Homotopy Type Theory type theory > history (Rev #4, changes)

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Idea

A type theory is a formal system in which every term has a ‘type’, and operations in the system are restricted to acting on specific types.

A number of type theories have been used or proposed for doing homotopy type theory.

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 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 : work in progress based on a proposal by Vladimir Voevodsky.
  • Two-level type theory?
  • cubical type theory? (which has various forms)

See also

Type theory’ on the nLab wiki.

Revision on September 4, 2018 at 00:43:48 by Mike Shulman. See the history of this page for a list of all contributions to it.