340 lines
10 KiB
Python
340 lines
10 KiB
Python
# Natural Language Toolkit: Combinatory Categorial Grammar
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#
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# Copyright (C) 2001-2023 NLTK Project
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# Author: Graeme Gange <ggange@csse.unimelb.edu.au>
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# URL: <https://www.nltk.org/>
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# For license information, see LICENSE.TXT
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"""
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CCG Combinators
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"""
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from abc import ABCMeta, abstractmethod
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from nltk.ccg.api import FunctionalCategory
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class UndirectedBinaryCombinator(metaclass=ABCMeta):
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"""
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Abstract class for representing a binary combinator.
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Merely defines functions for checking if the function and argument
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are able to be combined, and what the resulting category is.
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Note that as no assumptions are made as to direction, the unrestricted
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combinators can perform all backward, forward and crossed variations
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of the combinators; these restrictions must be added in the rule
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class.
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"""
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@abstractmethod
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def can_combine(self, function, argument):
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pass
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@abstractmethod
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def combine(self, function, argument):
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pass
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class DirectedBinaryCombinator(metaclass=ABCMeta):
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"""
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Wrapper for the undirected binary combinator.
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It takes left and right categories, and decides which is to be
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the function, and which the argument.
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It then decides whether or not they can be combined.
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"""
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@abstractmethod
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def can_combine(self, left, right):
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pass
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@abstractmethod
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def combine(self, left, right):
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pass
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class ForwardCombinator(DirectedBinaryCombinator):
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"""
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Class representing combinators where the primary functor is on the left.
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Takes an undirected combinator, and a predicate which adds constraints
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restricting the cases in which it may apply.
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"""
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def __init__(self, combinator, predicate, suffix=""):
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self._combinator = combinator
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self._predicate = predicate
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self._suffix = suffix
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def can_combine(self, left, right):
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return self._combinator.can_combine(left, right) and self._predicate(
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left, right
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)
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def combine(self, left, right):
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yield from self._combinator.combine(left, right)
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def __str__(self):
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return f">{self._combinator}{self._suffix}"
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class BackwardCombinator(DirectedBinaryCombinator):
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"""
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The backward equivalent of the ForwardCombinator class.
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"""
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def __init__(self, combinator, predicate, suffix=""):
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self._combinator = combinator
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self._predicate = predicate
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self._suffix = suffix
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def can_combine(self, left, right):
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return self._combinator.can_combine(right, left) and self._predicate(
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left, right
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)
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def combine(self, left, right):
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yield from self._combinator.combine(right, left)
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def __str__(self):
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return f"<{self._combinator}{self._suffix}"
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class UndirectedFunctionApplication(UndirectedBinaryCombinator):
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"""
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Class representing function application.
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Implements rules of the form:
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X/Y Y -> X (>)
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And the corresponding backwards application rule
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"""
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def can_combine(self, function, argument):
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if not function.is_function():
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return False
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return not function.arg().can_unify(argument) is None
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def combine(self, function, argument):
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if not function.is_function():
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return
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subs = function.arg().can_unify(argument)
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if subs is None:
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return
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yield function.res().substitute(subs)
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def __str__(self):
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return ""
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# Predicates for function application.
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# Ensures the left functor takes an argument on the right
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def forwardOnly(left, right):
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return left.dir().is_forward()
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# Ensures the right functor takes an argument on the left
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def backwardOnly(left, right):
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return right.dir().is_backward()
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# Application combinator instances
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ForwardApplication = ForwardCombinator(UndirectedFunctionApplication(), forwardOnly)
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BackwardApplication = BackwardCombinator(UndirectedFunctionApplication(), backwardOnly)
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class UndirectedComposition(UndirectedBinaryCombinator):
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"""
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Functional composition (harmonic) combinator.
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Implements rules of the form
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X/Y Y/Z -> X/Z (B>)
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And the corresponding backwards and crossed variations.
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"""
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def can_combine(self, function, argument):
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# Can only combine two functions, and both functions must
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# allow composition.
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if not (function.is_function() and argument.is_function()):
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return False
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if function.dir().can_compose() and argument.dir().can_compose():
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return not function.arg().can_unify(argument.res()) is None
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return False
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def combine(self, function, argument):
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if not (function.is_function() and argument.is_function()):
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return
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if function.dir().can_compose() and argument.dir().can_compose():
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subs = function.arg().can_unify(argument.res())
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if subs is not None:
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yield FunctionalCategory(
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function.res().substitute(subs),
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argument.arg().substitute(subs),
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argument.dir(),
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)
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def __str__(self):
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return "B"
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# Predicates for restricting application of straight composition.
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def bothForward(left, right):
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return left.dir().is_forward() and right.dir().is_forward()
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def bothBackward(left, right):
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return left.dir().is_backward() and right.dir().is_backward()
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# Predicates for crossed composition
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def crossedDirs(left, right):
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return left.dir().is_forward() and right.dir().is_backward()
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def backwardBxConstraint(left, right):
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# The functors must be crossed inwards
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if not crossedDirs(left, right):
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return False
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# Permuting combinators must be allowed
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if not left.dir().can_cross() and right.dir().can_cross():
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return False
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# The resulting argument category is restricted to be primitive
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return left.arg().is_primitive()
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# Straight composition combinators
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ForwardComposition = ForwardCombinator(UndirectedComposition(), forwardOnly)
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BackwardComposition = BackwardCombinator(UndirectedComposition(), backwardOnly)
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# Backward crossed composition
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BackwardBx = BackwardCombinator(
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UndirectedComposition(), backwardBxConstraint, suffix="x"
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)
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class UndirectedSubstitution(UndirectedBinaryCombinator):
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r"""
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Substitution (permutation) combinator.
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Implements rules of the form
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Y/Z (X\Y)/Z -> X/Z (<Sx)
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And other variations.
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"""
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def can_combine(self, function, argument):
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if function.is_primitive() or argument.is_primitive():
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return False
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# These could potentially be moved to the predicates, as the
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# constraints may not be general to all languages.
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if function.res().is_primitive():
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return False
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if not function.arg().is_primitive():
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return False
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if not (function.dir().can_compose() and argument.dir().can_compose()):
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return False
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return (function.res().arg() == argument.res()) and (
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function.arg() == argument.arg()
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)
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def combine(self, function, argument):
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if self.can_combine(function, argument):
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yield FunctionalCategory(
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function.res().res(), argument.arg(), argument.dir()
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)
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def __str__(self):
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return "S"
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# Predicate for forward substitution
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def forwardSConstraint(left, right):
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if not bothForward(left, right):
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return False
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return left.res().dir().is_forward() and left.arg().is_primitive()
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# Predicate for backward crossed substitution
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def backwardSxConstraint(left, right):
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if not left.dir().can_cross() and right.dir().can_cross():
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return False
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if not bothForward(left, right):
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return False
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return right.res().dir().is_backward() and right.arg().is_primitive()
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# Instances of substitution combinators
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ForwardSubstitution = ForwardCombinator(UndirectedSubstitution(), forwardSConstraint)
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BackwardSx = BackwardCombinator(UndirectedSubstitution(), backwardSxConstraint, "x")
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# Retrieves the left-most functional category.
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# ie, (N\N)/(S/NP) => N\N
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def innermostFunction(categ):
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while categ.res().is_function():
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categ = categ.res()
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return categ
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class UndirectedTypeRaise(UndirectedBinaryCombinator):
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"""
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Undirected combinator for type raising.
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"""
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def can_combine(self, function, arg):
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# The argument must be a function.
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# The restriction that arg.res() must be a function
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# merely reduces redundant type-raising; if arg.res() is
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# primitive, we have:
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# X Y\X =>(<T) Y/(Y\X) Y\X =>(>) Y
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# which is equivalent to
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# X Y\X =>(<) Y
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if not (arg.is_function() and arg.res().is_function()):
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return False
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arg = innermostFunction(arg)
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# left, arg_categ are undefined!
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subs = left.can_unify(arg_categ.arg())
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if subs is not None:
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return True
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return False
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def combine(self, function, arg):
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if not (
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function.is_primitive() and arg.is_function() and arg.res().is_function()
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):
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return
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# Type-raising matches only the innermost application.
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arg = innermostFunction(arg)
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subs = function.can_unify(arg.arg())
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if subs is not None:
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xcat = arg.res().substitute(subs)
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yield FunctionalCategory(
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xcat, FunctionalCategory(xcat, function, arg.dir()), -(arg.dir())
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)
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def __str__(self):
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return "T"
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# Predicates for type-raising
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# The direction of the innermost category must be towards
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# the primary functor.
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# The restriction that the variable must be primitive is not
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# common to all versions of CCGs; some authors have other restrictions.
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def forwardTConstraint(left, right):
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arg = innermostFunction(right)
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return arg.dir().is_backward() and arg.res().is_primitive()
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def backwardTConstraint(left, right):
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arg = innermostFunction(left)
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return arg.dir().is_forward() and arg.res().is_primitive()
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# Instances of type-raising combinators
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ForwardT = ForwardCombinator(UndirectedTypeRaise(), forwardTConstraint)
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BackwardT = BackwardCombinator(UndirectedTypeRaise(), backwardTConstraint)
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