natural deduction metalanguage, practical foundations
type theory (dependent, intensional, observational type theory, homotopy type theory)
computational trinitarianism =
propositions as types +programs as proofs +relation type theory/category theory
Simplicial type theory (Riehl & Shulman 2017, §3) is a homotopy type theory which introduces additional non-fibrant layers on top of Martin-Löf type theory to provide a logical calculus for a directed interval type and with it for geometric shapes, consisting of cube judgments, tope judgments, inequality topes, extension types, Segal space-types, Rezk complete-types, and covariant fibrations.
Emily Riehl, Michael Shulman, A type theory for synthetic -categories arXiv:1705.07442
Jonathan Weinberger, A Synthetic Perspective on -Category Theory: Fibrational and Semantic Aspects arXiv:2202.13132
Jonathan Weinberger, Strict stability of extension types arXiv:2203.07194
A proof assistant implementing simplicial type theory:
Last revised on June 21, 2022 at 01:30:47. See the history of this page for a list of all contributions to it.