def unify(lhs, rhs):
    res = {}
    try:
        unify_res(lhs, rhs, res)
    except Exception:
        return None
    return res


def unify_res(lhs, rhs, result):
    if lhs.name == 'VAR':
        unify_var(lhs, rhs, result)
    elif rhs.name == 'VAR':
        unify_var(rhs, lhs, result)
    else:
        left = lhs.children
        right = rhs.children
        if len(left) == len(right):
            for i in range(len(left)):
                unify_res(left[i], right[i], result)


def unify_var(var, rhs, result):
    if rhs.name in ['VAR', 'CONST', 'FUN'] and rhs.value != var.value:
        if var.value in result.keys() \
           and not result[var.value].equals(rhs):
            raise Exception('')
        else:
            result[var.value] = rhs