from typing import Optional, Set, Tuple from functools import lru_cache class Operation: def __init__(self, symbol: str, arity: int): self.symbol = symbol self.arity = arity self.hashed_value = hash(self.symbol) + self.arity def immutable(self, name, value): raise Exception("Operations are immutable") self.__setattr__ = immutable def __hash__(self): return self.hashed_value def __call__(self, *args): # Ensure the arity is met assert len(args) == self.arity # Ensure every argument is a term for t in args: assert isinstance(t, Term) return OpTerm(self, args) class Term: def __init__(self): pass def __lt__(self, y): return Inequation(self, y) class PropositionalVariable(Term): def __init__(self, name): self.name = name self.hashed_value = hash(self.name) def immutable(self, name, value): raise Exception("Propositional variables are immutable") self.__setattr__ = immutable def __hash__(self): return self.hashed_value def __str__(self): return self.name class OpTerm(Term): def __init__(self, operation: Operation, arguments): assert len(arguments) == operation.arity self.operation = operation self.arguments = arguments self.hashed_value = hash(self.operation) * hash(self.arguments) def immutable(self, name, value): raise Exception("Terms are immutable") self.__setattr__ = immutable def __hash__(self): return self.hashed_value def __str__(self): arg_strs = [str(a) for a in self.arguments] return self.operation.symbol + "(" + ",".join(arg_strs) + ")" # Standard operators Negation = Operation("¬", 1) Conjunction = Operation("∧", 2) Disjunction = Operation("∨", 2) Implication = Operation("→", 2) Necessitation = Operation("!", 1) class Inequation: def __init__(self, antecedant : Term, consequent: Term): self.antecedant = antecedant self.consequent = consequent def __str__(self): return str(self.antecedant) + "≤" + str(self.consequent) class InequalityRule: def __init__(self, premises : Set[Inequation], conclusion: Inequation): self.premises = premises self.conclusion = conclusion def __str__(self): str_premises = [str(p) for p in self.premises] str_premises2 = "{" + ",".join(str_premises) + "}" return str(str_premises2) + "=>" + str(self.conclusion) class Rule: def __init__(self, premises : Set[Term], conclusion: Term): self.premises = premises self.conclusion = conclusion def __str__(self): str_premises = [str(p) for p in self.premises] str_premises2 = "{" + ",".join(str_premises) + "}" return str(str_premises2) + "=>" + str(self.conclusion) class Logic: def __init__(self, operations: Set[Operation], rules: Set[Rule], name: Optional[str] = None): self.operations = operations self.rules = rules self.name = str(abs(hash(( frozenset(operations), frozenset(rules) ))))[:5] if name is None else name def get_prop_var_from_term(t: Term) -> Set[PropositionalVariable]: if isinstance(t, PropositionalVariable): return {t,} result: Set[PropositionalVariable] = set() for arg in t.arguments: result |= get_prop_var_from_term(arg) return result @lru_cache def get_propostional_variables(rules: Tuple[Rule]) -> Set[PropositionalVariable]: vars: Set[PropositionalVariable] = set() for rule in rules: # Get all vars in premises for premise in rule.premises: vars |= get_prop_var_from_term(premise) # Get vars in conclusion vars |= get_prop_var_from_term(rule.conclusion) return vars def get_operations_from_term(t: Term) -> Set[Operation]: if isinstance(t, PropositionalVariable): return set() result: Set[Operation] = {t.operation,} for arg in t.arguments: result |= get_operations_from_term(arg) return result