A Modal Lambda Calculus with Iteration and Case Constructs (1997)
| Venue: | TYPES FOR PROOFS AND PROGRAMS: INTERNATIONAL WORKSHOP, TYPES ’98, KLOSTER IRSEE |
| Citations: | 8 - 1 self |
BibTeX
@INPROCEEDINGS{Leleu97amodal,
author = {Pierre Leleu},
title = {A Modal Lambda Calculus with Iteration and Case Constructs},
booktitle = {TYPES FOR PROOFS AND PROGRAMS: INTERNATIONAL WORKSHOP, TYPES ’98, KLOSTER IRSEE},
year = {1997},
pages = {47--61},
publisher = {SpringerVerlag LNCS}
}
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Abstract
An extension of the simply-typed lambda-calculus allowing iteration and case reasoning over terms defined by means of higher order abstract syntax has recently been introduced by Joëlle Despeyroux, Frank Pfenning and Carsten Schürmann. This thorny mixing is achieved thanks to the help of the operator ` ' of modal logic IS4. Here we give a new presentation of their system, with reduction rules, instead of evaluation judgments, that compute the canonical forms of terms. Our presentation is based on a modal lambda-calculus that is better from the user's point of view, is more concise and we do not impose a particular strategy of reduction during the computation. Our system enjoys the decidability of typability, soundness of typed reduction with respect to typing rules, the Church-Rosser and strong normalization properties. Finally it is a conservative extension of the simply-typed lambda-calculus.
