A Relation Algebraic Semantics for a Lazy Functional Logic Language

We propose a special relation algebraic model as semantics for lazy functional logic languages. The resulting semantics provides several interesting advantages over former approaches for this class of languages. For once, the equational reasoning supported by an algebraic approach implies a great increase in the economy and readability of proofs. Second, the richly developed field of relation algebra provides a pool of theorems and insights that can now be utilized in reasoning about functional logic programs. A further advantage is the strong and simple correspondence between functional logic programs and the semantics developed here. This correspondence enables us to go both ways, i.e. from program to semantics and back. The latter direction is essential for using relation algebraic transformations to optimize functional logic code. Last but not least, the development of the relation algebraic formalization gave us valuable insights, especially with respect to the desired properties of function inversion.