Left corner

In formal language theory, the left corner of a production rule in a context-free grammar is the left-most symbol on the right side of the rule.[1]

For example, in the rule A→Xα, X is the left corner.

The left corner table associates to a symbol all possible left corners for that symbol, and the left corners of those symbols, etc.

Given the grammar

S → VP

S → NP VP

VP → V NP

NP → DET N

the left corner table is as follows.

Symbol	Left corner(s)
S	VP, NP, V, DET
NP	DET
VP	V

Left corners are used to add bottom-up filtering to a top-down parser, or top-down filtering to a bottom-up parser.

References

1. 9.3 Using Left-corner Tables, Patrick Blackburn and Kristina Striegnitz, Natural Language Processing Techniques in Prolog