Naive cubical type theory

Mathematical Structures in Computer Science 31:1205–1231 (2021)
  Copy   BIBTEX

Abstract

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality.

Author's Profile

Bruno Bentzen
Zhejiang University

Analytics

Added to PP
2022-08-25

Downloads
322 (#57,235)

6 months
154 (#24,995)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?