Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
7.2.2 Collecting trees: a better perspective
(12) We can make tree collection easier by putting additional information into the chart, so that the chart
can be regarded as a “packed forest” of subtrees from which any successful derivations can easily be
extracted. We call the forest “packed” because a single item in the chart can participate in many (even
infinitely many) trees.
One version of this idea was proposed by Tomita (1985), and Billot and Lang (1989) noticed the basic idea
mentioned in the introduction: that what we want is a certain way of computing the intersection between
a regular language (represented by a finite state machine) and a context free language (represented by
acontextfreegrammar).
(13) We can implement this idea as follows: in each item, we indicate which rule was used to create it, and
we also indicate the “internal” positions:
/* ckypSWI.pl
* E Stabler, Feb 2000
* CKY parser, augmented with rules for 0,3,4,5,6-tuples
*/
:- op(1200,xfx,:˜). % this is our object language "if"
:- [’closure-swi’]. % defines closure/2, uses inference/4
%verbose. % comment to reduce verbosity of chart construction
computeClosure(Input) :lexAxioms(0,Input,Axioms),
closure(Axioms, Chart),
nl, portray_clauses(Chart).
computeClosure(Input,Chart) :lexAxioms(0,Input,Axioms),
closure(Axioms, Chart).
lexAxioms(_Pos,[],L) :bagof0(((X,X):(A:˜[])),(A
:˜ []),L).
lexAxioms(Pos,[W|Ws],[((Pos,Pos1):(W:˜[]))|Axioms]) :-
Pos1 is Pos+1,
lexAxioms(Pos1,Ws,Axioms).
inference(reduce1,
[ (Pos,Pos1):(W:˜_) ],
((Pos,Pos1):(A:˜[W])),
[(A :˜ [W])] ).
inference(reduce2,
[ ((Pos,Pos1):(B:˜_)), ((Pos1,Pos2):(C:˜_))],
((Pos,Pos2):(A:˜[B,Pos1,C])),
[(A :˜ [B,C])] ).
inference(reduce3,
[ ((Pos,Pos1):(B:˜_)), ((Pos1,Pos2):(C:˜_)), ((Pos2,Pos3):(D:˜_))],
(Pos,(A:˜[B,Pos1,C,Pos2,D]),Pos3),
[(A :˜ [B,C,D])] ).
inference(reduce4,
[ ((Pos,Pos1):(B:˜_)), ((Pos1,Pos2):(C:˜_)), ((Pos2,Pos3):(D:˜_)), ((Pos3,Pos4):(E:˜_))],
((Pos,Pos4):(A:˜[B,Pos1,C,Pos2,D,Pos3,E])),
[(A :˜ [B,C,D,E])] ).
inference(reduce5,
[ ((Pos,Pos1):(B:˜_)), ((Pos1,Pos2):(C:˜_)), ((Pos2,Pos3):(D:˜_)), ((Pos3,Pos4):(E:˜_)), ((Pos4,Pos5):(F:˜_))],
((Pos,Pos5):(A:˜[B,Pos1,C,Pos2,D,Pos3,E,Pos4,F])),
[(A :˜ [B,C,D,E,F])] ).
inference(reduce6,
[ ((Pos,Pos1):(B:˜_)), ((Pos1,Pos2):(C:˜_)), ((Pos2,Pos3):(D:˜_)), ((Pos3,Pos4):(E:˜_)), ((Pos4,Pos5):(F:˜_)), ((Pos5,Pos6):(F:˜_))],
((Pos,Pos6):(A:˜[B,Pos1,C,Pos2,D,Pos3,E,Pos4,F,Pos5,G])),
[(A :˜ [B,C,D,E,F,G])] ).
portray_clauses([]).
portray_clauses([C|Cs]) :- portray_clause(C), portray_clauses(Cs).
bagof0(A,B,C) :- bagof(A,B,C), !.
bagof0(_,_,[]).
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