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1230 lines
37 KiB
Plaintext
1230 lines
37 KiB
Plaintext
.. Copyright (C) 2001-2019 NLTK Project
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.. For license information, see LICENSE.TXT
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==================================
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Feature Structures & Unification
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==================================
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>>> from __future__ import print_function
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>>> from nltk.featstruct import FeatStruct
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>>> from nltk.sem.logic import Variable, VariableExpression, Expression
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.. note:: For now, featstruct uses the older lambdalogic semantics
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module. Eventually, it should be updated to use the new first
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order predicate logic module.
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Overview
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~~~~~~~~
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A feature structure is a mapping from feature identifiers to feature
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values, where feature values can be simple values (like strings or
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ints), nested feature structures, or variables:
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>>> fs1 = FeatStruct(number='singular', person=3)
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>>> print(fs1)
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[ number = 'singular' ]
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[ person = 3 ]
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Feature structure may be nested:
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>>> fs2 = FeatStruct(type='NP', agr=fs1)
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>>> print(fs2)
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[ agr = [ number = 'singular' ] ]
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[ [ person = 3 ] ]
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[ ]
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[ type = 'NP' ]
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Variables are used to indicate that two features should be assigned
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the same value. For example, the following feature structure requires
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that the feature fs3['agr']['number'] be bound to the same value as the
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feature fs3['subj']['number'].
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>>> fs3 = FeatStruct(agr=FeatStruct(number=Variable('?n')),
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... subj=FeatStruct(number=Variable('?n')))
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>>> print(fs3)
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[ agr = [ number = ?n ] ]
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[ ]
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[ subj = [ number = ?n ] ]
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Feature structures are typically used to represent partial information
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about objects. A feature name that is not mapped to a value stands
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for a feature whose value is unknown (*not* a feature without a
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value). Two feature structures that represent (potentially
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overlapping) information about the same object can be combined by
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*unification*.
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>>> print(fs2.unify(fs3))
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[ agr = [ number = 'singular' ] ]
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[ [ person = 3 ] ]
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[ ]
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[ subj = [ number = 'singular' ] ]
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[ ]
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[ type = 'NP' ]
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When two inconsistent feature structures are unified, the unification
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fails and returns ``None``.
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>>> fs4 = FeatStruct(agr=FeatStruct(person=1))
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>>> print(fs4.unify(fs2))
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None
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>>> print(fs2.unify(fs4))
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None
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..
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>>> del fs1, fs2, fs3, fs4 # clean-up
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Feature Structure Types
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-----------------------
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There are actually two types of feature structure:
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- *feature dictionaries*, implemented by `FeatDict`, act like
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Python dictionaries. Feature identifiers may be strings or
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instances of the `Feature` class.
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- *feature lists*, implemented by `FeatList`, act like Python
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lists. Feature identifiers are integers.
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When you construct a feature structure using the `FeatStruct`
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constructor, it will automatically decide which type is appropriate:
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>>> type(FeatStruct(number='singular'))
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<class 'nltk.featstruct.FeatDict'>
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>>> type(FeatStruct([1,2,3]))
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<class 'nltk.featstruct.FeatList'>
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Usually, we will just use feature dictionaries; but sometimes feature
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lists can be useful too. Two feature lists will unify with each other
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only if they have equal lengths, and all of their feature values
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match. If you wish to write a feature list that contains 'unknown'
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values, you must use variables:
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>>> fs1 = FeatStruct([1,2,Variable('?y')])
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>>> fs2 = FeatStruct([1,Variable('?x'),3])
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>>> fs1.unify(fs2)
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[1, 2, 3]
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..
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>>> del fs1, fs2 # clean-up
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Parsing Feature Structure Strings
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---------------------------------
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Feature structures can be constructed directly from strings. Often,
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this is more convenient than constructing them directly. NLTK can
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parse most feature strings to produce the corresponding feature
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structures. (But you must restrict your base feature values to
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strings, ints, logic expressions (`nltk.sem.logic.Expression`), and a
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few other types discussed below).
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Feature dictionaries are written like Python dictionaries, except that
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keys are not put in quotes; and square brackets (``[]``) are used
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instead of braces (``{}``):
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>>> FeatStruct('[tense="past", agr=[number="sing", person=3]]')
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[agr=[number='sing', person=3], tense='past']
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If a feature value is a single alphanumeric word, then it does not
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need to be quoted -- it will be automatically treated as a string:
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>>> FeatStruct('[tense=past, agr=[number=sing, person=3]]')
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[agr=[number='sing', person=3], tense='past']
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Feature lists are written like python lists:
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>>> FeatStruct('[1, 2, 3]')
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[1, 2, 3]
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The expression ``[]`` is treated as an empty feature dictionary, not
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an empty feature list:
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>>> type(FeatStruct('[]'))
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<class 'nltk.featstruct.FeatDict'>
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Feature Paths
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-------------
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Features can be specified using *feature paths*, or tuples of feature
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identifiers that specify path through the nested feature structures to
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a value.
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>>> fs1 = FeatStruct('[x=1, y=[1,2,[z=3]]]')
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>>> fs1['y']
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[1, 2, [z=3]]
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>>> fs1['y', 2]
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[z=3]
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>>> fs1['y', 2, 'z']
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3
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..
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>>> del fs1 # clean-up
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Reentrance
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----------
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Feature structures may contain reentrant feature values. A *reentrant
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feature value* is a single feature structure that can be accessed via
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multiple feature paths.
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>>> fs1 = FeatStruct(x='val')
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>>> fs2 = FeatStruct(a=fs1, b=fs1)
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>>> print(fs2)
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[ a = (1) [ x = 'val' ] ]
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[ ]
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[ b -> (1) ]
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>>> fs2
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[a=(1)[x='val'], b->(1)]
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As you can see, reentrane is displayed by marking a feature structure
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with a unique identifier, in this case ``(1)``, the first time it is
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encountered; and then using the special form ``var -> id`` whenever it
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is encountered again. You can use the same notation to directly
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create reentrant feature structures from strings.
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>>> FeatStruct('[a=(1)[], b->(1), c=[d->(1)]]')
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[a=(1)[], b->(1), c=[d->(1)]]
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Reentrant feature structures may contain cycles:
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>>> fs3 = FeatStruct('(1)[a->(1)]')
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>>> fs3['a', 'a', 'a', 'a']
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(1)[a->(1)]
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>>> fs3['a', 'a', 'a', 'a'] is fs3
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True
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Unification preserves the reentrance relations imposed by both of the
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unified feature structures. In the feature structure resulting from
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unification, any modifications to a reentrant feature value will be
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visible using any of its feature paths.
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>>> fs3.unify(FeatStruct('[a=[b=12], c=33]'))
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(1)[a->(1), b=12, c=33]
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..
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>>> del fs1, fs2, fs3 # clean-up
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Feature Structure Equality
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--------------------------
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Two feature structures are considered equal if they assign the same
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values to all features, *and* they contain the same reentrances.
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>>> fs1 = FeatStruct('[a=(1)[x=1], b->(1)]')
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>>> fs2 = FeatStruct('[a=(1)[x=1], b->(1)]')
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>>> fs3 = FeatStruct('[a=[x=1], b=[x=1]]')
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>>> fs1 == fs1, fs1 is fs1
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(True, True)
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>>> fs1 == fs2, fs1 is fs2
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(True, False)
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>>> fs1 == fs3, fs1 is fs3
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(False, False)
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Note that this differs from how Python dictionaries and lists define
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equality -- in particular, Python dictionaries and lists ignore
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reentrance relations. To test two feature structures for equality
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while ignoring reentrance relations, use the `equal_values()` method:
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>>> fs1.equal_values(fs1)
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True
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>>> fs1.equal_values(fs2)
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True
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>>> fs1.equal_values(fs3)
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True
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..
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>>> del fs1, fs2, fs3 # clean-up
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Feature Value Sets & Feature Value Tuples
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-----------------------------------------
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`nltk.featstruct` defines two new data types that are intended to be
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used as feature values: `FeatureValueTuple` and `FeatureValueSet`.
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Both of these types are considered base values -- i.e., unification
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does *not* apply to them. However, variable binding *does* apply to
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any values that they contain.
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Feature value tuples are written with parentheses:
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>>> fs1 = FeatStruct('[x=(?x, ?y)]')
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>>> fs1
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[x=(?x, ?y)]
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>>> fs1.substitute_bindings({Variable('?x'): 1, Variable('?y'): 2})
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[x=(1, 2)]
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Feature sets are written with braces:
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>>> fs1 = FeatStruct('[x={?x, ?y}]')
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>>> fs1
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[x={?x, ?y}]
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>>> fs1.substitute_bindings({Variable('?x'): 1, Variable('?y'): 2})
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[x={1, 2}]
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In addition to the basic feature value tuple & set classes, nltk
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defines feature value unions (for sets) and feature value
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concatenations (for tuples). These are written using '+', and can be
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used to combine sets & tuples:
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>>> fs1 = FeatStruct('[x=((1, 2)+?z), z=?z]')
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>>> fs1
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[x=((1, 2)+?z), z=?z]
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>>> fs1.unify(FeatStruct('[z=(3, 4, 5)]'))
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[x=(1, 2, 3, 4, 5), z=(3, 4, 5)]
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Thus, feature value tuples and sets can be used to build up tuples
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and sets of values over the corse of unification. For example, when
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parsing sentences using a semantic feature grammar, feature sets or
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feature tuples can be used to build a list of semantic predicates as
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the sentence is parsed.
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As was mentioned above, unification does not apply to feature value
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tuples and sets. One reason for this that it's impossible to define a
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single correct answer for unification when concatenation is used.
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Consider the following example:
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>>> fs1 = FeatStruct('[x=(1, 2, 3, 4)]')
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>>> fs2 = FeatStruct('[x=(?a+?b), a=?a, b=?b]')
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If unification applied to feature tuples, then the unification
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algorithm would have to arbitrarily choose how to divide the tuple
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(1,2,3,4) into two parts. Instead, the unification algorithm refuses
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to make this decision, and simply unifies based on value. Because
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(1,2,3,4) is not equal to (?a+?b), fs1 and fs2 will not unify:
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>>> print(fs1.unify(fs2))
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None
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If you need a list-like structure that unification does apply to, use
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`FeatList`.
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..
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>>> del fs1, fs2 # clean-up
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Light-weight Feature Structures
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-------------------------------
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Many of the functions defined by `nltk.featstruct` can be applied
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directly to simple Python dictionaries and lists, rather than to
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full-fledged `FeatDict` and `FeatList` objects. In other words,
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Python ``dicts`` and ``lists`` can be used as "light-weight" feature
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structures.
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>>> # Note: pprint prints dicts sorted
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>>> from pprint import pprint
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>>> from nltk.featstruct import unify
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>>> pprint(unify(dict(x=1, y=dict()), dict(a='a', y=dict(b='b'))))
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{'a': 'a', 'x': 1, 'y': {'b': 'b'}}
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However, you should keep in mind the following caveats:
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- Python dictionaries & lists ignore reentrance when checking for
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equality between values. But two FeatStructs with different
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reentrances are considered nonequal, even if all their base
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values are equal.
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- FeatStructs can be easily frozen, allowing them to be used as
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keys in hash tables. Python dictionaries and lists can not.
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- FeatStructs display reentrance in their string representations;
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Python dictionaries and lists do not.
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- FeatStructs may *not* be mixed with Python dictionaries and lists
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(e.g., when performing unification).
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- FeatStructs provide a number of useful methods, such as `walk()`
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and `cyclic()`, which are not available for Python dicts & lists.
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In general, if your feature structures will contain any reentrances,
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or if you plan to use them as dictionary keys, it is strongly
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recommended that you use full-fledged `FeatStruct` objects.
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Custom Feature Values
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---------------------
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The abstract base class `CustomFeatureValue` can be used to define new
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base value types that have custom unification methods. For example,
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the following feature value type encodes a range, and defines
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unification as taking the intersection on the ranges:
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>>> from functools import total_ordering
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>>> from nltk.featstruct import CustomFeatureValue, UnificationFailure
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>>> @total_ordering
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... class Range(CustomFeatureValue):
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... def __init__(self, low, high):
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... assert low <= high
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... self.low = low
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... self.high = high
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... def unify(self, other):
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... if not isinstance(other, Range):
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... return UnificationFailure
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... low = max(self.low, other.low)
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... high = min(self.high, other.high)
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... if low <= high: return Range(low, high)
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... else: return UnificationFailure
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... def __repr__(self):
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... return '(%s<x<%s)' % (self.low, self.high)
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... def __eq__(self, other):
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... if not isinstance(other, Range):
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... return False
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... return (self.low == other.low) and (self.high == other.high)
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... def __lt__(self, other):
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... if not isinstance(other, Range):
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... return True
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... return (self.low, self.high) < (other.low, other.high)
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>>> fs1 = FeatStruct(x=Range(5,8), y=FeatStruct(z=Range(7,22)))
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>>> print(fs1.unify(FeatStruct(x=Range(6, 22))))
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[ x = (6<x<8) ]
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[ ]
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[ y = [ z = (7<x<22) ] ]
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>>> print(fs1.unify(FeatStruct(x=Range(9, 12))))
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None
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>>> print(fs1.unify(FeatStruct(x=12)))
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None
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>>> print(fs1.unify(FeatStruct('[x=?x, y=[z=?x]]')))
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[ x = (7<x<8) ]
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[ ]
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[ y = [ z = (7<x<8) ] ]
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Regression Tests
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~~~~~~~~~~~~~~~~
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Dictionary access methods (non-mutating)
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----------------------------------------
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>>> fs1 = FeatStruct(a=1, b=2, c=3)
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>>> fs2 = FeatStruct(x=fs1, y='x')
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Feature structures support all dictionary methods (excluding the class
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method `dict.fromkeys()`). Non-mutating methods:
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>>> sorted(fs2.keys()) # keys()
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['x', 'y']
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>>> sorted(fs2.values()) # values()
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[[a=1, b=2, c=3], 'x']
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>>> sorted(fs2.items()) # items()
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[('x', [a=1, b=2, c=3]), ('y', 'x')]
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>>> sorted(fs2) # __iter__()
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['x', 'y']
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>>> 'a' in fs2, 'x' in fs2 # __contains__()
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(False, True)
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>>> fs2.has_key('a'), fs2.has_key('x') # has_key()
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(False, True)
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>>> fs2['x'], fs2['y'] # __getitem__()
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([a=1, b=2, c=3], 'x')
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>>> fs2['a'] # __getitem__()
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Traceback (most recent call last):
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. . .
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KeyError: 'a'
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>>> fs2.get('x'), fs2.get('y'), fs2.get('a') # get()
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([a=1, b=2, c=3], 'x', None)
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>>> fs2.get('x', 'hello'), fs2.get('a', 'hello') # get()
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([a=1, b=2, c=3], 'hello')
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>>> len(fs1), len(fs2) # __len__
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(3, 2)
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>>> fs2.copy() # copy()
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[x=[a=1, b=2, c=3], y='x']
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>>> fs2.copy() is fs2 # copy()
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False
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Note: by default, `FeatStruct.copy()` does a deep copy. Use
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`FeatStruct.copy(deep=False)` for a shallow copy.
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..
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>>> del fs1, fs2 # clean-up.
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Dictionary access methods (mutating)
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------------------------------------
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>>> fs1 = FeatStruct(a=1, b=2, c=3)
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>>> fs2 = FeatStruct(x=fs1, y='x')
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Setting features (`__setitem__()`)
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>>> fs1['c'] = 5
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>>> fs1
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[a=1, b=2, c=5]
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>>> fs1['x'] = 12
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>>> fs1
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[a=1, b=2, c=5, x=12]
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>>> fs2['x', 'a'] = 2
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>>> fs2
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[x=[a=2, b=2, c=5, x=12], y='x']
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>>> fs1
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[a=2, b=2, c=5, x=12]
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Deleting features (`__delitem__()`)
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>>> del fs1['x']
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>>> fs1
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[a=2, b=2, c=5]
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>>> del fs2['x', 'a']
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>>> fs1
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[b=2, c=5]
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`setdefault()`:
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>>> fs1.setdefault('b', 99)
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2
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>>> fs1
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[b=2, c=5]
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>>> fs1.setdefault('x', 99)
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99
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>>> fs1
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[b=2, c=5, x=99]
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`update()`:
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>>> fs2.update({'a':'A', 'b':'B'}, c='C')
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>>> fs2
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[a='A', b='B', c='C', x=[b=2, c=5, x=99], y='x']
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`pop()`:
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>>> fs2.pop('a')
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'A'
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>>> fs2
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[b='B', c='C', x=[b=2, c=5, x=99], y='x']
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>>> fs2.pop('a')
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Traceback (most recent call last):
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. . .
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KeyError: 'a'
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>>> fs2.pop('a', 'foo')
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'foo'
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>>> fs2
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[b='B', c='C', x=[b=2, c=5, x=99], y='x']
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`clear()`:
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>>> fs1.clear()
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>>> fs1
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[]
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>>> fs2
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[b='B', c='C', x=[], y='x']
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`popitem()`:
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>>> sorted([fs2.popitem() for i in range(len(fs2))])
|
|
[('b', 'B'), ('c', 'C'), ('x', []), ('y', 'x')]
|
|
>>> fs2
|
|
[]
|
|
|
|
Once a feature structure has been frozen, it may not be mutated.
|
|
|
|
>>> fs1 = FeatStruct('[x=1, y=2, z=[a=3]]')
|
|
>>> fs1.freeze()
|
|
>>> fs1.frozen()
|
|
True
|
|
>>> fs1['z'].frozen()
|
|
True
|
|
|
|
>>> fs1['x'] = 5
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Frozen FeatStructs may not be modified.
|
|
>>> del fs1['x']
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Frozen FeatStructs may not be modified.
|
|
>>> fs1.clear()
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Frozen FeatStructs may not be modified.
|
|
>>> fs1.pop('x')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Frozen FeatStructs may not be modified.
|
|
>>> fs1.popitem()
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Frozen FeatStructs may not be modified.
|
|
>>> fs1.setdefault('x')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Frozen FeatStructs may not be modified.
|
|
>>> fs1.update(z=22)
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Frozen FeatStructs may not be modified.
|
|
|
|
..
|
|
>>> del fs1, fs2 # clean-up.
|
|
|
|
Feature Paths
|
|
-------------
|
|
Make sure that __getitem__ with feature paths works as intended:
|
|
|
|
>>> fs1 = FeatStruct(a=1, b=2,
|
|
... c=FeatStruct(
|
|
... d=FeatStruct(e=12),
|
|
... f=FeatStruct(g=55, h='hello')))
|
|
>>> fs1[()]
|
|
[a=1, b=2, c=[d=[e=12], f=[g=55, h='hello']]]
|
|
>>> fs1['a'], fs1[('a',)]
|
|
(1, 1)
|
|
>>> fs1['c','d','e']
|
|
12
|
|
>>> fs1['c','f','g']
|
|
55
|
|
|
|
Feature paths that select unknown features raise KeyError:
|
|
|
|
>>> fs1['c', 'f', 'e']
|
|
Traceback (most recent call last):
|
|
. . .
|
|
KeyError: ('c', 'f', 'e')
|
|
>>> fs1['q', 'p']
|
|
Traceback (most recent call last):
|
|
. . .
|
|
KeyError: ('q', 'p')
|
|
|
|
Feature paths that try to go 'through' a feature that's not a feature
|
|
structure raise KeyError:
|
|
|
|
>>> fs1['a', 'b']
|
|
Traceback (most recent call last):
|
|
. . .
|
|
KeyError: ('a', 'b')
|
|
|
|
Feature paths can go through reentrant structures:
|
|
|
|
>>> fs2 = FeatStruct('(1)[a=[b=[c->(1), d=5], e=11]]')
|
|
>>> fs2['a', 'b', 'c', 'a', 'e']
|
|
11
|
|
>>> fs2['a', 'b', 'c', 'a', 'b', 'd']
|
|
5
|
|
>>> fs2[tuple('abcabcabcabcabcabcabcabcabcabca')]
|
|
(1)[b=[c=[a->(1)], d=5], e=11]
|
|
|
|
Indexing requires strings, `Feature`\s, or tuples; other types raise a
|
|
TypeError:
|
|
|
|
>>> fs2[12]
|
|
Traceback (most recent call last):
|
|
. . .
|
|
TypeError: Expected feature name or path. Got 12.
|
|
>>> fs2[list('abc')]
|
|
Traceback (most recent call last):
|
|
. . .
|
|
TypeError: Expected feature name or path. Got ['a', 'b', 'c'].
|
|
|
|
Feature paths can also be used with `get()`, `has_key()`, and
|
|
`__contains__()`.
|
|
|
|
>>> fpath1 = tuple('abcabc')
|
|
>>> fpath2 = tuple('abcabz')
|
|
>>> fs2.get(fpath1), fs2.get(fpath2)
|
|
((1)[a=[b=[c->(1), d=5], e=11]], None)
|
|
>>> fpath1 in fs2, fpath2 in fs2
|
|
(True, False)
|
|
>>> fs2.has_key(fpath1), fs2.has_key(fpath2)
|
|
(True, False)
|
|
|
|
..
|
|
>>> del fs1, fs2 # clean-up
|
|
|
|
Reading Feature Structures
|
|
--------------------------
|
|
|
|
Empty feature struct:
|
|
|
|
>>> FeatStruct('[]')
|
|
[]
|
|
|
|
Test features with integer values:
|
|
|
|
>>> FeatStruct('[a=12, b=-33, c=0]')
|
|
[a=12, b=-33, c=0]
|
|
|
|
Test features with string values. Either single or double quotes may
|
|
be used. Strings are evaluated just like python strings -- in
|
|
particular, you can use escape sequences and 'u' and 'r' prefixes, and
|
|
triple-quoted strings.
|
|
|
|
>>> FeatStruct('[a="", b="hello", c="\'", d=\'\', e=\'"\']')
|
|
[a='', b='hello', c="'", d='', e='"']
|
|
>>> FeatStruct(r'[a="\\", b="\"", c="\x6f\\y", d="12"]')
|
|
[a='\\', b='"', c='o\\y', d='12']
|
|
>>> FeatStruct(r'[b=r"a\b\c"]')
|
|
[b='a\\b\\c']
|
|
>>> FeatStruct('[x="""a"""]')
|
|
[x='a']
|
|
|
|
Test parsing of reentrant feature structures.
|
|
|
|
>>> FeatStruct('[a=(1)[], b->(1)]')
|
|
[a=(1)[], b->(1)]
|
|
>>> FeatStruct('[a=(1)[x=1, y=2], b->(1)]')
|
|
[a=(1)[x=1, y=2], b->(1)]
|
|
|
|
Test parsing of cyclic feature structures.
|
|
|
|
>>> FeatStruct('[a=(1)[b->(1)]]')
|
|
[a=(1)[b->(1)]]
|
|
>>> FeatStruct('(1)[a=[b=[c->(1)]]]')
|
|
(1)[a=[b=[c->(1)]]]
|
|
|
|
Strings of the form "+name" and "-name" may be used to specify boolean
|
|
values.
|
|
|
|
>>> FeatStruct('[-bar, +baz, +foo]')
|
|
[-bar, +baz, +foo]
|
|
|
|
None, True, and False are recognized as values:
|
|
|
|
>>> FeatStruct('[bar=True, baz=False, foo=None]')
|
|
[+bar, -baz, foo=None]
|
|
|
|
Special features:
|
|
|
|
>>> FeatStruct('NP/VP')
|
|
NP[]/VP[]
|
|
>>> FeatStruct('?x/?x')
|
|
?x[]/?x[]
|
|
>>> print(FeatStruct('VP[+fin, agr=?x, tense=past]/NP[+pl, agr=?x]'))
|
|
[ *type* = 'VP' ]
|
|
[ ]
|
|
[ [ *type* = 'NP' ] ]
|
|
[ *slash* = [ agr = ?x ] ]
|
|
[ [ pl = True ] ]
|
|
[ ]
|
|
[ agr = ?x ]
|
|
[ fin = True ]
|
|
[ tense = 'past' ]
|
|
|
|
Here the slash feature gets coerced:
|
|
>>> FeatStruct('[*slash*=a, x=b, *type*="NP"]')
|
|
NP[x='b']/a[]
|
|
|
|
>>> FeatStruct('NP[sem=<bob>]/NP')
|
|
NP[sem=<bob>]/NP[]
|
|
>>> FeatStruct('S[sem=<walk(bob)>]')
|
|
S[sem=<walk(bob)>]
|
|
>>> print(FeatStruct('NP[sem=<bob>]/NP'))
|
|
[ *type* = 'NP' ]
|
|
[ ]
|
|
[ *slash* = [ *type* = 'NP' ] ]
|
|
[ ]
|
|
[ sem = <bob> ]
|
|
|
|
Playing with ranges:
|
|
|
|
>>> from nltk.featstruct import RangeFeature, FeatStructReader
|
|
>>> width = RangeFeature('width')
|
|
>>> reader = FeatStructReader([width])
|
|
>>> fs1 = reader.fromstring('[*width*=-5:12]')
|
|
>>> fs2 = reader.fromstring('[*width*=2:123]')
|
|
>>> fs3 = reader.fromstring('[*width*=-7:-2]')
|
|
>>> fs1.unify(fs2)
|
|
[*width*=(2, 12)]
|
|
>>> fs1.unify(fs3)
|
|
[*width*=(-5, -2)]
|
|
>>> print(fs2.unify(fs3)) # no overlap in width.
|
|
None
|
|
|
|
The slash feature has a default value of 'False':
|
|
|
|
>>> print(FeatStruct('NP[]/VP').unify(FeatStruct('NP[]'), trace=1))
|
|
<BLANKLINE>
|
|
Unification trace:
|
|
/ NP[]/VP[]
|
|
|\ NP[]
|
|
|
|
|
| Unify feature: *type*
|
|
| / 'NP'
|
|
| |\ 'NP'
|
|
| |
|
|
| +-->'NP'
|
|
|
|
|
| Unify feature: *slash*
|
|
| / VP[]
|
|
| |\ False
|
|
| |
|
|
X X <-- FAIL
|
|
None
|
|
|
|
The demo structures from category.py. They all parse, but they don't
|
|
do quite the right thing, -- ?x vs x.
|
|
|
|
>>> FeatStruct(pos='n', agr=FeatStruct(number='pl', gender='f'))
|
|
[agr=[gender='f', number='pl'], pos='n']
|
|
>>> FeatStruct(r'NP[sem=<bob>]/NP')
|
|
NP[sem=<bob>]/NP[]
|
|
>>> FeatStruct(r'S[sem=<app(?x, ?y)>]')
|
|
S[sem=<?x(?y)>]
|
|
>>> FeatStruct('?x/?x')
|
|
?x[]/?x[]
|
|
>>> FeatStruct('VP[+fin, agr=?x, tense=past]/NP[+pl, agr=?x]')
|
|
VP[agr=?x, +fin, tense='past']/NP[agr=?x, +pl]
|
|
>>> FeatStruct('S[sem = <app(?subj, ?vp)>]')
|
|
S[sem=<?subj(?vp)>]
|
|
|
|
>>> FeatStruct('S')
|
|
S[]
|
|
|
|
The parser also includes support for reading sets and tuples.
|
|
|
|
>>> FeatStruct('[x={1,2,2,2}, y={/}]')
|
|
[x={1, 2}, y={/}]
|
|
>>> FeatStruct('[x=(1,2,2,2), y=()]')
|
|
[x=(1, 2, 2, 2), y=()]
|
|
>>> print(FeatStruct('[x=(1,[z=(1,2,?x)],?z,{/})]'))
|
|
[ x = (1, [ z = (1, 2, ?x) ], ?z, {/}) ]
|
|
|
|
Note that we can't put a featstruct inside a tuple, because doing so
|
|
would hash it, and it's not frozen yet:
|
|
|
|
>>> print(FeatStruct('[x={[]}]'))
|
|
Traceback (most recent call last):
|
|
. . .
|
|
TypeError: FeatStructs must be frozen before they can be hashed.
|
|
|
|
There's a special syntax for taking the union of sets: "{...+...}".
|
|
The elements should only be variables or sets.
|
|
|
|
>>> FeatStruct('[x={?a+?b+{1,2,3}}]')
|
|
[x={?a+?b+{1, 2, 3}}]
|
|
|
|
There's a special syntax for taking the concatenation of tuples:
|
|
"(...+...)". The elements should only be variables or tuples.
|
|
|
|
>>> FeatStruct('[x=(?a+?b+(1,2,3))]')
|
|
[x=(?a+?b+(1, 2, 3))]
|
|
|
|
Parsing gives helpful messages if your string contains an error.
|
|
|
|
>>> FeatStruct('[a=, b=5]]')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Error parsing feature structure
|
|
[a=, b=5]]
|
|
^ Expected value
|
|
>>> FeatStruct('[a=12 22, b=33]')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Error parsing feature structure
|
|
[a=12 22, b=33]
|
|
^ Expected comma
|
|
>>> FeatStruct('[a=5] [b=6]')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Error parsing feature structure
|
|
[a=5] [b=6]
|
|
^ Expected end of string
|
|
>>> FeatStruct(' *++*')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Error parsing feature structure
|
|
*++*
|
|
^ Expected open bracket or identifier
|
|
>>> FeatStruct('[x->(1)]')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Error parsing feature structure
|
|
[x->(1)]
|
|
^ Expected bound identifier
|
|
>>> FeatStruct('[x->y]')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Error parsing feature structure
|
|
[x->y]
|
|
^ Expected identifier
|
|
>>> FeatStruct('')
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Error parsing feature structure
|
|
<BLANKLINE>
|
|
^ Expected open bracket or identifier
|
|
|
|
|
|
Unification
|
|
-----------
|
|
Very simple unifications give the expected results:
|
|
|
|
>>> FeatStruct().unify(FeatStruct())
|
|
[]
|
|
>>> FeatStruct(number='singular').unify(FeatStruct())
|
|
[number='singular']
|
|
>>> FeatStruct().unify(FeatStruct(number='singular'))
|
|
[number='singular']
|
|
>>> FeatStruct(number='singular').unify(FeatStruct(person=3))
|
|
[number='singular', person=3]
|
|
|
|
Merging nested structures:
|
|
|
|
>>> fs1 = FeatStruct('[A=[B=b]]')
|
|
>>> fs2 = FeatStruct('[A=[C=c]]')
|
|
>>> fs1.unify(fs2)
|
|
[A=[B='b', C='c']]
|
|
>>> fs2.unify(fs1)
|
|
[A=[B='b', C='c']]
|
|
|
|
A basic case of reentrant unification
|
|
|
|
>>> fs4 = FeatStruct('[A=(1)[B=b], E=[F->(1)]]')
|
|
>>> fs5 = FeatStruct("[A=[C='c'], E=[F=[D='d']]]")
|
|
>>> fs4.unify(fs5)
|
|
[A=(1)[B='b', C='c', D='d'], E=[F->(1)]]
|
|
>>> fs5.unify(fs4)
|
|
[A=(1)[B='b', C='c', D='d'], E=[F->(1)]]
|
|
|
|
More than 2 paths to a value
|
|
|
|
>>> fs1 = FeatStruct("[a=[],b=[],c=[],d=[]]")
|
|
>>> fs2 = FeatStruct('[a=(1)[], b->(1), c->(1), d->(1)]')
|
|
>>> fs1.unify(fs2)
|
|
[a=(1)[], b->(1), c->(1), d->(1)]
|
|
|
|
fs1[a] gets unified with itself
|
|
|
|
>>> fs1 = FeatStruct('[x=(1)[], y->(1)]')
|
|
>>> fs2 = FeatStruct('[x=(1)[], y->(1)]')
|
|
>>> fs1.unify(fs2)
|
|
[x=(1)[], y->(1)]
|
|
|
|
Bound variables should get forwarded appropriately
|
|
|
|
>>> fs1 = FeatStruct('[A=(1)[X=x], B->(1), C=?cvar, D=?dvar]')
|
|
>>> fs2 = FeatStruct('[A=(1)[Y=y], B=(2)[Z=z], C->(1), D->(2)]')
|
|
>>> fs1.unify(fs2)
|
|
[A=(1)[X='x', Y='y', Z='z'], B->(1), C->(1), D->(1)]
|
|
>>> fs2.unify(fs1)
|
|
[A=(1)[X='x', Y='y', Z='z'], B->(1), C->(1), D->(1)]
|
|
|
|
Cyclic structure created by unification.
|
|
|
|
>>> fs1 = FeatStruct('[F=(1)[], G->(1)]')
|
|
>>> fs2 = FeatStruct('[F=[H=(2)[]], G->(2)]')
|
|
>>> fs3 = fs1.unify(fs2)
|
|
>>> fs3
|
|
[F=(1)[H->(1)], G->(1)]
|
|
>>> fs3['F'] is fs3['G']
|
|
True
|
|
>>> fs3['F'] is fs3['G']['H']
|
|
True
|
|
>>> fs3['F'] is fs3['G']['H']['H']
|
|
True
|
|
>>> fs3['F'] is fs3['F']['H']['H']['H']['H']['H']['H']['H']['H']
|
|
True
|
|
|
|
Cyclic structure created w/ variables.
|
|
|
|
>>> fs1 = FeatStruct('[F=[H=?x]]')
|
|
>>> fs2 = FeatStruct('[F=?x]')
|
|
>>> fs3 = fs1.unify(fs2, rename_vars=False)
|
|
>>> fs3
|
|
[F=(1)[H->(1)]]
|
|
>>> fs3['F'] is fs3['F']['H']
|
|
True
|
|
>>> fs3['F'] is fs3['F']['H']['H']
|
|
True
|
|
>>> fs3['F'] is fs3['F']['H']['H']['H']['H']['H']['H']['H']['H']
|
|
True
|
|
|
|
Unifying w/ a cyclic feature structure.
|
|
|
|
>>> fs4 = FeatStruct('[F=[H=[H=[H=(1)[]]]], K->(1)]')
|
|
>>> fs3.unify(fs4)
|
|
[F=(1)[H->(1)], K->(1)]
|
|
>>> fs4.unify(fs3)
|
|
[F=(1)[H->(1)], K->(1)]
|
|
|
|
Variable bindings should preserve reentrance.
|
|
|
|
>>> bindings = {}
|
|
>>> fs1 = FeatStruct("[a=?x]")
|
|
>>> fs2 = fs1.unify(FeatStruct("[a=[]]"), bindings)
|
|
>>> fs2['a'] is bindings[Variable('?x')]
|
|
True
|
|
>>> fs2.unify(FeatStruct("[b=?x]"), bindings)
|
|
[a=(1)[], b->(1)]
|
|
|
|
Aliased variable tests
|
|
|
|
>>> fs1 = FeatStruct("[a=?x, b=?x]")
|
|
>>> fs2 = FeatStruct("[b=?y, c=?y]")
|
|
>>> bindings = {}
|
|
>>> fs3 = fs1.unify(fs2, bindings)
|
|
>>> fs3
|
|
[a=?x, b=?x, c=?x]
|
|
>>> bindings
|
|
{Variable('?y'): Variable('?x')}
|
|
>>> fs3.unify(FeatStruct("[a=1]"))
|
|
[a=1, b=1, c=1]
|
|
|
|
If we keep track of the bindings, then we can use the same variable
|
|
over multiple calls to unify.
|
|
|
|
>>> bindings = {}
|
|
>>> fs1 = FeatStruct('[a=?x]')
|
|
>>> fs2 = fs1.unify(FeatStruct('[a=[]]'), bindings)
|
|
>>> fs2.unify(FeatStruct('[b=?x]'), bindings)
|
|
[a=(1)[], b->(1)]
|
|
>>> bindings
|
|
{Variable('?x'): []}
|
|
|
|
..
|
|
>>> del fs1, fs2, fs3, fs4, fs5 # clean-up
|
|
|
|
Unification Bindings
|
|
--------------------
|
|
|
|
>>> bindings = {}
|
|
>>> fs1 = FeatStruct('[a=?x]')
|
|
>>> fs2 = FeatStruct('[a=12]')
|
|
>>> fs3 = FeatStruct('[b=?x]')
|
|
>>> fs1.unify(fs2, bindings)
|
|
[a=12]
|
|
>>> bindings
|
|
{Variable('?x'): 12}
|
|
>>> fs3.substitute_bindings(bindings)
|
|
[b=12]
|
|
>>> fs3 # substitute_bindings didn't mutate fs3.
|
|
[b=?x]
|
|
>>> fs2.unify(fs3, bindings)
|
|
[a=12, b=12]
|
|
|
|
>>> bindings = {}
|
|
>>> fs1 = FeatStruct('[a=?x, b=1]')
|
|
>>> fs2 = FeatStruct('[a=5, b=?x]')
|
|
>>> fs1.unify(fs2, bindings)
|
|
[a=5, b=1]
|
|
>>> sorted(bindings.items())
|
|
[(Variable('?x'), 5), (Variable('?x2'), 1)]
|
|
|
|
..
|
|
>>> del fs1, fs2, fs3 # clean-up
|
|
|
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Expressions
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-----------
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>>> e = Expression.fromstring('\\P y.P(z,y)')
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>>> fs1 = FeatStruct(x=e, y=Variable('z'))
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>>> fs2 = FeatStruct(y=VariableExpression(Variable('John')))
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>>> fs1.unify(fs2)
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[x=<\P y.P(John,y)>, y=<John>]
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Remove Variables
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----------------
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>>> FeatStruct('[a=?x, b=12, c=[d=?y]]').remove_variables()
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[b=12, c=[]]
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>>> FeatStruct('(1)[a=[b=?x,c->(1)]]').remove_variables()
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(1)[a=[c->(1)]]
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Equality & Hashing
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------------------
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The `equal_values` method checks whether two feature structures assign
|
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the same value to every feature. If the optional argument
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``check_reentrances`` is supplied, then it also returns false if there
|
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is any difference in the reentrances.
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>>> a = FeatStruct('(1)[x->(1)]')
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>>> b = FeatStruct('(1)[x->(1)]')
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>>> c = FeatStruct('(1)[x=[x->(1)]]')
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>>> d = FeatStruct('[x=(1)[x->(1)]]')
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>>> e = FeatStruct('(1)[x=[x->(1), y=1], y=1]')
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>>> def compare(x,y):
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... assert x.equal_values(y, True) == y.equal_values(x, True)
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... assert x.equal_values(y, False) == y.equal_values(x, False)
|
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... if x.equal_values(y, True):
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... assert x.equal_values(y, False)
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... print('equal values, same reentrance')
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... elif x.equal_values(y, False):
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... print('equal values, different reentrance')
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... else:
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... print('different values')
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>>> compare(a, a)
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equal values, same reentrance
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|
>>> compare(a, b)
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|
equal values, same reentrance
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|
>>> compare(a, c)
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|
equal values, different reentrance
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|
>>> compare(a, d)
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equal values, different reentrance
|
|
>>> compare(c, d)
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|
equal values, different reentrance
|
|
>>> compare(a, e)
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different values
|
|
>>> compare(c, e)
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|
different values
|
|
>>> compare(d, e)
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|
different values
|
|
>>> compare(e, e)
|
|
equal values, same reentrance
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|
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Feature structures may not be hashed until they are frozen:
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|
|
>>> hash(a)
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Traceback (most recent call last):
|
|
. . .
|
|
TypeError: FeatStructs must be frozen before they can be hashed.
|
|
>>> a.freeze()
|
|
>>> v = hash(a)
|
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|
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Feature structures define hash consistently. The following example
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looks at the hash value for each (fs1,fs2) pair; if their hash values
|
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are not equal, then they must not be equal. If their hash values are
|
|
equal, then display a message, and indicate whether their values are
|
|
indeed equal. Note that c and d currently have the same hash value,
|
|
even though they are not equal. That is not a bug, strictly speaking,
|
|
but it wouldn't be a bad thing if it changed.
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|
|
>>> for fstruct in (a, b, c, d, e):
|
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... fstruct.freeze()
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>>> for fs1_name in 'abcde':
|
|
... for fs2_name in 'abcde':
|
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... fs1 = locals()[fs1_name]
|
|
... fs2 = locals()[fs2_name]
|
|
... if hash(fs1) != hash(fs2):
|
|
... assert fs1 != fs2
|
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... else:
|
|
... print('%s and %s have the same hash value,' %
|
|
... (fs1_name, fs2_name))
|
|
... if fs1 == fs2: print('and are equal')
|
|
... else: print('and are not equal')
|
|
a and a have the same hash value, and are equal
|
|
a and b have the same hash value, and are equal
|
|
b and a have the same hash value, and are equal
|
|
b and b have the same hash value, and are equal
|
|
c and c have the same hash value, and are equal
|
|
c and d have the same hash value, and are not equal
|
|
d and c have the same hash value, and are not equal
|
|
d and d have the same hash value, and are equal
|
|
e and e have the same hash value, and are equal
|
|
|
|
..
|
|
>>> del a, b, c, d, e, v # clean-up
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|
|
Tracing
|
|
-------
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|
|
|
>>> fs1 = FeatStruct('[a=[b=(1)[], c=?x], d->(1), e=[f=?x]]')
|
|
>>> fs2 = FeatStruct('[a=(1)[c="C"], e=[g->(1)]]')
|
|
>>> fs1.unify(fs2, trace=True)
|
|
<BLANKLINE>
|
|
Unification trace:
|
|
/ [a=[b=(1)[], c=?x], d->(1), e=[f=?x]]
|
|
|\ [a=(1)[c='C'], e=[g->(1)]]
|
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|
|
|
| Unify feature: a
|
|
| / [b=[], c=?x]
|
|
| |\ [c='C']
|
|
| |
|
|
| | Unify feature: a.c
|
|
| | / ?x
|
|
| | |\ 'C'
|
|
| | |
|
|
| | +-->Variable('?x')
|
|
| |
|
|
| +-->[b=[], c=?x]
|
|
| Bindings: {?x: 'C'}
|
|
|
|
|
| Unify feature: e
|
|
| / [f=?x]
|
|
| |\ [g=[c='C']]
|
|
| |
|
|
| +-->[f=?x, g=[b=[], c=?x]]
|
|
| Bindings: {?x: 'C'}
|
|
|
|
|
+-->[a=(1)[b=(2)[], c='C'], d->(2), e=[f='C', g->(1)]]
|
|
Bindings: {?x: 'C'}
|
|
[a=(1)[b=(2)[], c='C'], d->(2), e=[f='C', g->(1)]]
|
|
>>>
|
|
>>> fs1 = FeatStruct('[a=?x, b=?z, c=?z]')
|
|
>>> fs2 = FeatStruct('[a=?y, b=?y, c=?q]')
|
|
>>> #fs1.unify(fs2, trace=True)
|
|
>>>
|
|
|
|
..
|
|
>>> del fs1, fs2 # clean-up
|
|
|
|
Unification on Dicts & Lists
|
|
----------------------------
|
|
It's possible to do unification on dictionaries:
|
|
|
|
>>> from nltk.featstruct import unify
|
|
>>> pprint(unify(dict(x=1, y=dict(z=2)), dict(x=1, q=5)), width=1)
|
|
{'q': 5, 'x': 1, 'y': {'z': 2}}
|
|
|
|
It's possible to do unification on lists as well:
|
|
|
|
>>> unify([1, 2, 3], [1, Variable('x'), 3])
|
|
[1, 2, 3]
|
|
|
|
Mixing dicts and lists is fine:
|
|
|
|
>>> pprint(unify([dict(x=1, y=dict(z=2)),3], [dict(x=1, q=5),3]),
|
|
... width=1)
|
|
[{'q': 5, 'x': 1, 'y': {'z': 2}}, 3]
|
|
|
|
Mixing dicts and FeatStructs is discouraged:
|
|
|
|
>>> unify(dict(x=1), FeatStruct(x=1))
|
|
Traceback (most recent call last):
|
|
. . .
|
|
ValueError: Mixing FeatStruct objects with Python dicts and lists is not supported.
|
|
|
|
But you can do it if you really want, by explicitly stating that both
|
|
dictionaries and FeatStructs should be treated as feature structures:
|
|
|
|
>>> unify(dict(x=1), FeatStruct(x=1), fs_class=(dict, FeatStruct))
|
|
{'x': 1}
|
|
|
|
Finding Conflicts
|
|
-----------------
|
|
|
|
>>> from nltk.featstruct import conflicts
|
|
>>> fs1 = FeatStruct('[a=[b=(1)[c=2], d->(1), e=[f->(1)]]]')
|
|
>>> fs2 = FeatStruct('[a=[b=[c=[x=5]], d=[c=2], e=[f=[c=3]]]]')
|
|
>>> for path in conflicts(fs1, fs2):
|
|
... print('%-8s: %r vs %r' % ('.'.join(path), fs1[path], fs2[path]))
|
|
a.b.c : 2 vs [x=5]
|
|
a.e.f.c : 2 vs 3
|
|
|
|
..
|
|
>>> del fs1, fs2 # clean-up
|
|
|
|
Retracting Bindings
|
|
-------------------
|
|
|
|
>>> from nltk.featstruct import retract_bindings
|
|
>>> bindings = {}
|
|
>>> fs1 = FeatStruct('[a=?x, b=[c=?y]]')
|
|
>>> fs2 = FeatStruct('[a=(1)[c=[d=1]], b->(1)]')
|
|
>>> fs3 = fs1.unify(fs2, bindings)
|
|
>>> print(fs3)
|
|
[ a = (1) [ c = [ d = 1 ] ] ]
|
|
[ ]
|
|
[ b -> (1) ]
|
|
>>> pprint(bindings)
|
|
{Variable('?x'): [c=[d=1]], Variable('?y'): [d=1]}
|
|
>>> retract_bindings(fs3, bindings)
|
|
[a=?x, b=?x]
|
|
>>> pprint(bindings)
|
|
{Variable('?x'): [c=?y], Variable('?y'): [d=1]}
|
|
|
|
Squashed Bugs
|
|
~~~~~~~~~~~~~
|
|
In svn rev 5167, unifying two feature structures that used the same
|
|
variable would cause those variables to become aliased in the output.
|
|
|
|
>>> fs1 = FeatStruct('[a=?x]')
|
|
>>> fs2 = FeatStruct('[b=?x]')
|
|
>>> fs1.unify(fs2)
|
|
[a=?x, b=?x2]
|
|
|
|
There was a bug in svn revision 5172 that caused `rename_variables` to
|
|
rename variables to names that are already used.
|
|
|
|
>>> FeatStruct('[a=?x, b=?x2]').rename_variables(
|
|
... vars=[Variable('?x')])
|
|
[a=?x3, b=?x2]
|
|
>>> fs1 = FeatStruct('[a=?x]')
|
|
>>> fs2 = FeatStruct('[a=?x, b=?x2]')
|
|
>>> fs1.unify(fs2)
|
|
[a=?x, b=?x2]
|
|
|
|
There was a bug in svn rev 5167 that caused us to get the following
|
|
example wrong. Basically the problem was that we only followed
|
|
'forward' pointers for other, not self, when unifying two feature
|
|
structures. (nb: this test assumes that features are unified in
|
|
alphabetical order -- if they are not, it might pass even if the bug
|
|
is present.)
|
|
|
|
>>> fs1 = FeatStruct('[a=[x=1], b=?x, c=?x]')
|
|
>>> fs2 = FeatStruct('[a=(1)[], b->(1), c=[x=2]]')
|
|
>>> print(fs1.unify(fs2))
|
|
None
|
|
|
|
..
|
|
>>> del fs1, fs2 # clean-up
|