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arXiv · 1201.1705

On completeness of reducibility candidates as a semantics of strong normalization

Denis Cousineau
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Abstract

This paper defines a sound and complete semantic criterion, based on reducibility candidates, for strong normalization of theories expressed in minimal deduction modulo à la Curry. The use of Curry-style proof-terms allows to build this criterion on the classic notion of pre-Heyting algebras and makes that criterion concern all theories expressed in minimal deduction modulo. Compared to using Church-style proof-terms, this method provides both a simpler definition of the criterion and a simpler proof of its completeness.

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Denis Cousineau. 2012-02-15. On completeness of reducibility candidates as a semantics of strong normalization. https://doi.org/10.2168/lmcs-8(1%3A3)2012

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