Normalization proofs for the un-typed μμ'-calculus

A long-standing open problem of Parigot has been solved by David and Nour, namely, they gave a syntactical and arithmetical proof of the strong normalization of the untyped μμ'-reduction. In connection with this, we present in this paper a proof of the weak normalization of the μ and μ'-ru...

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Veröffentlicht in:AIMS mathematics Jg. 5; H. 4; S. 3702 - 3713
Hauptverfasser: Battyányi, Péter, Nour, Karim
Format: Journal Article
Sprache:Englisch
Veröffentlicht: AIMS Press 2020
Schlagworte:
normalization algorithm
strong normalization
weak normalization
λμ-calculus
μμ'-calculus
ISSN:2473-6988, 2473-6988
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Zusammenfassung:A long-standing open problem of Parigot has been solved by David and Nour, namely, they gave a syntactical and arithmetical proof of the strong normalization of the untyped μμ'-reduction. In connection with this, we present in this paper a proof of the weak normalization of the μ and μ'-rules. The algorithm works by induction on the complexity of the term. Our algorithm does not necessarily give a unique normal form: sometimes we may get different normal forms depending on our choice. We also give a simpler proof of the strong normalization of the same reduction. Our proof is based on a notion of a norm defined on the terms.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020239