CANONICITY AND HOMOTOPY CANONICITY FOR CUBICAL TYPE THEORY
Artikel i vetenskaplig tidskrift, 2022

Cubical type theory provides a constructive justification of homotopy type theory. 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. We present in this article two canonicity results, both proved by a sconing argument: a homotopy canonicity result, every natural number is path equal to a numeral, even if we take away the equations defining the lifting operation on the type structure, and a canonicity result, which uses these equations in a crucial way. Both proofs are done internally in a presheaf model.

univalence

Artin glueing

canonicity

sconing

cubical type theory

Författare

Thierry Coquand

Chalmers, Data- och informationsteknik, Computing Science, Logik och Typer

Göteborgs universitet

Simon Huber

Göteborgs universitet

Christian Sattler

Chalmers, Data- och informationsteknik, Computing Science, Logik och Typer

Logical Methods in Computer Science

1860-5974 (ISSN)

Vol. 18 1 35

Ämneskategorier

Algebra och logik

Datavetenskap (datalogi)

DOI

10.46298/LMCS-18(1:28)2022

Mer information

Senast uppdaterat

2022-04-05