Analysis of a Guard Condition in Type Theory (Preliminary Report)

Abstract : We present a realizability interpretation of co-inductive types based on partial equivalence relations (per's). We extract from the per's interpreta- tion sound rules to type recursive definitions. These recursive definitions are needed to introduce «infinite» and «total» objects of co-inductive type such as an infinite stream or a non-terminating process. We show that the proposed type system enjoys the basic syntactic properties of subject reduction and strong normalization with respect to a confluent rewriting system first studied by Gimenez. We also compare the proposed type system with those studied by Coquand and Gimenez. In particular, we provide a semantic reconstruction of Gimenez's system which suggests a rule to type nested recursive definitions.
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RR-3300, INRIA. 1997
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  • HAL Id : inria-00073388, version 1



Roberto M. Amadio, Solange Coupet-Grimal. Analysis of a Guard Condition in Type Theory (Preliminary Report). RR-3300, INRIA. 1997. 〈inria-00073388〉



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