#
Homotopy Type Theory

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: a proposal by Vladimir Voevodsky.
- Two-level type theory?
- cubical type theory? (which has various forms)

## See also

‘Type theory’ on the nLab wiki.