Work

Homotopy Canonicity for Cubical Type Theory

Year: 2019

Type: article

Abstract: Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices. In this paper we show by a sconing argument that if we remove these equations for the path lifting operation from the system, we still retain homotopy canonicity: every natural number is path equal to a numeral.

Source: DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)

DOI: 10.4230/lipics.fscd.2019.11

Authors: Coquand, Thierry, Huber, Simon, Sattler, Christian

Institution: University of Gothenburg

Language: English

Topic: Logic, programming, and type systems

Subfield: Software

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2912640558

FWCI: 5.56

Cites: 6

Cited by: 19

Related to: 10