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Reports Year : 1997

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

Solange Coupet-Grimal
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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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Other [cs.OH]
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Dates and versions

inria-00073388 , version 1 (24-05-2006)

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  • HAL Id : inria-00073388 , version 1

Cite

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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