The Abstraction and Instantiation of String-Matching Programs

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. To Neil Jones, for his 60th birthday. ∗Extended version of an article to appear in Neil Jones’s Festschrift. Corresponding authors: Torben Amtoft ([email protected]) and Olivier Danvy ([email protected]). †Basic Research in Computer Science (www.brics.dk), funded by the Danish National Research Foundation.