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A resource aware semantics for a focused intuitionistic calculus

Published online by Cambridge University Press:  22 May 2017

DELIA KESNER  and
DANIEL VENTURA
DELIA KESNER
Affiliation:
IRIF, CNRS, Univ. Paris-Diderot, Paris, France Email: kesner@pps.univ-paris-diderot.fr
DANIEL VENTURA
Affiliation:
INF, Univ. Federal de Goiás, Goiânia, Brazil Email: daniel@inf.ufg.br
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Abstract

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We investigate a new computational interpretation for an intuitionistic focused sequent calculus which is compatible with a resource aware semantics. For that, we associate to Herbelin's syntax a type system based on non-idempotent intersection types, together with a set of reduction rules – inspired from the substitution at a distance paradigm – that preserves (and decreases the size of) typing derivations. The non-idempotent approach allows us to use very simple combinatorial arguments, only based on this measure decreasingness, to characterize linear-head and strongly normalizing terms by means of typability. For the sake of completeness, we also study typability (and the corresponding strong normalization characterization) in the calculus obtained from the former one by projecting the explicit cuts.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Special Issue 1: Special Issue: Best Papers Presented at ICTAC 2015 , January 2019 , pp. 93 - 126
Copyright
Copyright © Cambridge University Press 2017 

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