Homotopy Type Theory type theory > history (Rev #10, changes)

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List of examples

This page lists some of the type theories and variations that have been used or proposed for doing homotopy type theory.

  • The system presented known in asBook HoTT presented in the HoTT book, chapter 1 and appendix A.
  • Martin-Löf Intensional Type Theory: the original.
  • The Calculus Of Constructions?: the basis of the Coq proof assistant.
  • Agda: based on Martin-Löf type theory, extended by a flexible scheme for specifying inductive definitions.
  • Homotopy Type System: a proposal by Vladimir Voevodsky.
  • Two-level type theory?
  • cubical type theory? (which has various forms)

See also

Type theory’ on the nLab wiki.

category: type theory

Revision on May 27, 2020 at 18:39:54 by Ali Caglayan. See the history of this page for a list of all contributions to it.