## Explicit Cyclic Substitutions (1993)

Citations: | 25 - 2 self |

### BibTeX

@INPROCEEDINGS{Rose93explicitcyclic,

author = {Kristoffer Høgsbro Rose},

title = {Explicit Cyclic Substitutions},

booktitle = {},

year = {1993},

pages = {36--50},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

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