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

Stabler - Lx 185/209 2003
3.5 The top-down parser
D
the
DP
D’
NP
N’
N
penguin
IP
I’
I VP
V’
V
swims
V’
AdvP
Adv’
Adv
beautifully
(24) Any TD proof can be represented as a tree, so let’s modify the TD provable ˜ predicate so that it not
(25)
only finds proofs, but also builds tree representations of the proofs that it finds.
Recall that the TD ?˜ predicate is defined this way:
/*
* file: td.pl = ll.pl
*
*/
:- op(1200,xfx,:˜). % this is our object language "if"
:- op(1100,xfx,?˜). % provability predicate
[] ?˜ [].
(S0 ?˜ Goals0) :- infer(S0,Goals0,S,Goals), (S ?˜ Goals).
infer(S,[A|C], S,DC) :- (A :˜ D), append(D,C,DC). % ll
infer([A|S],[A|C], S,C). % scan
append([],L,L).
append([E|L],M,[E|N]) :- append(L,M,N).
The predicate ?˜ takes 2 arguments: the list of lexical axioms (the “input string”) and the list of goals
to be proven, respectively.
In the second rule, when subgoal A expands to subgoals D, we want to build a tree that shows a node
labeled A dominating these subgoals.
(26) The parser is trickier; going through it carefully will be left as an optional exercise. We add a third
argument in which to hold the proof trees.
/*
* file: tdp.pl = llp.pl
*/
:- op(1200,xfx,:˜). % this is our object language "if"
:- op(1100,xfx,?˜). % provability predicate
:- op(500,yfx,@). % metalanguage functor to separate goals from trees
[] ?˜ []@[].
(S0 ?˜ Goals0@T0) :- infer(S0,Goals0@T0,S,Goals@T), (S ?˜ Goals@T).
infer(S,[A|C]@[A/DTs|CTs],S,DC@DCTs) :- (A :˜ D), new_goals(D,C,CTs,DC,DCTs,DTs). \% ll
infer([A|S],[A|C]@[A/[]|CTs],S,C@CTs). \% scan
%new_goals(NewGoals,OldGoals,OldTrees,AllGoals,AllTrees,NewTrees)
new_goals([],Gs,Ts,Gs,Ts,[]).
new_goals([G|Gs0],Gs1,Ts1,[G|Gs2],[T|Ts2],[T|Ts]) :- new_goals(Gs0,Gs1,Ts1,Gs2,Ts2,Ts).
In this code new_goals really does three related things at once. In the second clause of ?˜, for example,
the call to new_goals
i. appends goals D and C to obtain the new goal sequence DC;
ii. for each element of D, it adds a tree T to the list CTs of trees, yielding DCTs; and
iii. each added tree T is also put into the list of trees DTs corresponding to D.
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