ECC, an Extended Calculus of Constructions
نویسنده
چکیده
We present a higher-order calculus ECC which can be seen as an extension of the calculus of constructions CH88] by adding strong sum types and a fully cumulative type hierarchy. ECC turns out to be rather expressive so that mathematical theories can be abstractly described and abstract mathematics may be adequately formalized. It is shown that ECC is strongly normalizing and has other nice proof-theoretic properties. An !?Set (realizability) model is described to show how the essential properties of the calculus can be captured set-theoretically.
منابع مشابه
The Extended Calculus of Constructions (ECC) with Inductive Types
Luo’s Extended Calculus of donstructions (ECC) is a higher order functional calculus based on Coquand’s and Huet’s Calculus of Constructions, but has in addition strong sums and a predicative cumulative type hierarchy. In this paper I introduce inductive types on the predicative type levels of ECC. I also show how the o-Set model for ECC can be extended to a model for this augmented calculus. '...
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