A Relation Algebraic Semantics for a Lazy Functional Logic Language

We propose a relation algebraic semantics along with a concrete model for lazy functional logic languages. The resulting semantics provides several interesting advantages over former approaches for this class of languages. On the one hand, the high abstraction level of relation algebra allows equational reasoning leading to concise proofs about functional logic programs. On the other hand the proposed approach features, in contrast to former approaches with a comparable level of abstraction, an explicit modeling of sharing. The latter property gives rise to the expectation that the presented framework can be used to clarify notions currently discussed in the field of functional logic languages, like constructive negation, function inversion and encapsulated search. All of these topics have proved to involve subtle problems in the context of sharing and laziness in the past.