from typing import Any, TypeVar

from .semigroups_representation import MyFiniteSemigroup, MyFiniteMonoid, MyFiniteGroup

import act4e_interfaces as I

A = TypeVar("A")
B = TypeVar("B")


class SolFiniteSemigroupMorphismsChecks(I.FiniteSemigroupMorphismsChecks):
    def is_semigroup_morphism(self, a: I.FiniteSemigroup[A], b: I.FiniteSemigroup[B], f: I.FiniteMap[A, B]) -> bool:
        # Semigroup preserves the structure
        # f(xy) = f(x) f(y) for all x, y in a
        # converse:
        # there is an x or a y in a such that
        # f(xy) neq f(x) f(y)
        for x in a.carrier().elements():
            for y in a.carrier().elements():
                inside = f(a.compose(x, y))
                outside = b.compose(f(x), f(y))
                if not b.carrier().equal(inside, outside):
                    return False
        return True

    def is_monoid_morphism(self, a: I.FiniteMonoid[A], b: I.FiniteMonoid[B], f: I.FiniteMap[A, B]) -> bool:
        # Monoid morphism is a semigroup morphism that maps identity to identity
        if not self.is_semigroup_morphism(a, b, f):
            return False

        if not b.carrier().equal(b.identity(), f(a.identity())):
            return False

        return True


    def is_group_morphism(self, a: I.FiniteGroup[A], b: I.FiniteGroup[B], f: I.FiniteMap[A, B]) -> bool:
        # Group morphism preserve
        # f(xy) = f(x)f(y) for all x, y in a
        # converse is
        # exists x, y in a such that
        # f(xy) neq f(x)f(y)
        for x in a.carrier().elements():
            for y in a.carrier().elements():
                inside = f(a.compose(x, y))
                outside = b.compose(f(x), f(y))
                if not b.carrier().equal(inside, outside):
                    return False
        return True