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# Natural Language Toolkit: Combinatory Categorial Grammar
#
# Copyright (C) 2001-2012 NLTK Project
# Author: Graeme Gange <ggange@csse.unimelb.edu.au>
# URL: <http://www.nltk.org/>
# For license information, see LICENSE.TXT
from nltk.parse import ParserI
from nltk.internals import Counter
from nltk.ccg.api import FunctionalCategory
class UndirectedBinaryCombinator(object):
"""
Abstract class for representing a binary combinator.
Merely defines functions for checking if the function and argument
are able to be combined, and what the resulting category is.
Note that as no assumptions are made as to direction, the unrestricted
combinators can perform all backward, forward and crossed variations
of the combinators; these restrictions must be added in the rule
class.
"""
def can_combine(self, function, argument):
raise NotImplementedError()
def combine (self,function,argument):
raise NotImplementedError()
class DirectedBinaryCombinator(object):
"""
Wrapper for the undirected binary combinator.
It takes left and right categories, and decides which is to be
the function, and which the argument.
It then decides whether or not they can be combined.
"""
def can_combine(self, left, right):
raise NotImplementedError()
def combine(self, left, right):
raise NotImplementedError()
class ForwardCombinator(DirectedBinaryCombinator):
'''
Class representing combinators where the primary functor is on the left.
Takes an undirected combinator, and a predicate which adds constraints
restricting the cases in which it may apply.
'''
def __init__(self, combinator, predicate, suffix=''):
self._combinator = combinator
self._predicate = predicate
self._suffix = suffix
def can_combine(self, left, right):
return (self._combinator.can_combine(left,right) and
self._predicate(left,right))
def combine(self, left, right):
for cat in self._combinator.combine(left,right):
yield cat
def __str__(self):
return '>' + str(self._combinator) + self._suffix
class BackwardCombinator(DirectedBinaryCombinator):
'''
The backward equivalent of the ForwardCombinator class.
'''
def __init__(self, combinator, predicate, suffix=''):
self._combinator = combinator
self._predicate = predicate
self._suffix = suffix
def can_combine(self, left, right):
return (self._combinator.can_combine(right, left) and
self._predicate(left,right))
def combine(self, left, right):
for cat in self._combinator.combine(right, left):
yield cat
def __str__(self):
return '<' + str(self._combinator) + self._suffix
class UndirectedFunctionApplication(UndirectedBinaryCombinator):
"""
Class representing function application.
Implements rules of the form:
X/Y Y -> X (>)
And the corresponding backwards application rule
"""
def can_combine(self, function, argument):
if not function.is_function():
return False
return not function.arg().can_unify(argument) is None
def combine(self,function,argument):
if not function.is_function():
return
subs = function.arg().can_unify(argument)
if subs is None:
return
yield function.res().substitute(subs)
def __str__(self):
return ''
# Predicates for function application.
# Ensures the left functor takes an argument on the right
def forwardOnly(left,right):
return left.dir().is_forward()
# Ensures the right functor takes an argument on the left
def backwardOnly(left,right):
return right.dir().is_backward()
# Application combinator instances
ForwardApplication = ForwardCombinator(UndirectedFunctionApplication(),
forwardOnly)
BackwardApplication = BackwardCombinator(UndirectedFunctionApplication(),
backwardOnly)
class UndirectedComposition(UndirectedBinaryCombinator):
"""
Functional composition (harmonic) combinator.
Implements rules of the form
X/Y Y/Z -> X/Z (B>)
And the corresponding backwards and crossed variations.
"""
def can_combine(self, function, argument):
# Can only combine two functions, and both functions must
# allow composition.
if not (function.is_function() and argument.is_function()):
return False
if function.dir().can_compose() and argument.dir().can_compose():
return not function.arg().can_unify(argument.res()) is None
return False
def combine(self, function, argument):
if not (function.is_function() and argument.is_function()):
return
if function.dir().can_compose() and argument.dir().can_compose():
subs = function.arg().can_unify(argument.res())
if not subs is None:
yield FunctionalCategory(function.res().substitute(subs),
argument.arg().substitute(subs),argument.dir())
def __str__(self):
return 'B'
# Predicates for restricting application of straight composition.
def bothForward(left,right):
return left.dir().is_forward() and right.dir().is_forward()
def bothBackward(left,right):
return left.dir().is_backward() and right.dir().is_backward()
# Predicates for crossed composition
def crossedDirs(left,right):
return left.dir().is_forward() and right.dir().is_backward()
def backwardBxConstraint(left,right):
# The functors must be crossed inwards
if not crossedDirs(left, right):
return False
# Permuting combinators must be allowed
if not left.dir().can_cross() and right.dir().can_cross():
return False
# The resulting argument category is restricted to be primitive
return left.arg().is_primitive()
# Straight composition combinators
ForwardComposition = ForwardCombinator(UndirectedComposition(),
forwardOnly)
BackwardComposition = BackwardCombinator(UndirectedComposition(),
backwardOnly)
# Backward crossed composition
BackwardBx = BackwardCombinator(UndirectedComposition(),backwardBxConstraint,
suffix='x')
class UndirectedSubstitution(UndirectedBinaryCombinator):
"""
Substitution (permutation) combinator.
Implements rules of the form
Y/Z (X\Y)/Z -> X/Z (<Sx)
And other variations.
"""
def can_combine(self, function, argument):
if function.is_primitive() or argument.is_primitive():
return False
# These could potentially be moved to the predicates, as the
# constraints may not be general to all languages.
if function.res().is_primitive():
return False
if not function.arg().is_primitive():
return False
if not (function.dir().can_compose() and argument.dir().can_compose()):
return False
return (function.res().arg() == argument.res()) and (function.arg() == argument.arg())
def combine(self,function,argument):
if self.can_combine(function,argument):
yield FunctionalCategory(function.res().res(),argument.arg(),argument.dir())
def __str__(self):
return 'S'
# Predicate for forward substitution
def forwardSConstraint(left, right):
if not bothForward(left, right):
return False
return left.res().dir().is_forward() and left.arg().is_primitive()
# Predicate for backward crossed substitution
def backwardSxConstraint(left,right):
if not left.dir().can_cross() and right.dir().can_cross():
return False
if not bothForward(left, right):
return False
return right.res().dir().is_backward() and right.arg().is_primitive()
# Instances of substitution combinators
ForwardSubstitution = ForwardCombinator(UndirectedSubstitution(),
forwardSConstraint)
BackwardSx = BackwardCombinator(UndirectedSubstitution(),
backwardSxConstraint,'x')
# Retrieves the left-most functional category.
# ie, (N\N)/(S/NP) => N\N
def innermostFunction(categ):
while categ.res().is_function():
categ = categ.res()
return categ
class UndirectedTypeRaise(UndirectedBinaryCombinator):
'''
Undirected combinator for type raising.
'''
def can_combine(self,function,arg):
# The argument must be a function.
# The restriction that arg.res() must be a function
# merely reduces redundant type-raising; if arg.res() is
# primitive, we have:
# X Y\X =>(<T) Y/(Y\X) Y\X =>(>) Y
# which is equivalent to
# X Y\X =>(<) Y
if not (arg.is_function() and arg.res().is_function()):
return False
arg = innermostFunction(arg)
# left, arg_categ are undefined!
subs = left.can_unify(arg_categ.arg())
if subs is not None:
return True
return False
def combine(self,function,arg):
if not (function.is_primitive() and \
arg.is_function() and arg.res().is_function()):
return
# Type-raising matches only the innermost application.
arg = innermostFunction(arg)
subs = function.can_unify(arg.arg())
if subs is not None:
xcat = arg.res().substitute(subs)
yield FunctionalCategory(xcat,
FunctionalCategory(xcat,function,arg.dir()),
-(arg.dir()))
def __str__(self):
return 'T'
# Predicates for type-raising
# The direction of the innermost category must be towards
# the primary functor.
# The restriction that the variable must be primitive is not
# common to all versions of CCGs; some authors have other restrictions.
def forwardTConstraint(left,right):
arg = innermostFunction(right)
return arg.dir().is_backward() and arg.res().is_primitive()
def backwardTConstraint(left,right):
arg = innermostFunction(left)
return arg.dir().is_forward() and arg.res().is_primitive()
# Instances of type-raising combinators
ForwardT = ForwardCombinator(UndirectedTypeRaise(), forwardTConstraint)
BackwardT = BackwardCombinator(UndirectedTypeRaise(), backwardTConstraint)
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