Embedding Multiset Constraints into a Lazy Functional Logic Language

1 I n t r o d u c t i o n The combination of different declarative paradigms (specially functional and logic programming) has been widely treated in the literature (see [12] for a survey). Many approaches to the integration of functional and logic programming take constructor-based conditional term rewriting systems as programs. In order to deal properly with non-strict functions, lazy functional logic languages use strict equality, which regards two expressions as equal iff they have the same constructor normal form. Moreover, lazy narrowing (a notion introduced in [20] and refined in [1,17]) is often chosen as the goal solving mechanism. As shown in [10], classical equational logic does not supply an adequate semantics for lazy functional logic programming, and a suitably defined constructor based rewriting logic provides a more convenient semantic framework. In two recent papers [3, 4] we have extended the approach from [10] with algebraic polymorphic types, i.e., parametric datatypes whose data constructors are governed by a given set C of equational axioms. The aim of the present paper is to investigate implementation techniques for an extended instance of the framework from [3, 4]. More precisely, we consider a language Seta 1 which provides the algebraic datatype Mset(a), the data constructors ~ ]~ :-+ Mset(a) (to build the empty multiset) and ~ "1"9 : (a, Mset(a)) -+ Mset(a) (to add an element to a multiset), required to fulfill the equational * This research has been partially supported by the the Spanish National Project TIC95-0433-C03-01 "CPD" and the Esprit Bt~A Working Group EP-22457 "CCLIr'. 1 Seta is not an acronym, but simply the spanish word for mushroom.