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An Intuitionistic Set-theoretical Model of the Extended Calculus of Constructions

Werner's set-theoretical model is one of the most intuitive models of ECC. It combines a functional view of predicative universes with a collapsed view of the impredicative sort Prop. However this model of Prop is so coarse that the principle of excluded middle holds. In this paper, we interpret Prop into a topological space (a special case of Heyting algebra) to make it more intuitionistic without sacrificing simplicity. We prove soundness and show some applications of our model.

preprint2015arXivOpen access
Masahiro Sato
Logic in Computer Science
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Masahiro Sato

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