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Erschienen in:
2014 | OriginalPaper | Buchkapitel
A Model of Countable Nondeterminism in Guarded Type Theory
verfasst von : Aleš Bizjak, Lars Birkedal, Marino Miculan
Erschienen in: Rewriting and Typed Lambda Calculi
Verlag: Springer International Publishing
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We show how to construct a logical relation for countable nondeterminism in a guarded type theory, corresponding to the internal logic of the topos
Sh
ω
1
of sheaves over
ω
1
. In contrast to earlier work on abstract step-indexed models, we not only construct the logical relations in the guarded type theory, but also give an internal proof of the adequacy of the model with respect to standard contextual equivalence. To state and prove adequacy of the logical relation, we introduce a new propositional modality. In connection with this modality we show why it is necessary to work in the logic of bf Sh
ω
1
.