Explicit Cyclic Substitutions

In this paper we consider rewrite systems that describe the-calculus enriched with recursive and non-recursive local deenitions by generalizing thèexplicit substitutions' used by Abadi, Cardelli, Curien, and L evy 1] to describe sharing in-terms. This leads tòexplicit cyclic substitutions' that can describe the mutual sharing of local recursive deenitions. We demonstrate how this may be used to describe standard binding constructions (let and letrec)|directly using substitution and xed point induction as well as using`small-step' rewriting semantics where substitution is interleaved with the mechanics of the following-reductions. With this we hope to contribute to the synthesis of denotational and operational speciications of sharing and recursion.