Undecidability of Equality in the Free Locally Cartesian Closed Category
Résumé
We show that a version of Martin-Löf type theory with extensional identity, a unit type N 1 , Σ, Π, 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 then show that equality in this category is undecidable by reducing it to the undecidability of convertibility in combinatory logic.
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Est une version de hal-01579415 Article Simon Castellan, Pierre Clairambault, Peter Dybjer. Undecidability of Equality in the Free Locally Cartesian Closed Category (Extended Version). Logical Methods in Computer Science, 2017, ⟨10.23638/LMCS-13(4:22)2017⟩. ⟨hal-01579415⟩