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Strong Normalization of Classical Natural Deduction with Disjunction

Identifieur interne : 000194 ( Istex/Corpus ); précédent : 000193; suivant : 000195

Strong Normalization of Classical Natural Deduction with Disjunction

Auteurs : Philippe De Groote

Source :

RBID : ISTEX:0903F7C71808D6C42127185BF5D5FC97A202603D

Abstract

Abstract: We introduce λμ →∧∨⊥ an extension of Parigot’s λμ-calculus where disjunction is taken as a primitive. The associated reduction rela- tion, which includes the permutative conversions related to disjunction, is Church-Rosser, strongly normalizing, and such that the normal de- ductions satisfy the subformula property. From a computer science point of view, λμ →∧∨⊥ may be seen as the core of a typed cbn functional language featuring product, coproduct, and control operators.

Url:
DOI: 10.1007/3-540-45413-6_17

Links to Exploration step

ISTEX:0903F7C71808D6C42127185BF5D5FC97A202603D

Le document en format XML

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<affiliation>E-mail: Philippe.de.Groote@loria.fr</affiliation>
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<abstract lang="en">Abstract: We introduce λμ →∧∨⊥ an extension of Parigot’s λμ-calculus where disjunction is taken as a primitive. The associated reduction rela- tion, which includes the permutative conversions related to disjunction, is Church-Rosser, strongly normalizing, and such that the normal de- ductions satisfy the subformula property. From a computer science point of view, λμ →∧∨⊥ may be seen as the core of a typed cbn functional language featuring product, coproduct, and control operators.</abstract>
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<affiliation>Cornell University, NY, USA</affiliation>
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<namePart type="given">Jan</namePart>
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<affiliation>Utrecht University, The Netherlands</affiliation>
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