MSP Strathclyde Lecure - Conor McBride on Bi-directional Typing
I've only seen 15 minutes of this but it looks like it's going to be a really great lecture. Who invented this stuff? (Thierry Coquand, Benjamin Pierce and David Turner, I think). Google suggests it was a bunch of people hacking on compilers in the 90s. It's funny how you can produce really pretty theories doing stuff like that, isn't it? It's as if there's a kind of implicit discipline of mechanism. There is a survey article here: Bidirectional Typing by Jana Dunfield and Neel Krishnaswami. But note the remark at 1:02:35 . Maybe see 4.1. "Turning CCω Bidirectional" of Meven Lennon-Bertrand's PhD Thesis (2022): Bidirectional Typing for the Calculus of Inductive Constructions . I wonder if you can use this algorithm to derive custom type systems from programs, or is that too weird an idea? See Girard, Lafont & Taylor's Proofs and Types , Section 3.3 on the significance of the Curry Howard Correspondence: This talk is a lot better than th...