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.