518 lines
19 KiB
Plaintext
518 lines
19 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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Discourse Representation Theory
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================================
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>>> from nltk.sem import logic
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>>> from nltk.inference import TableauProver
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Overview
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========
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A DRS can be created with the ``DRS()`` constructor. This takes two arguments: a list of
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discourse referents and list of conditions. .
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>>> from nltk.sem.drt import *
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>>> dexpr = DrtExpression.fromstring
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>>> man_x = dexpr('man(x)')
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>>> walk_x = dexpr('walk(x)')
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>>> x = dexpr('x')
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>>> print(DRS([x], [man_x, walk_x]))
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([x],[man(x), walk(x)])
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The ``parse()`` method can also be applied directly to DRS
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expressions, which allows them to be specified more
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easily.
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>>> drs1 = dexpr('([x],[man(x),walk(x)])')
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>>> print(drs1)
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([x],[man(x), walk(x)])
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DRSs can be *merged* using the ``+`` operator.
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>>> drs2 = dexpr('([y],[woman(y),stop(y)])')
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>>> drs3 = drs1 + drs2
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>>> print(drs3)
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(([x],[man(x), walk(x)]) + ([y],[woman(y), stop(y)]))
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>>> print(drs3.simplify())
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([x,y],[man(x), walk(x), woman(y), stop(y)])
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We can embed DRSs as components of an ``implies`` condition.
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>>> s = '([], [(%s -> %s)])' % (drs1, drs2)
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>>> print(dexpr(s))
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([],[(([x],[man(x), walk(x)]) -> ([y],[woman(y), stop(y)]))])
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The ``fol()`` method converts DRSs into FOL formulae.
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>>> print(dexpr(r'([x],[man(x), walks(x)])').fol())
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exists x.(man(x) & walks(x))
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>>> print(dexpr(r'([],[(([x],[man(x)]) -> ([],[walks(x)]))])').fol())
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all x.(man(x) -> walks(x))
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In order to visualize a DRS, the ``pretty_format()`` method can be used.
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>>> print(drs3.pretty_format())
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_________ __________
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| x | | y |
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(|---------| + |----------|)
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| man(x) | | woman(y) |
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| walk(x) | | stop(y) |
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|_________| |__________|
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Parse to semantics
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------------------
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..
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>>> logic._counter._value = 0
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DRSs can be used for building compositional semantics in a feature
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based grammar. To specify that we want to use DRSs, the appropriate
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logic parser needs be passed as a parameter to ``load_earley()``
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>>> from nltk.parse import load_parser
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>>> from nltk.sem.drt import DrtParser
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>>> parser = load_parser('grammars/book_grammars/drt.fcfg', trace=0, logic_parser=DrtParser())
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>>> for tree in parser.parse('a dog barks'.split()):
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... print(tree.label()['SEM'].simplify())
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...
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([x],[dog(x), bark(x)])
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Alternatively, a ``FeatStructReader`` can be passed with the ``logic_parser`` set on it
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>>> from nltk.featstruct import FeatStructReader
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>>> from nltk.grammar import FeatStructNonterminal
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>>> parser = load_parser('grammars/book_grammars/drt.fcfg', trace=0, fstruct_reader=FeatStructReader(fdict_class=FeatStructNonterminal, logic_parser=DrtParser()))
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>>> for tree in parser.parse('every girl chases a dog'.split()):
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... print(tree.label()['SEM'].simplify().normalize())
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...
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([],[(([z1],[girl(z1)]) -> ([z2],[dog(z2), chase(z1,z2)]))])
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Unit Tests
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==========
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Parser
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------
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>>> print(dexpr(r'([x,y],[sees(x,y)])'))
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([x,y],[sees(x,y)])
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>>> print(dexpr(r'([x],[man(x), walks(x)])'))
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([x],[man(x), walks(x)])
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>>> print(dexpr(r'\x.([],[man(x), walks(x)])'))
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\x.([],[man(x), walks(x)])
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>>> print(dexpr(r'\x.\y.([],[sees(x,y)])'))
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\x y.([],[sees(x,y)])
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>>> print(dexpr(r'([x,y],[(x = y)])'))
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([x,y],[(x = y)])
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>>> print(dexpr(r'([x,y],[(x != y)])'))
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([x,y],[-(x = y)])
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>>> print(dexpr(r'\x.([],[walks(x)])(john)'))
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(\x.([],[walks(x)]))(john)
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>>> print(dexpr(r'\R.\x.([],[big(x,R)])(\y.([],[mouse(y)]))'))
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(\R x.([],[big(x,R)]))(\y.([],[mouse(y)]))
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>>> print(dexpr(r'(([x],[walks(x)]) + ([y],[runs(y)]))'))
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(([x],[walks(x)]) + ([y],[runs(y)]))
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>>> print(dexpr(r'(([x,y],[walks(x), jumps(y)]) + (([z],[twos(z)]) + ([w],[runs(w)])))'))
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(([x,y],[walks(x), jumps(y)]) + ([z],[twos(z)]) + ([w],[runs(w)]))
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>>> print(dexpr(r'((([],[walks(x)]) + ([],[twos(x)])) + ([],[runs(x)]))'))
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(([],[walks(x)]) + ([],[twos(x)]) + ([],[runs(x)]))
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>>> print(dexpr(r'((([],[walks(x)]) + ([],[runs(x)])) + (([],[threes(x)]) + ([],[fours(x)])))'))
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(([],[walks(x)]) + ([],[runs(x)]) + ([],[threes(x)]) + ([],[fours(x)]))
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>>> print(dexpr(r'(([],[walks(x)]) -> ([],[runs(x)]))'))
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(([],[walks(x)]) -> ([],[runs(x)]))
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>>> print(dexpr(r'([x],[PRO(x), sees(John,x)])'))
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([x],[PRO(x), sees(John,x)])
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>>> print(dexpr(r'([x],[man(x), -([],[walks(x)])])'))
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([x],[man(x), -([],[walks(x)])])
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>>> print(dexpr(r'([],[(([x],[man(x)]) -> ([],[walks(x)]))])'))
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([],[(([x],[man(x)]) -> ([],[walks(x)]))])
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>>> print(dexpr(r'DRS([x],[walk(x)])'))
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([x],[walk(x)])
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>>> print(dexpr(r'DRS([x][walk(x)])'))
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([x],[walk(x)])
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>>> print(dexpr(r'([x][walk(x)])'))
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([x],[walk(x)])
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``simplify()``
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--------------
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>>> print(dexpr(r'\x.([],[man(x), walks(x)])(john)').simplify())
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([],[man(john), walks(john)])
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>>> print(dexpr(r'\x.\y.([z],[dog(z),sees(x,y)])(john)(mary)').simplify())
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([z],[dog(z), sees(john,mary)])
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>>> print(dexpr(r'\R x.([],[big(x,R)])(\y.([],[mouse(y)]))').simplify())
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\x.([],[big(x,\y.([],[mouse(y)]))])
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>>> print(dexpr(r'(([x],[walks(x)]) + ([y],[runs(y)]))').simplify())
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([x,y],[walks(x), runs(y)])
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>>> print(dexpr(r'(([x,y],[walks(x), jumps(y)]) + (([z],[twos(z)]) + ([w],[runs(w)])))').simplify())
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([w,x,y,z],[walks(x), jumps(y), twos(z), runs(w)])
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>>> print(dexpr(r'((([],[walks(x)]) + ([],[runs(x)]) + ([],[threes(x)]) + ([],[fours(x)])))').simplify())
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([],[walks(x), runs(x), threes(x), fours(x)])
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>>> dexpr(r'([x],[man(x)])+([x],[walks(x)])').simplify() == \
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... dexpr(r'([x,z1],[man(x), walks(z1)])')
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True
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>>> dexpr(r'([y],[boy(y), (([x],[dog(x)]) -> ([],[chase(x,y)]))])+([x],[run(x)])').simplify() == \
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... dexpr(r'([y,z1],[boy(y), (([x],[dog(x)]) -> ([],[chase(x,y)])), run(z1)])')
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True
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>>> dexpr(r'\Q.(([x],[john(x),walks(x)]) + Q)(([x],[PRO(x),leaves(x)]))').simplify() == \
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... dexpr(r'([x,z1],[john(x), walks(x), PRO(z1), leaves(z1)])')
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True
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>>> logic._counter._value = 0
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>>> print(dexpr('([],[(([x],[dog(x)]) -> ([e,y],[boy(y), chase(e), subj(e,x), obj(e,y)]))])+([e,x],[PRO(x), run(e), subj(e,x)])').simplify().normalize().normalize())
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([e02,z5],[(([z3],[dog(z3)]) -> ([e01,z4],[boy(z4), chase(e01), subj(e01,z3), obj(e01,z4)])), PRO(z5), run(e02), subj(e02,z5)])
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``fol()``
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-----------
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>>> print(dexpr(r'([x,y],[sees(x,y)])').fol())
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exists x y.sees(x,y)
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>>> print(dexpr(r'([x],[man(x), walks(x)])').fol())
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exists x.(man(x) & walks(x))
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>>> print(dexpr(r'\x.([],[man(x), walks(x)])').fol())
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\x.(man(x) & walks(x))
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>>> print(dexpr(r'\x y.([],[sees(x,y)])').fol())
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\x y.sees(x,y)
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>>> print(dexpr(r'\x.([],[walks(x)])(john)').fol())
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\x.walks(x)(john)
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>>> print(dexpr(r'\R x.([],[big(x,R)])(\y.([],[mouse(y)]))').fol())
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(\R x.big(x,R))(\y.mouse(y))
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>>> print(dexpr(r'(([x],[walks(x)]) + ([y],[runs(y)]))').fol())
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(exists x.walks(x) & exists y.runs(y))
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>>> print(dexpr(r'(([],[walks(x)]) -> ([],[runs(x)]))').fol())
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(walks(x) -> runs(x))
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>>> print(dexpr(r'([x],[PRO(x), sees(John,x)])').fol())
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exists x.(PRO(x) & sees(John,x))
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>>> print(dexpr(r'([x],[man(x), -([],[walks(x)])])').fol())
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exists x.(man(x) & -walks(x))
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>>> print(dexpr(r'([],[(([x],[man(x)]) -> ([],[walks(x)]))])').fol())
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all x.(man(x) -> walks(x))
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>>> print(dexpr(r'([x],[man(x) | walks(x)])').fol())
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exists x.(man(x) | walks(x))
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>>> print(dexpr(r'P(x) + ([x],[walks(x)])').fol())
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(P(x) & exists x.walks(x))
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``resolve_anaphora()``
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----------------------
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>>> from nltk.sem.drt import AnaphoraResolutionException
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>>> print(resolve_anaphora(dexpr(r'([x,y,z],[dog(x), cat(y), walks(z), PRO(z)])')))
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([x,y,z],[dog(x), cat(y), walks(z), (z = [x,y])])
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>>> print(resolve_anaphora(dexpr(r'([],[(([x],[dog(x)]) -> ([y],[walks(y), PRO(y)]))])')))
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([],[(([x],[dog(x)]) -> ([y],[walks(y), (y = x)]))])
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>>> print(resolve_anaphora(dexpr(r'(([x,y],[]) + ([],[PRO(x)]))')).simplify())
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([x,y],[(x = y)])
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>>> try: print(resolve_anaphora(dexpr(r'([x],[walks(x), PRO(x)])')))
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... except AnaphoraResolutionException as e: print(e)
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Variable 'x' does not resolve to anything.
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>>> print(resolve_anaphora(dexpr('([e01,z6,z7],[boy(z6), PRO(z7), run(e01), subj(e01,z7)])')))
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([e01,z6,z7],[boy(z6), (z7 = z6), run(e01), subj(e01,z7)])
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``equiv()``:
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----------------
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>>> a = dexpr(r'([x],[man(x), walks(x)])')
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>>> b = dexpr(r'([x],[walks(x), man(x)])')
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>>> print(a.equiv(b, TableauProver()))
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True
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``replace()``:
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--------------
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>>> a = dexpr(r'a')
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>>> w = dexpr(r'w')
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>>> x = dexpr(r'x')
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>>> y = dexpr(r'y')
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>>> z = dexpr(r'z')
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replace bound
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-------------
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>>> print(dexpr(r'([x],[give(x,y,z)])').replace(x.variable, a, False))
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([x],[give(x,y,z)])
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>>> print(dexpr(r'([x],[give(x,y,z)])').replace(x.variable, a, True))
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([a],[give(a,y,z)])
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replace unbound
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---------------
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>>> print(dexpr(r'([x],[give(x,y,z)])').replace(y.variable, a, False))
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([x],[give(x,a,z)])
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>>> print(dexpr(r'([x],[give(x,y,z)])').replace(y.variable, a, True))
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([x],[give(x,a,z)])
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replace unbound with bound
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--------------------------
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>>> dexpr(r'([x],[give(x,y,z)])').replace(y.variable, x, False) == \
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... dexpr('([z1],[give(z1,x,z)])')
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True
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>>> dexpr(r'([x],[give(x,y,z)])').replace(y.variable, x, True) == \
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... dexpr('([z1],[give(z1,x,z)])')
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True
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replace unbound with unbound
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----------------------------
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>>> print(dexpr(r'([x],[give(x,y,z)])').replace(y.variable, z, False))
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([x],[give(x,z,z)])
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>>> print(dexpr(r'([x],[give(x,y,z)])').replace(y.variable, z, True))
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([x],[give(x,z,z)])
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replace unbound
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---------------
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>>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(z.variable, a, False))
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(([x],[P(x,y,a)]) + ([y],[Q(x,y,a)]))
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>>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(z.variable, a, True))
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(([x],[P(x,y,a)]) + ([y],[Q(x,y,a)]))
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replace bound
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-------------
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>>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(x.variable, a, False))
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(([x],[P(x,y,z)]) + ([y],[Q(x,y,z)]))
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>>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(x.variable, a, True))
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(([a],[P(a,y,z)]) + ([y],[Q(a,y,z)]))
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replace unbound with unbound
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----------------------------
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>>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(z.variable, a, False))
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(([x],[P(x,y,a)]) + ([y],[Q(x,y,a)]))
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>>> print(dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,z)])').replace(z.variable, a, True))
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(([x],[P(x,y,a)]) + ([y],[Q(x,y,a)]))
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replace unbound with bound on same side
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---------------------------------------
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>>> dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,w)])').replace(z.variable, x, False) == \
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... dexpr(r'(([z1],[P(z1,y,x)]) + ([y],[Q(z1,y,w)]))')
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True
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>>> dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,w)])').replace(z.variable, x, True) == \
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... dexpr(r'(([z1],[P(z1,y,x)]) + ([y],[Q(z1,y,w)]))')
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True
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replace unbound with bound on other side
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----------------------------------------
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>>> dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,w)])').replace(w.variable, x, False) == \
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... dexpr(r'(([z1],[P(z1,y,z)]) + ([y],[Q(z1,y,x)]))')
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True
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>>> dexpr(r'([x],[P(x,y,z)])+([y],[Q(x,y,w)])').replace(w.variable, x, True) == \
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... dexpr(r'(([z1],[P(z1,y,z)]) + ([y],[Q(z1,y,x)]))')
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True
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replace unbound with double bound
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---------------------------------
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>>> dexpr(r'([x],[P(x,y,z)])+([x],[Q(x,y,w)])').replace(z.variable, x, False) == \
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... dexpr(r'(([z1],[P(z1,y,x)]) + ([z1],[Q(z1,y,w)]))')
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True
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>>> dexpr(r'([x],[P(x,y,z)])+([x],[Q(x,y,w)])').replace(z.variable, x, True) == \
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... dexpr(r'(([z1],[P(z1,y,x)]) + ([z1],[Q(z1,y,w)]))')
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True
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regression tests
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----------------
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>>> d = dexpr('([x],[A(c), ([y],[B(x,y,z,a)])->([z],[C(x,y,z,a)])])')
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>>> print(d)
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([x],[A(c), (([y],[B(x,y,z,a)]) -> ([z],[C(x,y,z,a)]))])
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>>> print(d.pretty_format())
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____________________________________
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| x |
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|------------------------------------|
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| A(c) |
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| ____________ ____________ |
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| | y | | z | |
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| (|------------| -> |------------|) |
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| | B(x,y,z,a) | | C(x,y,z,a) | |
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| |____________| |____________| |
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|____________________________________|
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>>> print(str(d))
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([x],[A(c), (([y],[B(x,y,z,a)]) -> ([z],[C(x,y,z,a)]))])
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>>> print(d.fol())
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exists x.(A(c) & all y.(B(x,y,z,a) -> exists z.C(x,y,z,a)))
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>>> print(d.replace(Variable('a'), DrtVariableExpression(Variable('r'))))
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([x],[A(c), (([y],[B(x,y,z,r)]) -> ([z],[C(x,y,z,r)]))])
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>>> print(d.replace(Variable('x'), DrtVariableExpression(Variable('r'))))
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([x],[A(c), (([y],[B(x,y,z,a)]) -> ([z],[C(x,y,z,a)]))])
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>>> print(d.replace(Variable('y'), DrtVariableExpression(Variable('r'))))
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([x],[A(c), (([y],[B(x,y,z,a)]) -> ([z],[C(x,y,z,a)]))])
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>>> print(d.replace(Variable('z'), DrtVariableExpression(Variable('r'))))
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([x],[A(c), (([y],[B(x,y,r,a)]) -> ([z],[C(x,y,z,a)]))])
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>>> print(d.replace(Variable('x'), DrtVariableExpression(Variable('r')), True))
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([r],[A(c), (([y],[B(r,y,z,a)]) -> ([z],[C(r,y,z,a)]))])
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>>> print(d.replace(Variable('y'), DrtVariableExpression(Variable('r')), True))
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([x],[A(c), (([r],[B(x,r,z,a)]) -> ([z],[C(x,r,z,a)]))])
|
|
>>> print(d.replace(Variable('z'), DrtVariableExpression(Variable('r')), True))
|
|
([x],[A(c), (([y],[B(x,y,r,a)]) -> ([r],[C(x,y,r,a)]))])
|
|
>>> print(d == dexpr('([l],[A(c), ([m],[B(l,m,z,a)])->([n],[C(l,m,n,a)])])'))
|
|
True
|
|
>>> d = dexpr('([],[([x,y],[B(x,y,h), ([a,b],[dee(x,a,g)])])->([z,w],[cee(x,y,f), ([c,d],[E(x,c,d,e)])])])')
|
|
>>> sorted(d.free())
|
|
[Variable('B'), Variable('E'), Variable('e'), Variable('f'), Variable('g'), Variable('h')]
|
|
>>> sorted(d.variables())
|
|
[Variable('B'), Variable('E'), Variable('e'), Variable('f'), Variable('g'), Variable('h')]
|
|
>>> sorted(d.get_refs(True))
|
|
[Variable('a'), Variable('b'), Variable('c'), Variable('d'), Variable('w'), Variable('x'), Variable('y'), Variable('z')]
|
|
>>> sorted(d.conds[0].get_refs(False))
|
|
[Variable('x'), Variable('y')]
|
|
>>> print(dexpr('([x,y],[A(x,y), (x=y), ([],[B(x,y)])->([],[C(x,y)]), ([x,y],[D(x,y)])->([],[E(x,y)]), ([],[F(x,y)])->([x,y],[G(x,y)])])').eliminate_equality())
|
|
([x],[A(x,x), (([],[B(x,x)]) -> ([],[C(x,x)])), (([x,y],[D(x,y)]) -> ([],[E(x,y)])), (([],[F(x,x)]) -> ([x,y],[G(x,y)]))])
|
|
>>> print(dexpr('([x,y],[A(x,y), (x=y)]) -> ([],[B(x,y)])').eliminate_equality())
|
|
(([x],[A(x,x)]) -> ([],[B(x,x)]))
|
|
>>> print(dexpr('([x,y],[A(x,y)]) -> ([],[B(x,y), (x=y)])').eliminate_equality())
|
|
(([x,y],[A(x,y)]) -> ([],[B(x,x)]))
|
|
>>> print(dexpr('([x,y],[A(x,y), (x=y), ([],[B(x,y)])])').eliminate_equality())
|
|
([x],[A(x,x), ([],[B(x,x)])])
|
|
>>> print(dexpr('([x,y],[A(x,y), ([],[B(x,y), (x=y)])])').eliminate_equality())
|
|
([x,y],[A(x,y), ([],[B(x,x)])])
|
|
>>> print(dexpr('([z8 z9 z10],[A(z8), z8=z10, z9=z10, B(z9), C(z10), D(z10)])').eliminate_equality())
|
|
([z9],[A(z9), B(z9), C(z9), D(z9)])
|
|
|
|
>>> print(dexpr('([x,y],[A(x,y), (x=y), ([],[B(x,y)]), ([x,y],[C(x,y)])])').eliminate_equality())
|
|
([x],[A(x,x), ([],[B(x,x)]), ([x,y],[C(x,y)])])
|
|
>>> print(dexpr('([x,y],[A(x,y)]) + ([],[B(x,y), (x=y)]) + ([],[C(x,y)])').eliminate_equality())
|
|
([x],[A(x,x), B(x,x), C(x,x)])
|
|
>>> print(dexpr('([x,y],[B(x,y)])+([x,y],[C(x,y)])').replace(Variable('y'), DrtVariableExpression(Variable('x'))))
|
|
(([x,y],[B(x,y)]) + ([x,y],[C(x,y)]))
|
|
>>> print(dexpr('(([x,y],[B(x,y)])+([],[C(x,y)]))+([],[D(x,y)])').replace(Variable('y'), DrtVariableExpression(Variable('x'))))
|
|
(([x,y],[B(x,y)]) + ([],[C(x,y)]) + ([],[D(x,y)]))
|
|
>>> print(dexpr('(([],[B(x,y)])+([],[C(x,y)]))+([],[D(x,y)])').replace(Variable('y'), DrtVariableExpression(Variable('x'))))
|
|
(([],[B(x,x)]) + ([],[C(x,x)]) + ([],[D(x,x)]))
|
|
>>> print(dexpr('(([],[B(x,y), ([x,y],[A(x,y)])])+([],[C(x,y)]))+([],[D(x,y)])').replace(Variable('y'), DrtVariableExpression(Variable('x'))).normalize())
|
|
(([],[B(z3,z1), ([z2,z3],[A(z3,z2)])]) + ([],[C(z3,z1)]) + ([],[D(z3,z1)]))
|
|
|
|
|
|
Parse errors
|
|
============
|
|
|
|
>>> def parse_error(drtstring):
|
|
... try: dexpr(drtstring)
|
|
... except logic.LogicalExpressionException as e: print(e)
|
|
|
|
>>> parse_error(r'')
|
|
End of input found. Expression expected.
|
|
<BLANKLINE>
|
|
^
|
|
>>> parse_error(r'(')
|
|
End of input found. Expression expected.
|
|
(
|
|
^
|
|
>>> parse_error(r'()')
|
|
Unexpected token: ')'. Expression expected.
|
|
()
|
|
^
|
|
>>> parse_error(r'([')
|
|
End of input found. Expected token ']'.
|
|
([
|
|
^
|
|
>>> parse_error(r'([,')
|
|
',' is an illegal variable name. Constants may not be quantified.
|
|
([,
|
|
^
|
|
>>> parse_error(r'([x,')
|
|
End of input found. Variable expected.
|
|
([x,
|
|
^
|
|
>>> parse_error(r'([]')
|
|
End of input found. Expected token '['.
|
|
([]
|
|
^
|
|
>>> parse_error(r'([][')
|
|
End of input found. Expected token ']'.
|
|
([][
|
|
^
|
|
>>> parse_error(r'([][,')
|
|
Unexpected token: ','. Expression expected.
|
|
([][,
|
|
^
|
|
>>> parse_error(r'([][]')
|
|
End of input found. Expected token ')'.
|
|
([][]
|
|
^
|
|
>>> parse_error(r'([x][man(x)]) |')
|
|
End of input found. Expression expected.
|
|
([x][man(x)]) |
|
|
^
|
|
|
|
Pretty Printing
|
|
===============
|
|
|
|
>>> dexpr(r"([],[])").pretty_print()
|
|
__
|
|
| |
|
|
|--|
|
|
|__|
|
|
|
|
>>> dexpr(r"([],[([x],[big(x), dog(x)]) -> ([],[bark(x)]) -([x],[walk(x)])])").pretty_print()
|
|
_____________________________
|
|
| |
|
|
|-----------------------------|
|
|
| ________ _________ |
|
|
| | x | | | |
|
|
| (|--------| -> |---------|) |
|
|
| | big(x) | | bark(x) | |
|
|
| | dog(x) | |_________| |
|
|
| |________| |
|
|
| _________ |
|
|
| | x | |
|
|
| __ |---------| |
|
|
| | | walk(x) | |
|
|
| |_________| |
|
|
|_____________________________|
|
|
|
|
>>> dexpr(r"([x,y],[x=y]) + ([z],[dog(z), walk(z)])").pretty_print()
|
|
_________ _________
|
|
| x y | | z |
|
|
(|---------| + |---------|)
|
|
| (x = y) | | dog(z) |
|
|
|_________| | walk(z) |
|
|
|_________|
|
|
|
|
>>> dexpr(r"([],[([x],[]) | ([y],[]) | ([z],[dog(z), walk(z)])])").pretty_print()
|
|
_______________________________
|
|
| |
|
|
|-------------------------------|
|
|
| ___ ___ _________ |
|
|
| | x | | y | | z | |
|
|
| (|---| | |---| | |---------|) |
|
|
| |___| |___| | dog(z) | |
|
|
| | walk(z) | |
|
|
| |_________| |
|
|
|_______________________________|
|
|
|
|
>>> dexpr(r"\P.\Q.(([x],[]) + P(x) + Q(x))(\x.([],[dog(x)]))").pretty_print()
|
|
___ ________
|
|
\ | x | \ | |
|
|
/\ P Q.(|---| + P(x) + Q(x))( /\ x.|--------|)
|
|
|___| | dog(x) |
|
|
|________|
|
|
|
|
|