We present a method for compiling pattern matching on lazy languages based on previous work by Laville and Huet-Levy. It consists of coding ambiguous linear sets of patterns using "Term Decomposition," and producing non ambiguous sets over terms with structural constraints on variables. The method can also be applied to strict languages giving a match algorithm that includes only unavoidable tests when such an algorithm exists.

We study the problem of pattern matching in order-sorted languages whose evaluation strategy is lazy. We propose an extension of the Puel-Suarez 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 oe is a sort greater than j, the variable x j is a pattern and t oe is a term of sort oe to be matc...

Abstract. We give a complete characterization of the class of functions that are the intensional behaviours of Primitive Recursive algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers. AMS Subject Classification. — Give AMS classification codes —. 1.