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A Semantic Normalization Proof for Inductive Types

Lisa Allali 1 Paul Brauner 2 
2 PAREO - Formal islands: foundations and applications
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Semantics methods have been used to prove cut elimination theorems for a long time. It is only recently that they have been extended to prove strong normalization results. For instance using the notion of super-consistency that is a semantic criterion for theories expressed in deduction modulo implying strong normalization. However, the strong normalization of System T has always been reluctant to such semantic methods. In this paper we give a semantic normalization proof of system T using the super consistency of some theory. We then extend the result to every strictly positive inductive type and discuss the extension to predicate logic.
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Submitted on : Monday, May 19, 2008 - 1:55:39 PM
Last modification on : Wednesday, February 2, 2022 - 3:51:17 PM
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Lisa Allali, Paul Brauner. A Semantic Normalization Proof for Inductive Types. [Research Report] 2008, pp.21. ⟨inria-00280410v2⟩

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