On completeness of reducibility candidates as a semantics of strong normalization
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 m...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2012-02-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/845/pdf |
| Summary: | 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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| ISSN: | 1860-5974 |