Left corner

{{Short description|Part of a production rule in a context-free grammar}}

{{one source |date=April 2024}}

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.[http://cs.union.edu/~striegnk/courses/nlp-with-prolog/html/node55.html 9.3 Using Left-corner Tables], Patrick Blackburn and Kristina Striegnitz, Natural Language Processing Techniques in Prolog

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.