452 lines
16 KiB
Python
452 lines
16 KiB
Python
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# Natural Language Toolkit: Linear Logic
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#
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# Author: Dan Garrette <dhgarrette@gmail.com>
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#
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# Copyright (C) 2001-2018 NLTK Project
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# URL: <http://nltk.org/>
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# For license information, see LICENSE.TXT
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from __future__ import print_function, unicode_literals
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from six import string_types
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from nltk.internals import Counter
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from nltk.compat import python_2_unicode_compatible
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from nltk.sem.logic import LogicParser, APP
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_counter = Counter()
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class Tokens(object):
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#Punctuation
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OPEN = '('
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CLOSE = ')'
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#Operations
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IMP = '-o'
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PUNCT = [OPEN, CLOSE]
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TOKENS = PUNCT + [IMP]
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class LinearLogicParser(LogicParser):
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"""A linear logic expression parser."""
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def __init__(self):
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LogicParser.__init__(self)
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self.operator_precedence = {APP: 1, Tokens.IMP: 2, None: 3}
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self.right_associated_operations += [Tokens.IMP]
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def get_all_symbols(self):
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return Tokens.TOKENS
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def handle(self, tok, context):
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if tok not in Tokens.TOKENS:
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return self.handle_variable(tok, context)
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elif tok == Tokens.OPEN:
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return self.handle_open(tok, context)
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def get_BooleanExpression_factory(self, tok):
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if tok == Tokens.IMP:
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return ImpExpression
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else:
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return None
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def make_BooleanExpression(self, factory, first, second):
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return factory(first, second)
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def attempt_ApplicationExpression(self, expression, context):
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"""Attempt to make an application expression. If the next tokens
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are an argument in parens, then the argument expression is a
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function being applied to the arguments. Otherwise, return the
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argument expression."""
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if self.has_priority(APP, context):
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if self.inRange(0) and self.token(0) == Tokens.OPEN:
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self.token() #swallow then open paren
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argument = self.process_next_expression(APP)
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self.assertNextToken(Tokens.CLOSE)
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expression = ApplicationExpression(expression, argument, None)
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return expression
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def make_VariableExpression(self, name):
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if name[0].isupper():
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return VariableExpression(name)
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else:
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return ConstantExpression(name)
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@python_2_unicode_compatible
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class Expression(object):
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_linear_logic_parser = LinearLogicParser()
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@classmethod
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def fromstring(cls, s):
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return cls._linear_logic_parser.parse(s)
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def applyto(self, other, other_indices=None):
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return ApplicationExpression(self, other, other_indices)
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def __call__(self, other):
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return self.applyto(other)
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def __repr__(self):
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return '<%s %s>' % (self.__class__.__name__, self)
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@python_2_unicode_compatible
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class AtomicExpression(Expression):
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def __init__(self, name, dependencies=None):
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"""
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:param name: str for the constant name
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:param dependencies: list of int for the indices on which this atom is dependent
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"""
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assert isinstance(name, string_types)
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self.name = name
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if not dependencies:
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dependencies = []
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self.dependencies = dependencies
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def simplify(self, bindings=None):
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"""
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If 'self' is bound by 'bindings', return the atomic to which it is bound.
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Otherwise, return self.
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:param bindings: ``BindingDict`` A dictionary of bindings used to simplify
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:return: ``AtomicExpression``
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"""
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if bindings and self in bindings:
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return bindings[self]
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else:
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return self
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def compile_pos(self, index_counter, glueFormulaFactory):
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"""
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From Iddo Lev's PhD Dissertation p108-109
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:param index_counter: ``Counter`` for unique indices
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:param glueFormulaFactory: ``GlueFormula`` for creating new glue formulas
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:return: (``Expression``,set) for the compiled linear logic and any newly created glue formulas
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"""
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self.dependencies = []
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return (self, [])
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def compile_neg(self, index_counter, glueFormulaFactory):
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"""
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From Iddo Lev's PhD Dissertation p108-109
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:param index_counter: ``Counter`` for unique indices
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:param glueFormulaFactory: ``GlueFormula`` for creating new glue formulas
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:return: (``Expression``,set) for the compiled linear logic and any newly created glue formulas
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"""
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self.dependencies = []
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return (self, [])
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def initialize_labels(self, fstruct):
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self.name = fstruct.initialize_label(self.name.lower())
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def __eq__(self, other):
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return self.__class__ == other.__class__ and self.name == other.name
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def __ne__(self, other):
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return not self == other
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def __str__(self):
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accum = self.name
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if self.dependencies:
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accum += "%s" % self.dependencies
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return accum
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def __hash__(self):
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return hash(self.name)
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class ConstantExpression(AtomicExpression):
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def unify(self, other, bindings):
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"""
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If 'other' is a constant, then it must be equal to 'self'. If 'other' is a variable,
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then it must not be bound to anything other than 'self'.
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:param other: ``Expression``
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:param bindings: ``BindingDict`` A dictionary of all current bindings
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:return: ``BindingDict`` A new combined dictionary of of 'bindings' and any new binding
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:raise UnificationException: If 'self' and 'other' cannot be unified in the context of 'bindings'
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"""
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assert isinstance(other, Expression)
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if isinstance(other, VariableExpression):
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try:
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return bindings + BindingDict([(other, self)])
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except VariableBindingException:
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pass
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elif self == other:
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return bindings
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raise UnificationException(self, other, bindings)
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class VariableExpression(AtomicExpression):
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def unify(self, other, bindings):
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"""
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'self' must not be bound to anything other than 'other'.
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:param other: ``Expression``
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:param bindings: ``BindingDict`` A dictionary of all current bindings
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:return: ``BindingDict`` A new combined dictionary of of 'bindings' and the new binding
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:raise UnificationException: If 'self' and 'other' cannot be unified in the context of 'bindings'
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"""
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assert isinstance(other, Expression)
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try:
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if self == other:
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return bindings
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else:
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return bindings + BindingDict([(self, other)])
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except VariableBindingException:
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raise UnificationException(self, other, bindings)
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@python_2_unicode_compatible
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class ImpExpression(Expression):
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def __init__(self, antecedent, consequent):
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"""
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:param antecedent: ``Expression`` for the antecedent
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:param consequent: ``Expression`` for the consequent
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"""
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assert isinstance(antecedent, Expression)
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assert isinstance(consequent, Expression)
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self.antecedent = antecedent
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self.consequent = consequent
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def simplify(self, bindings=None):
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return self.__class__(self.antecedent.simplify(bindings), self.consequent.simplify(bindings))
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def unify(self, other, bindings):
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"""
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Both the antecedent and consequent of 'self' and 'other' must unify.
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:param other: ``ImpExpression``
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:param bindings: ``BindingDict`` A dictionary of all current bindings
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:return: ``BindingDict`` A new combined dictionary of of 'bindings' and any new bindings
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:raise UnificationException: If 'self' and 'other' cannot be unified in the context of 'bindings'
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"""
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assert isinstance(other, ImpExpression)
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try:
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return bindings + self.antecedent.unify(other.antecedent, bindings) + self.consequent.unify(other.consequent, bindings)
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except VariableBindingException:
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raise UnificationException(self, other, bindings)
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def compile_pos(self, index_counter, glueFormulaFactory):
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"""
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From Iddo Lev's PhD Dissertation p108-109
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:param index_counter: ``Counter`` for unique indices
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:param glueFormulaFactory: ``GlueFormula`` for creating new glue formulas
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:return: (``Expression``,set) for the compiled linear logic and any newly created glue formulas
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"""
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(a, a_new) = self.antecedent.compile_neg(index_counter, glueFormulaFactory)
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(c, c_new) = self.consequent.compile_pos(index_counter, glueFormulaFactory)
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return (ImpExpression(a,c), a_new + c_new)
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def compile_neg(self, index_counter, glueFormulaFactory):
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"""
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From Iddo Lev's PhD Dissertation p108-109
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:param index_counter: ``Counter`` for unique indices
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:param glueFormulaFactory: ``GlueFormula`` for creating new glue formulas
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:return: (``Expression``,list of ``GlueFormula``) for the compiled linear logic and any newly created glue formulas
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"""
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(a, a_new) = self.antecedent.compile_pos(index_counter, glueFormulaFactory)
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(c, c_new) = self.consequent.compile_neg(index_counter, glueFormulaFactory)
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fresh_index = index_counter.get()
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c.dependencies.append(fresh_index)
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new_v = glueFormulaFactory('v%s' % fresh_index, a, set([fresh_index]))
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return (c, a_new + c_new + [new_v])
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def initialize_labels(self, fstruct):
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self.antecedent.initialize_labels(fstruct)
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self.consequent.initialize_labels(fstruct)
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def __eq__(self, other):
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return self.__class__ == other.__class__ and \
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self.antecedent == other.antecedent and self.consequent == other.consequent
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def __ne__(self, other):
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return not self == other
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def __str__(self):
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return "%s%s %s %s%s" % (
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Tokens.OPEN, self.antecedent, Tokens.IMP, self.consequent, Tokens.CLOSE)
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def __hash__(self):
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return hash('%s%s%s' % (hash(self.antecedent), Tokens.IMP, hash(self.consequent)))
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@python_2_unicode_compatible
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class ApplicationExpression(Expression):
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def __init__(self, function, argument, argument_indices=None):
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"""
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:param function: ``Expression`` for the function
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:param argument: ``Expression`` for the argument
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:param argument_indices: set for the indices of the glue formula from which the argument came
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:raise LinearLogicApplicationException: If 'function' cannot be applied to 'argument' given 'argument_indices'.
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"""
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function_simp = function.simplify()
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argument_simp = argument.simplify()
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assert isinstance(function_simp, ImpExpression)
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assert isinstance(argument_simp, Expression)
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bindings = BindingDict()
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try:
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if isinstance(function, ApplicationExpression):
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bindings += function.bindings
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if isinstance(argument, ApplicationExpression):
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bindings += argument.bindings
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bindings += function_simp.antecedent.unify(argument_simp, bindings)
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except UnificationException as e:
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raise LinearLogicApplicationException('Cannot apply %s to %s. %s' % (function_simp, argument_simp, e))
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# If you are running it on complied premises, more conditions apply
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if argument_indices:
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# A.dependencies of (A -o (B -o C)) must be a proper subset of argument_indices
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if not set(function_simp.antecedent.dependencies) < argument_indices:
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raise LinearLogicApplicationException('Dependencies unfulfilled when attempting to apply Linear Logic formula %s to %s' % (function_simp, argument_simp))
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if set(function_simp.antecedent.dependencies) == argument_indices:
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raise LinearLogicApplicationException('Dependencies not a proper subset of indices when attempting to apply Linear Logic formula %s to %s' % (function_simp, argument_simp))
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self.function = function
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self.argument = argument
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self.bindings = bindings
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def simplify(self, bindings=None):
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"""
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Since function is an implication, return its consequent. There should be
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no need to check that the application is valid since the checking is done
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by the constructor.
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:param bindings: ``BindingDict`` A dictionary of bindings used to simplify
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:return: ``Expression``
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"""
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if not bindings:
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bindings = self.bindings
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return self.function.simplify(bindings).consequent
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def __eq__(self, other):
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return self.__class__ == other.__class__ and \
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self.function == other.function and self.argument == other.argument
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def __ne__(self, other):
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return not self == other
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def __str__(self):
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return "%s" % self.function + Tokens.OPEN + "%s" % self.argument + Tokens.CLOSE
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def __hash__(self):
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return hash('%s%s%s' % (hash(self.antecedent), Tokens.OPEN, hash(self.consequent)))
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@python_2_unicode_compatible
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class BindingDict(object):
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def __init__(self, bindings=None):
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"""
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:param bindings:
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list [(``VariableExpression``, ``AtomicExpression``)] to initialize the dictionary
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dict {``VariableExpression``: ``AtomicExpression``} to initialize the dictionary
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"""
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self.d = {}
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if isinstance(bindings, dict):
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bindings = bindings.items()
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if bindings:
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for (v, b) in bindings:
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self[v] = b
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def __setitem__(self, variable, binding):
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"""
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A binding is consistent with the dict if its variable is not already bound, OR if its
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variable is already bound to its argument.
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:param variable: ``VariableExpression`` The variable bind
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:param binding: ``Expression`` The expression to which 'variable' should be bound
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:raise VariableBindingException: If the variable cannot be bound in this dictionary
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"""
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assert isinstance(variable, VariableExpression)
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assert isinstance(binding, Expression)
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assert variable != binding
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existing = self.d.get(variable, None)
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if not existing or binding == existing:
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self.d[variable] = binding
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else:
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raise VariableBindingException('Variable %s already bound to another value' % (variable))
|
||
|
|
|
||
|
|
def __getitem__(self, variable):
|
||
|
|
"""
|
||
|
|
Return the expression to which 'variable' is bound
|
||
|
|
"""
|
||
|
|
assert isinstance(variable, VariableExpression)
|
||
|
|
|
||
|
|
intermediate = self.d[variable]
|
||
|
|
while intermediate:
|
||
|
|
try:
|
||
|
|
intermediate = self.d[intermediate]
|
||
|
|
except KeyError:
|
||
|
|
return intermediate
|
||
|
|
|
||
|
|
def __contains__(self, item):
|
||
|
|
return item in self.d
|
||
|
|
|
||
|
|
def __add__(self, other):
|
||
|
|
"""
|
||
|
|
:param other: ``BindingDict`` The dict with which to combine self
|
||
|
|
:return: ``BindingDict`` A new dict containing all the elements of both parameters
|
||
|
|
:raise VariableBindingException: If the parameter dictionaries are not consistent with each other
|
||
|
|
"""
|
||
|
|
try:
|
||
|
|
combined = BindingDict()
|
||
|
|
for v in self.d:
|
||
|
|
combined[v] = self.d[v]
|
||
|
|
for v in other.d:
|
||
|
|
combined[v] = other.d[v]
|
||
|
|
return combined
|
||
|
|
except VariableBindingException:
|
||
|
|
raise VariableBindingException('Attempting to add two contradicting'\
|
||
|
|
' VariableBindingsLists: %s, %s' % (self, other))
|
||
|
|
|
||
|
|
def __ne__(self, other):
|
||
|
|
return not self == other
|
||
|
|
|
||
|
|
def __eq__(self, other):
|
||
|
|
if not isinstance(other, BindingDict):
|
||
|
|
raise TypeError
|
||
|
|
return self.d == other.d
|
||
|
|
|
||
|
|
def __str__(self):
|
||
|
|
return '{' + ', '.join('%s: %s' % (v, self.d[v]) for v in self.d) + '}'
|
||
|
|
|
||
|
|
def __repr__(self):
|
||
|
|
return 'BindingDict: %s' % self
|
||
|
|
|
||
|
|
class VariableBindingException(Exception):
|
||
|
|
pass
|
||
|
|
|
||
|
|
class UnificationException(Exception):
|
||
|
|
def __init__(self, a, b, bindings):
|
||
|
|
Exception.__init__(self, 'Cannot unify %s with %s given %s' % (a, b, bindings))
|
||
|
|
|
||
|
|
class LinearLogicApplicationException(Exception):
|
||
|
|
pass
|
||
|
|
|
||
|
|
|
||
|
|
def demo():
|
||
|
|
lexpr = Expression.fromstring
|
||
|
|
|
||
|
|
print(lexpr(r'f'))
|
||
|
|
print(lexpr(r'(g -o f)'))
|
||
|
|
print(lexpr(r'((g -o G) -o G)'))
|
||
|
|
print(lexpr(r'g -o h -o f'))
|
||
|
|
print(lexpr(r'(g -o f)(g)').simplify())
|
||
|
|
print(lexpr(r'(H -o f)(g)').simplify())
|
||
|
|
print(lexpr(r'((g -o G) -o G)((g -o f))').simplify())
|
||
|
|
print(lexpr(r'(H -o H)((g -o f))').simplify())
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == '__main__':
|
||
|
|
demo()
|