On completeness of reducibility candidates as a semantics of strong normalization

Details On completeness of reducibility candidates as a semantics of strong normalization On completeness of reducibility candidates as a semantics of strong normalization

2012-01-09

arxiv.org/abs/1201.1705v2

LMCS 8 (1:3) 2012

Computer Science

Logic in Computer Science

24 pages

Scientific paper

10.2168/LMCS-8(1:3)2012

This paper defines a sound and complete semantic criterion, based on reducibility candidates, for strong normalization of theories expressed in minimal deduction modulo \`a 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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