matmod/model.py

"""
Defining what it means to be a model
"""
from common import set_to_str
from logic import (
PropositionalVariable, get_propostional_variables, Logic, Term,
Operation, Conjunction, Disjunction, Implication
)
from typing import Set, Dict, Tuple, Optional
from functools import lru_cache
from itertools import combinations, chain, product
from copy import deepcopy


__all__ = ['ModelValue', 'ModelFunction', 'Model']



class ModelValue:
    def __init__(self, name):
        self.name = name
        self.hashed_value = hash(self.name)
        def immutable(self, name, value):
            raise Exception("Model values are immutable")
        self.__setattr__ = immutable
    def __str__(self):
        return self.name
    def __hash__(self):
        return self.hashed_value
    def __eq__(self, other):
        return isinstance(other, ModelValue) and self.name == other.name
    def __lt__(self, other):
        assert isinstance(other, ModelValue)
        return ModelOrderConstraint(self, other)


class ModelFunction:
    def __init__(self, arity: int, mapping, operation_name = ""):
        self.operation_name = operation_name
        self.arity = arity

        # Correct input to always be a tuple
        corrected_mapping = dict()
        for k, v in mapping.items():
            if isinstance(k, tuple):
                assert len(k) == arity
                corrected_mapping[k] = v
            elif isinstance(k, list):
                assert len(k) == arity
                corrected_mapping[tuple(k)] = v
            else: # Assume it's atomic
                assert arity == 1
                corrected_mapping[(k,)] = v

        self.mapping = corrected_mapping

    def __str__(self):
        str_dict = dict()
        for k, v in self.mapping.items():
            inputstr = "(" + ", ".join(str(ki) for ki in k) + ")"
            str_dict[inputstr] = str(v)
        return str(str_dict)

    def __call__(self, *args):
        return self.mapping[args]

    # def __eq__(self, other):
    #     return isinstance(other, ModelFunction) and self.name == other.name and self.arity == other.arity

class ModelOrderConstraint:
    # a < b
    def __init__(self, a: ModelValue, b: ModelValue):
        self.a = a
        self.b = b
    def __hash__(self):
        return hash(self.a) * hash(self.b)
    def __eq__(self, other):
        return isinstance(other, ModelOrderConstraint) and \
            self.a == other.a and self.b == other.b

class Model:
    def __init__(
            self,
            carrier_set: Set[ModelValue],
            logical_operations: Set[ModelFunction],
            designated_values: Set[ModelValue],
            ordering: Optional[Set[ModelOrderConstraint]] = None
    ):
        assert designated_values <= carrier_set
        self.carrier_set = carrier_set
        self.logical_operations = logical_operations
        self.designated_values = designated_values
        self.ordering = ordering  if ordering is not None else set()
        # TODO: Make sure ordering is "valid"
        # That is: transitive, etc.

    def __str__(self):
        result = f"""Carrier Set: {set_to_str(self.carrier_set)}
Designated Values: {set_to_str(self.designated_values)}
"""
        for function in self.logical_operations:
            result += f"{str(function)}\n"

        return result


def evaluate_term(t: Term, f: Dict[PropositionalVariable, ModelValue], interpretation: Dict[Operation, ModelFunction]) -> ModelValue:
    if isinstance(t, PropositionalVariable):
        return f[t]

    model_function = interpretation[t.operation]
    model_arguments = []
    for logic_arg in t.arguments:
        model_arg = evaluate_term(logic_arg, f, interpretation)
        model_arguments.append(model_arg)

    return model_function(*model_arguments)

def all_model_valuations(
        pvars: Tuple[PropositionalVariable],
        mvalues: Tuple[ModelValue]):

    possible_valuations = [mvalues for _ in pvars]
    all_possible_values = product(*possible_valuations)

    for valuation in all_possible_values:
        mapping: Dict[PropositionalVariable, ModelValue] = dict()
        assert len(pvars) == len(valuation)
        for pvar, value in zip(pvars, valuation):
            mapping[pvar] = value
        yield mapping

@lru_cache
def all_model_valuations_cached(
        pvars: Tuple[PropositionalVariable],
        mvalues: Tuple[ModelValue]):
    return list(all_model_valuations(pvars, mvalues))

def rule_ordering_satisfied(model: Model, interpretation: Dict[Operation, ModelFunction]) -> bool:
    """
    Currently testing whether this function helps with runtime...
    """
    if Conjunction in interpretation:
        possible_inputs = ((a, b) for (a, b) in product(model.carrier_set, model.carrier_set))
        for a, b in possible_inputs:
            output = interpretation[Conjunction](a, b)
            if a < b in model.ordering and output != a:
                print("RETURNING FALSE")
                return False
            if b < a in model.ordering and output != b:
                print("RETURNING FALSE")
                return False

    if Disjunction in interpretation:
        possible_inputs = ((a, b) for (a, b) in product(model.carrier_set, model.carrier_set))
        for a, b in possible_inputs:
            output = interpretation[Disjunction](a, b)
            if a < b in model.ordering and output != b:
                print("RETURNING FALSE")
                return False
            if b < a in model.ordering and output != a:
                print("RETURNING FALSE")
                return False

    return True



def satisfiable(logic: Logic, model: Model, interpretation: Dict[Operation, ModelFunction]) -> bool:
    pvars = tuple(get_propostional_variables(tuple(logic.rules)))
    mappings = all_model_valuations_cached(pvars, tuple(model.carrier_set))

    # NOTE: Does not look like rule ordering is helping for finding
    # models of R...
    if not rule_ordering_satisfied(model, interpretation):
        return False

    for mapping in mappings:
        for rule in logic.rules:
            premise_met = True
            premise_ts = set()
            for premise in rule.premises:
                premise_t = evaluate_term(premise, mapping, interpretation)
                if premise_t not in model.designated_values:
                    premise_met = False
                    break
                premise_ts.add(premise_t)

            if not premise_met:
                continue

            consequent_t = evaluate_term(rule.conclusion, mapping, interpretation)

            if consequent_t not in model.designated_values:
                return False

    return True


def model_closure(initial_set: Set[ModelValue], mfunctions: Set[ModelFunction]):
    last_set: Set[ModelValue] = set()
    current_set: Set[ModelValue] = initial_set

    while last_set != current_set:
        last_set = deepcopy(current_set)

        for mfun in mfunctions:
            # Get output for every possible input configuration
            # from last_set
            for args in product(*(last_set for _ in range(mfun.arity))):
                current_set.add(mfun(*args))

    return current_set

def violates_vsp(model: Model, interpretation: Dict[Operation, ModelFunction]) -> bool:
    """
    Tells you whether a model violates the
    variable sharing property.

    If it returns false, it is still possible that
    the variable sharing property is violated
    just that we didn't check for the appopriate
    subalgebras.
    """

    impfunction = interpretation[Implication]

    # Compute I the set of tuples (x, y) where
    # x -> y does not take a designiated value
    I: Set[Tuple[ModelValue, ModelValue]] = set()

    for (x, y) in product(model.carrier_set, model.carrier_set):
        if impfunction(x, y) not in model.designated_values:
            I.add((x, y))

    # Construct the powerset without the empty set
    s = list(I)
    I_power = chain.from_iterable(combinations(s, r) for r in range(1, len(s) + 1))
    # ((x1, y1)), ((x1, y1), (x2, y2)), ...

    for xys in I_power:
        # Compute the closure of all operations
        # with just the xs
        xs = {xy[0] for xy in xys}
        carrier_set_left: Set[ModelValue] = model_closure(xs, model.logical_operations)

        # Compute the closure of all operations
        # with just the ys
        ys = {xy[1] for xy in xys}
        carrier_set_right: Set[ModelValue] = model_closure(ys, model.logical_operations)

        # If the carrier set intersects, then we violate VSP
        if len(carrier_set_left & carrier_set_right) > 0:
            print("FAIL: Carrier sets intersect")
            return True

        for (x2, y2) in product(carrier_set_left, carrier_set_right):
            if impfunction(x2, y2) in model.designated_values:
                print(f"({x2}, {y2}) take on a designated value")
                return True

    return False