Pattern Matching in Order-Sorted Languages

We study the problem of pattern matching in order-sorted languages whose evaluation strategy is lazy. We propose an extension of the Puel-Suárez compilation scheme to function definitions via order-sorted patterns. Basically, a list of ordered and possibly ambiguous linear patterns is transformed into a set of disjoint order-sorted constrained terms. This set is in turn transformed according to some normalization rules in order to build a pattern matching tree (PMT). Variables of order-sorted constrained terms now have not only structure, but also subsort constraints. Accordingly, discrimination trees are defined to have edges labeled with either structure or subsort constraints. Due to this latter kind of edge, we are not always forced to reduce terms to normal forms during the pattern matching process, taking advantage in this way of the lazy reduction scheme. For example, suppose is a sort greater than , the variable x is a pattern and t is a term of sort to be matched. If t reduces to a term whose sort is a subsort of , it is already decidable that the term obtained matches x , even if it is not in normal form. We show that the PMT is optimal if a decidable property of sequentiality holds for the sets generated during the compilation process. Our method turns out to be applicable for strict languages as well.