A Terminating and Confluent Linear Lambda Calculus

We present a rewriting system for the linear lambda calculus corresponding to the {!, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \b...

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Hauptverfasser: Ohta, Yo, Hasegawa, Masahito
Format: Buchkapitel
Sprache:eng
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Zusammenfassung:We present a rewriting system for the linear lambda calculus corresponding to the {!, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\multimap$\end{document}}-fragment of intuitionistic linear logic. This rewriting system is shown to be strongly normalizing, and Church-Rosser modulo the trivial commuting conversion. Thus it provides a simple decision method for the equational theory of the linear lambda calculus. As an application we prove the strong normalization of the simply typed computational lambda calculus by giving a reduction-preserving translation into the linear lambda calculus.
ISSN:0302-9743
1611-3349
DOI:10.1007/11805618_13