We still have to introduce caching. Since the functions "Binaries" and "Units" de-
pend only on the grammar and not on the input string
itself,
they can be precomputed
and set up in a table. They can be queried via a table lookup using (Lookup ...); no
testing or waiting is required. We cache "Derivations" to provide us the recognition table.
This yields a pure bottom-up recognizer, presented below, with its name changed from
Derivations to CKY.
Algorithm VII The kernel of Cocke-Kasami- Younger algorithm
Invoke (member 'S (CKY [0,n]))
Define (CKY [i,j])
s
case j-i = 1 (Lookup (Units (input i j)))
case j-i > 1
(Union for k in (i+1 to j-1)
(Unio ...
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