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Defining λ-typed λ-calculi by axiomatizing the typing relation

Identifieur interne : 002B27 ( Istex/Corpus ); précédent : 002B26; suivant : 002B28

Defining λ-typed λ-calculi by axiomatizing the typing relation

Auteurs : Philippe De Groote

Source :

RBID : ISTEX:B6B8EB490F8D0635111C082E34EF2121FDA240DE

Abstract

Abstract: We present a uniform framework for defining different gl-typed λ-calculi in terms of systems to derive typing judgements, akin to Barendregt's Pure Type Systems [3]. We first introduce a calculus called λλ and study its abstract properties. These are, among others, the property of Church-Rosser, the property of subject reduction, and the one of strong normalization. Then we show how to extend λλ to obtain an inferential definition. of Nederpelt's Λ [20]. One may also extend λλ to get inferential definitions of van Daalen Λ β [24], and de Bruijn's ΛΔ [9] and we argue that these new inferential definitions are well suited for language-theoretic investigations.

Url:
DOI: 10.1007/3-540-56503-5_73

Links to Exploration step

ISTEX:B6B8EB490F8D0635111C082E34EF2121FDA240DE

Le document en format XML

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