The Stunner: Linear System T is Diverging!

Iowa Type Theory Commute

In this episode, I shoot down last episode's proposal -- at least in the version I discussed -- based on an amazing observation from an astonishing paper, "Gödel’s system T revisited", by Alves, Fernández, Florido, and Mackie. Linear System T is diverging, as they reveal through a short but clever example. It is even diverging if one requires that the iterator can only be reduced when the function to be iterated is closed (no free variables). This extraordinary observation does not sink Victor's idea of basing type theory on a terminating untyped core language, but it does sink the specific language he and I were thinking about, namely affine lambda calculus plus structural recursion.

My notes are here.