The Abstraction and Instantiation of String-Matching Programs

Abstract

We consider a naive, quadratic string matcher testing whether a
pattern occurs in a text; we equip it with a cache mediating its access to the
text; and we abstract the traversal policy of the pattern, the cache, and
the text. We then specialize this abstracted program with respect to a
pattern, using the off-the-shelf partial evaluator Similix.
Instantiating the abstracted program with a left-to-right traversal policy
yields the linear-time behavior of Knuth, Morris and Pratt's string
matcher. Instantiating it with a right-to-left policy yields the linear-time
behavior of Boyer and Moore's string matcher.