DMCA
Preservation of Strong Normalisation in Named Lambda Calculi with Explicit Substitution and Garbage Collection (1995)
| Venue: | IN CSN-95: COMPUTER SCIENCE IN THE NETHERLANDS |
| Citations: | 77 - 7 self |
BibTeX
@INPROCEEDINGS{Bloo95preservationof,
author = {Roel Bloo and Kristoffer H. Rose},
title = {Preservation of Strong Normalisation in Named Lambda Calculi with Explicit Substitution and Garbage Collection},
booktitle = {IN CSN-95: COMPUTER SCIENCE IN THE NETHERLANDS},
year = {1995},
pages = {62--72},
publisher = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
In this paper we introduce and study a new lambda-calculus with explicit substitution, lambda-xgc, which has two distinguishing features: first, it retains the use of traditional variable names, specifying terms modulo renaming; this simplifies the reduction system. Second, it includes reduction rules for explicit garbage collection; this simplifies several proofs. We show that lambda-xgc is a conservative extension which preserves strong normalisation (PSN) of the untyped lambda-calculus. The result is obtained in a modular way by first proving it for garbage-free reduction and then extending to `reductions in garbage'. This provides insight into the counterexample to PSN for lambda-sigma of Melliès (1995); we exploit the abstract nature of lambda-xgc to show how PSN is in conflict with any reasonable substitution composition rule (except for trivial composition rules of which we mention one). Key words: lambda calculus, explicit substitution, strong normalisation, garbage collection.
Keyphrases
explicit substitution strong normalisation garbage collection named lambda calculus explicit garbage collection reduction rule traditional variable name modular way garbage-free reduction reduction system key word conservative extension several proof lambda calculus reasonable substitution composition rule untyped lambda-calculus distinguishing feature trivial composition rule abstract nature
