Michael Mislove
Abstract
In this quarter's Semantics column we revisit the topic of Homotopy Type Theory and its applications to constructive mathematics and computation. This continues a theme we began with an overview of the HoTT Program by Steve Awodey and Bob Harper in the January 2015 column [1]. In this month's column, Thierry Coquand describes a number of recent results about presheaf models of univalence, which taken together answer some fundamental questions about HoTT. While this is a hot topic among those who have been following its development, it's probably worthwhile reviewing some of the background, for those who aren't familiar with the details. For those who want more information, I recommend Steve and Bob's article, as well as the introduction to the HoTT Book [2].
- Awodey, S. and R. Harper, Homotopy Type Theory: unified foundations of mathematics and computation, SIGLOG Newsletter 2(1), January, 2015, URL: https://dl.acm.org/citation.cfm?id=2728816&picked=prox Google Scholar
Digital Library
- Homotopy Type Theory: Univalent Foundations of Mathematics, URL: https://homotopytypetheory.org/bookGoogle Scholar
- Scott, D., Relating theories of the lambda calculus, in: J. R. Hindley and J. P. Seldin, editors, To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus, and Formalism, Academic Press (1980), pp.403--450.Google Scholar
Index Terms
- Semantics column
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