Undecidability of Equality in the Free Locally Cartesian Closed Category (Extended Version)
Artikel i vetenskaplig tidskrift, 2017

We show that a version of Martin-Lof type theory with an extensional identity type former I, a unit type N-1, Sigma-types, Pi-types, and a base type is a free category with families (supporting these type formers) both in a 1- and a 2-categorical sense. It follows that the underlying category of contexts is a free locally cartesian closed category in a 2-categorical sense because of a previously proved biequivalence. We show that equality in this category is undecidable by reducing it to the undecidability of convertibility in combinatory logic. Essentially the same construction also shows a slightly strengthened form of the result that equality in extensional Martin-Lof type theory with one universe is undecidable.

Locally Cartesian Closed Categories

Extensional Type Theory

Undecidability

Författare

S. Castellan

P. Clairambault

Peter Dybjer

Chalmers, Data- och informationsteknik, Datavetenskap

Logical Methods in Computer Science

1860-5974 (ISSN)

Vol. 13

Ämneskategorier

Datavetenskap (datalogi)

DOI

10.23638/lmcs-13(4