from sympy.logic.boolalg import conjuncts
from sympy.assumptions import Q, ask


class AskHandler(object):
    """Base class that all Ask Handlers must inherit"""
    pass


class CommonHandler(AskHandler):
    """Defines some useful methods common to most Handlers """

    @staticmethod
    def NaN(expr, assumptions):
        return False

    @staticmethod
    def AlwaysTrue(expr, assumptions):
        return True

    @staticmethod
    def AlwaysFalse(expr, assumptions):
        return False


class AskCommutativeHandler(CommonHandler):
    """
    Handler for key 'commutative'
    """

    @staticmethod
    def Symbol(expr, assumptions):
        """Objects are expected to be commutative unless otherwise stated"""
        assumps = conjuncts(assumptions)
        if Q.commutative(expr) in assumps:
            return True
        elif ~Q.commutative(expr) in assumps:
            return False
        return True

    @staticmethod
    def Basic(expr, assumptions):
        for arg in expr.args:
            if not ask(Q.commutative(arg), assumptions):
                return False
        return True

    @staticmethod
    def Number(expr, assumptions):
        return True

    @staticmethod
    def NaN(expr, assumptions):
        return True


class TautologicalHandler(AskHandler):
    """Wrapper allowing to query the truth value of a boolean expression."""

    @staticmethod
    def bool(expr, assumptions):
        return expr

    @staticmethod
    def AppliedPredicate(expr, assumptions):
        return ask(expr, assumptions)

    @staticmethod
    def Not(expr, assumptions):
        value = ask(expr.args[0], assumptions=assumptions)
        if value in (True, False):
            return not value
        else:
            return None

    @staticmethod
    def Or(expr, assumptions):
        result = False
        for arg in expr.args:
            p = ask(arg, assumptions=assumptions)
            if p is True:
                return True
            if p is None:
                result = None
        return result

    @staticmethod
    def And(expr, assumptions):
        result = True
        for arg in expr.args:
            p = ask(arg, assumptions=assumptions)
            if p is False:
                return False
            if p is None:
                result = None
        return result

    @staticmethod
    def Implies(expr, assumptions):
        p, q = expr.args
        return ask(~p | q, assumptions=assumptions)

    @staticmethod
    def Equivalent(expr, assumptions):
        p, q = expr.args
        pt = ask(p, assumptions=assumptions)
        if pt is None:
            return None
        qt = ask(q, assumptions=assumptions)
        if qt is None:
            return None
        return pt == qt


#### Helper methods
def test_closed_group(expr, assumptions, key):
    """
    Test for membership in a group with respect
    to the current operation
    """
    result = True
    for arg in expr.args:
        _out = ask(key(arg), assumptions)
        if _out is None:
            break
        elif _out is False:
            if result:
                result = False
            else:
                break
    else:
        return result
