The Church-Rosser Property for . . . (1992)
| Venue: | Seventh Annual IEEE Symposium on Logic in Computer Science |
BibTeX
@INPROCEEDINGS{Geuvers92thechurch-rosser,
author = {Herman Geuvers},
title = {The Church-Rosser Property for . . .},
booktitle = {Seventh Annual IEEE Symposium on Logic in Computer Science},
year = {1992},
pages = {453--460},
publisher = {IEEE Computer Society Press}
}
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Abstract
In this paper we investigate the Church-Rosser property (CR) for Pure Type Systems with fij- reduction. For Pure Type Systems with only fi- reduction, CR on well typed terms follows immediately from CR on the so called 'pseudoterms' and subject reduction. For fij-reduction, CR on the set of pseudoterms is just false, as was shown by [Nederpelt 1973]. Here we prove that CR (for fij) on the well-typed terms of a fixed type holds, which is the maximum we can expect in view of Nederpelts counterexample. The proof is given for a large class of Pure Type systems that contains e.g. LF (for which CR for fij was proved by [Salvesen 1989] and [Coquand 1991]), F, F! and the Calculus of Constructions. In the proof, one key lemma (a very weak form of CR for fij on pseudoterms) takes a central position. It is remarkable that in the proof of this key lemma the counterexample to CR for fij is essentially used. 1 Introduction Simply typed lambda calculus (from now on denoted by !) and polymorphic ...
