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.

Extensional Type Theory

Locally Cartesian Closed Categories



Simon Castellan

Centre national de la recherche scientifique (CNRS)

Pierre Clairambault

Centre national de la recherche scientifique (CNRS)

Peter Dybjer

Chalmers, Data- och informationsteknik, Datavetenskap

Logical Methods in Computer Science

1860-5974 (ISSN)

Vol. 13


Datavetenskap (datalogi)