M types

M types are types of coinductive trees on top of a dependent type theory.

In homotopy type theory

In the presence of W types, natural numbers and Voevodsky's univalence axiom, indexed M types are definable. This is shown by Ahrens et al. 2015.

References

Ahrens, Benedikt, Paolo Capriotti, and Régis Spadotti. 2015. ‘Non-Wellfounded Trees in Homotopy Type Theory’. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015), edited by Thorsten Altenkirch, 38:17–30. Leibniz International Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPIcs.TLCA.2015.17.

@InProceedings{ahrens_2015,
  author =	{Benedikt Ahrens and Paolo Capriotti and R{\'e}gis Spadotti},
  title =	{{Non-Wellfounded Trees in Homotopy Type Theory}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{17--30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  year =	{2015},
  volume =	{38},
  editor =	{Thorsten Altenkirch},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  doi =		{10.4230/LIPIcs.TLCA.2015.17},
}