sawT:
return
sawF = True
else:
return
return sawT
def _fuzzy_group(args, quick_exit=False):
"""Return True if all args are True, None if there is any None else False
unless ``quick_exit`` is True (then return None as soon as a second False
is seen.
``_fuzzy_group`` is like ``fuzzy_and`` except that it is more
conservative in returning a False, waiting to make sure that all
arguments are True or False and returning None if any arguments are
None. It also has the capability of permiting only a single False and
returning None if more than one is seen. For example, the presence of a
single transcendental amongst rationals would indicate that the group is
no longer rational; but a second transcendental in the group would make the
determination impossible.
Examples
========
>>> from sympy.core.logic import _fuzzy_group
By default, multiple Falses mean the group is broken:
>>> _fuzzy_group([False, False, True])
False
If multiple Falses mean the group status is unknown then set
`quick_exit` to True so None can be returned when the 2nd False is seen:
>>> _fuzzy_group([False, False, True], quick_exit=True)
But if only a single False is seen then the group is known to
be broken:
>>> _fuzzy_group([False, True, True], quick_exit=True)
False
"""
saw_other = False
for a in args:
if a is True:
continue
if a is None:
return
if quick_exit and saw_other:
return
saw_other = True
return not saw_other
def fuzzy_bool(x):
"""Return True, False or None according to x.
Whereas bool(x) returns True or False, fuzzy_bool allows
for the None value and non-false values (which become None), too.
Examples
========
>>> from sympy.core.logic import fuzzy_bool
>>> from sympy.abc import x
>>> fuzzy_bool(x), fuzzy_bool(None)
(None, None)
>>> bool(x), bool(None)
(True, False)
"""
if x is None:
return None
if x in (True, False):
return bool(x)
def fuzzy_and(args):
"""Return True (all True), False (any False) or None.
Examples
========
>>> from sympy.core.logic import fuzzy_and
>>> from sympy import Dummy
If you had a list of objects to test the commutivity of
and you want the fuzzy_and logic applied, passing an
iterator will allow the commutativity to only be computed
as many times as necessary. With this list, False can be
returned after analyzing the first symbol:
>>> syms = [Dummy(commutative=False), Dummy()]
>>> fuzzy_and(s.is_commutative for s in syms)
False
That False would require less work than if a list of pre-computed
items was sent:
>>> fuzzy_and([s.is_commutative for s in syms])
False
"""
rv = True
for ai in args:
ai = fuzzy_bool(ai)
if ai is False:
return False
if rv: # this will stop updating if a None is ever trapped
rv = ai
return rv
def fuzzy_not(v):
"""
Not in fuzzy logic
Return None if `v` is None else `not v`.
Examples
========
>>> from sympy.core.logic import fuzzy_not
>>> fuzzy_not(True)
False
>>> fuzzy_not(None)
>>> fuzzy_not(False)
True
"""
if v is None:
return v
else:
return not v
def fuzzy_or(args):
"""
Or in fuzzy logic. Returns True (any True), False (all False), or None
See the docstrings of fuzzy_and and fuzzy_not for more info. fuzzy_or is
related to the two by the standard De Morgan's law.
>>> from sympy.core.logic import fuzzy_or
>>> fuzzy_or([True, False])
True
>>> fuzzy_or([True, None])
True
>>> fuzzy_or([False, False])
False
>>> print(fuzzy_or([False, None]))
None
"""
rv = False
for ai in args:
ai = fuzzy_bool(ai)
if ai is True:
return True
if rv is False: # this will stop updating if a None is ever trapped
rv = ai
return rv
def fuzzy_xor(args):
"""Return None if any element of args is not True or False, else
True (if there are an odd number of True elements), else False."""
t = f = 0
for a in args:
ai = fuzzy_bool(a)
if ai:
t += 1
elif ai is False:
f += 1
else:
return
return t % 2 == 1
def fuzzy_nand(args):
"""Return False if all args are True, True if they are all False,
else None."""
return fuzzy_not(fuzzy_and(args))
class Logic:
"""Logical expression"""
# {} 'op' -> LogicClass
op_2class: dict[str, type[Logic]] = {}
def __new__(cls, *args):
obj = object.__new__(cls)
obj.args = args
return obj
def __getnewargs__(self):
return self.args
def __hash__(self):
return hash((type(self).__name__,) + tuple(self.args))
def __eq__(a, b):
if not isinstance(b, type(a)):
return False
else:
return a.args == b.args
def __ne__(a, b):
if not isinstance(b, type(a)):
return True
else:
return a.args != b.args
def __lt__(self, other):
if self.__cmp__(other) == -1:
return True
return False
def __cmp__(self, other):
if type(self) is not type(other):
a = str(type(self))
b = str(type(other))
else:
a = self.args
b = other.args
return (a > b) - (a < b)
def __str__(self):
return '%s(%s)' % (self.__class__.__name__,
', '.join(str(a) for a in self.args))
__repr__ = __str__
@staticmethod
def fromstring(text):
"""Logic from string with space around & and | but none after !.
e.g.
!a & b | c
"""
lexpr = None # current logical expression
schedop = None # scheduled operation
for term in text.split():
# operation symbol
if term in '&|':
if schedop is not None:
raise ValueError(
'double op forbidden: "%s %s"' % (term, schedop))
if lexpr is None:
raise ValueError(
'%s cannot be in the beginning of expression' % term)
schedop = term
continue
if '&' in term or '|' in term:
raise ValueError('& and | must have space around them')
if term[0] == '!':
if len(term) == 1:
raise ValueError('do not include space after "!"')
term = Not(term[1:])
# already scheduled operation, e.g. '&'
if schedop:
lexpr = Logic.op_2class[schedop](lexpr, term)
schedop = None
continue
# this should be atom
if lexpr is not None:
raise ValueError(
'missing op between "%s" and "%s"' % (lexpr, term))
lexpr = term
# let's check that we ended up in correct state
if schedop is not None:
raise ValueError('premature end-of-expression in "%s"' % text)
if lexpr is None:
raise ValueError('"%s" is empty' % text)
# everything looks good now
return lexpr
class AndOr_Base(Logic):
def __new__(cls, *args):
bargs = []
for a in args:
if a == cls.op_x_notx:
return a
elif a == (not cls.op_x_notx):
continue # skip this argument
bargs.append(a)
args = sorted(set(cls.flatten(bargs)), key=hash)
for a in args:
if Not(a) in args:
return cls.op_x_notx
if len(args) == 1:
return args.pop()
elif len(args) == 0:
return not cls.op_x_notx
return Logic.__new__(cls, *args)
@classmethod
def flatten(cls, args):
# quick-n-dirty flattening for And and Or
args_queue = list(args)
res = []
while True:
try:
arg = args_queue.pop(0)
except IndexError:
break
if isinstance(arg, Logic):
if isinstance(arg, cls):
args_queue.extend(arg.args)
continue
res.append(arg)
args = tuple(res)
return args
class And(AndOr_Base):
op_x_notx = False
def _eval_propagate_not(self):
# !(a&b&c ...) == !a | !b | !c ...
return Or(*[Not(a) for a in self.args])
# (a|b|...) & c == (a&c) | (b&c) | ...
def expand(self):
# first locate Or
for i, arg in enumerate(self.args):
if isinstance(arg, Or):
arest = self.args[:i] + self.args[i + 1:]
orterms = [And(*(arest + (a,))) for a in arg.args]
for j in range(len(orterms)):
if isinstance(orterms[j], Logic):
orterms[j] = orterms[j].expand()
res = Or(*orterms)
return res
return self
class Or(AndOr_Base):
op_x_notx = True
def _eval_propagate_not(self):
# !(a|b|c ...) == !a & !b & !c ...
return And(*[Not(a) for a in self.args])
class Not(Logic):
def __new__(cls, arg):
if isinstance(arg, str):
return Logic.__new__(cls, arg)
elif isinstance(arg, bool):
return not arg
elif isinstance(arg, Not):
return arg.args[0]
elif isinstance(arg, Logic):
# XXX this is a hack to expand right from the beginning
arg = arg._eval_propagate_not()
return arg
else:
raise ValueError('Not: unknown argument %r' % (arg,))
@property
def arg(self):
return self.args[0]
Logic.op_2class['&'] = And
Logic.op_2class['|'] = Or
Logic.op_2class['!'] = Not
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