Preservation of Strong Normalisation in Named Lambda Calculi with Explicit Substitution and Garbage Collection

In this paper we introduce and study a new-calculus with explicit substitution, xgc, which has two distinguishing features: rst, it retains the use of traditional variable names, specifying terms modulo renaming; this simpliies the reduction system. Second, it includes reduction rules for explicit garbage collection; this simpliies several proofs. We show that xgc is a conservative extension which preserves strong normalisation (PSN) of the untyped-calculus. The result is obtained in a modular way by rst proving it for garbage-free reduction and then extending tòreductions in garbage'. This provides insight into the counterexample to PSN for of Melli es (1995); we exploit the abstract nature of xgc to show how PSN is in connict with any reasonable substitution composition rule (except for trivial composition rules of which we mention one).