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

Stabler - Lx 185/209 2003
6.3 LC parsing
(16) Left corner parsing is intermediate between top-down and bottom-up. Like LR, LC parsers adopt a
(17)
strategy of “listening first,” but after listening to a “left corner,” the rest of the expansion is predicted.
In a constituent formed by applying a rewrite rule A → BCD, the “left corner” is just the first constituent
on the right side – B in the production A → BCD.
LC recognition is defined this way: 24
G, Γ ,S ⊢ G [axiom] for definite clauses Γ ,goalG, S ⊆ Σ ∗
G, Γ ,S ⊢ (?-¬q1,C)
G, Γ ,S ⊢ (?-q2,...,qn, ¬p, C)
G, Γ ,S ⊢ (?-¬q1,p,C)
G, Γ ,S ⊢ (?-q2,...,qn,C)
G, Γ ,wS ⊢ (?-C)
G, Γ ,S ⊢ (?-¬w,C)
[shift]
[lc] if (p:-q1,...,qn) ∈ Γ
[lc-complete] if (p:-q1,...,qn) ∈ Γ
G, Γ ,wS ⊢ (?-w,C) [shift-complete] =scan
G, Γ ,S ⊢ (?-C)
We want to allow the recognizer to handle empty productions, that is, productions (p:-q1,...,qn) ∈ Γ
where n = 0. We do this by saying that is such productions, the “left corner” is the empty string. With
this policy, the n = 0 instances of the lc rules can be written this way:
G, Γ ,S ⊢ (?-C)
G, Γ ,S ⊢ (?-¬p, C)
[lc-e] if (p:-[]) ∈ Γ
G, Γ ,S ⊢ (?-p, C) [lc-e-complete] if (p:-[]) ∈ Γ
G, Γ ,S ⊢ (?-C)
(18) Exercise: Use simple propositional reasoning of the sort shown in (2) on page 75 and in (10) on page
80 to show that the following inference step is sound. (tricky!)
G, Γ ,S ⊢ (?-¬r,q)
G, Γ ,S ⊢ (?-s,¬p, q)
82
[lc] if (p:-r,s) ∈ Γ