Optimal solutions to pattern matching problems

Abstract

We define a General Pattern Matching problem and we show that several compiling problems in programming languages, like pattern Matching in ML and the calling mechanism of Prolog can be formalized as instances of the General Pattern Matching problem. As a consequence of this, the solutions of the general problem which are compiling algorithms can be instantiated into compiling algorithms for the instances. In particular, the proof of the decidability of the existence of optimal solutions is a proof of the decidability of the instances. This approach can be used for the meta-compilation of pattern-matching problems, for the implementation of languages or systems that contain different instances of the general problem and for the implementation of systems using Call by Name style of evaluation for which completeness and optimality are equivalent.