"""Logic expressions handling

NOTE
----

at present this is mainly needed for facts.py , feel free however to improve
this stuff for general purpose.
"""
from sympy.core.compatibility import iterable, cmp

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.
    """
    if x is None:
        return None
    return bool(x)

def fuzzy_and(*args):
    """Return True (all True), False (any False) or None.

    If `a` is an iterable it must not be empty; it
    can be an iterator.

    >>> 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
    """

    if len(args) == 2:
        a, b = [fuzzy_bool(i) for i in args]
        if a is True and b is True:
            return True
        elif a is False or b is False:
            return False
    elif (len(args) == 1 and iterable(args[0]) or
        len(args) > 2):
        if len(args) == 1:
            args = args[0]
        if args:
            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
    if not args:
        raise ValueError('fuzzy_and needs at least 1 argument')
    elif len(args) == 1:
        return fuzzy_bool(args[0])

def fuzzy_not(v):
    """'not' in fuzzy logic"""
    if v is None:
        return v
    else:
        return not v

class Logic(object):
    """Logical expression"""
    # {} 'op' -> LogicClass
    op_2class = {}

    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__(cls, other):
        if cls.__cmp__(other) == -1:
            return True
        return False


    def __cmp__(a, b):
        if type(a) is not type(b):
            return cmp( str(type(a)), str(type(b)) )

        else:
            return cmp(a.args, b.args)

    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

           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 term[0] == '!':
                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 = cls.flatten(bargs)
        args = set(args)

        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, *sorted(args, key=hash))


    @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 in range(len(self.args)):
            arg = self.args[i]
            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

        else:
            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