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Type Checking with Universes

by: Robert Harper, Robert Pollack
Theoretical Computer Science, Vol. 89, No. 1. (1991), pp. 107-136.


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Various formulations of constructive type theories have been proposed to serve as the basis for machine-assisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collection of type-forming operations. Universes are of interest for a variety of reasons, some philosophical (predicative vs. impredicative type theories), some theoretical (limitations on the closure...


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