Cumulative Inductive Types In Coq

@inproceedings{Timany2018CumulativeIT,
  title={Cumulative Inductive Types In Coq},
  author={Amin Timany and Matthieu Sozeau},
  booktitle={FSCD},
  year={2018}
}
In order to avoid well-known paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type0 : Type1 : · · · . Such type systems are called cumulative if for any type A we have that A : Typei implies A : Typei+1. The Predicative Calculus of Inductive Constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present the… CONTINUE READING

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