Type Checking with Universes

@article{Harper1991TypeCW,
  title={Type Checking with Universes},
  author={Robert Harper and Robert Pollack},
  journal={Theor. Comput. Sci.},
  year={1991},
  volume={89},
  pages={107-136}
}
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 properties… CONTINUE READING
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