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Bottom Up Filtering

Bottom Up Filtering. We know the current input word must serve as the first word in the derivation of the unexpanded node the parser is currently processing. Therefore the parser should not consider grammar rule for which the current word cannot serve as the " left corner "

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Bottom Up Filtering

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  1. Bottom Up Filtering • We know the current input word must serve as the first word in the derivation of the unexpanded node the parser is currently processing. • Therefore the parser should not consider grammar rule for which the current word cannot serve as the "left corner" • The left corner is the first word (or preterminal node) along the left edge of a derivation.

  2. Left Corner fl fl The nodes Verb and prefer are each left corners of VP

  3. Left Corner • B is a left corner of A iffA * Bαfor non-terminal A, pre-terminal B and symbol string α. • Possible left corners of all non-terminal categories can be determined in advance and placed in a table.

  4. Example of Left Corner Table

  5. How to use the Left Corner Table • If attempting to parse category A, only consider rules A → Bαfor which category(current input)  LeftCorners(B) • S → NP VPS → Aux NP VPS → VP

  6. Next Week • Problems with top down parser • left recursion • repeated work • Early Algorithm • Assignment • See J & M ch 10

  7. Top Down Implementation • Parser takes form of predicate parse(C,S1,S) : parse a constitutent C starting with input string S1 and ending with input string S.?- parse(s,[the,dog,barked],[]). • If C is a pre-terminal category, check, use lexicon to determine that current input word has that category. • Otherwise expand C using grammar rules and parse rhs constitutents.

  8. Top Down Parser parse(C,[Word|S],S) :- word(C,Word). parse(C,S1,S) :- rule(C,Cs), parse_list(Cs,S1,S). parse_list([],S,S). parse_list([C|Cs],S1,S) :- parse(C,S1,S2), parse_list(Cs,S2,S).

  9. % Grammar rule(s,[np,vp]). rule(np,[d,n]). rule(vp,[v]). rule(vp,[v,np]). % Lexicon word(d,the). word(n,dog). word(n,cat). word(n,dogs). word(n,cats). word(v,chase). word(v,chases). Recoding the Grammar/Lexicon

  10. Shift/Reduce Algorithm • Two data structures • input string • stack • Repeat until input is exhausted • Shift word to stack • Reduce stack using grammar and lexicon until no further reductions • Unlike top down, algorithm does not require category to be specified in advance. It simply finds all possible trees.

  11. Shift/Reduce Operation →| Step Action Stack Input 0 (start) the dog barked 1 shift the dog barked 2 reduce d dog barked 3 shift dog d barked 4 reduce n d barked 5 reduce np barked 6 shift barked np 7 reduce v np 8 reduce vp np 9 reduce s

  12. parse(S,Res) :- sr(S,[],Res). sr(S,Stk,Res) :- shift(Stk,S,NewStk,S1), reduce(NewStk,RedStk), sr(RedStk,S1,Res). sr([],Res,Res). shift(X,[H|Y],[H|X],Y). reduce(Stk,RedStk) :- brule(Stk,Stk2), reduce(Stk2,RedStk). reduce(Stk,Stk). Shift/Reduce Implementation

  13. Notice that the reduce operation always operates on the leftmost elements of the stack. Rules are stored in reverse order. We can reuse existing lexicon reduce(Stk,RedStk) :- brule(Stk,Stk2), reduce(Stk2,RedStk). reduce(Stk,Stk). %grammar brule([vp,np|X],[s|X]). brule([n,d|X],[np|X]). brule([np,v|X],[vp|X]). brule([np,v|X],[vp|X]). %interface to lexicon brule([Word|X],[C|X] :- word(C,Word). Shift/Reduce Implementation

  14. Principles for success • Left recursive structures must be found, not predicted • Empty categories must be predicted, not found • An alternative way to fix things • Grammar transformations can fix both left-recursion and epsilon productions • But then you parse the same language but with different trees

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