Two questions about binders

John Power – 15 June 2022

At the end of my last talk, I was asked two main questions about binders. One asked for examples, and the other asked about the relationship between the signatures I outlined and those in Max's work with Steve and me. I propose to address both questions. The leading examples of this account of binders are given by the lambda calculus, which, in regard to binders, is not much different to first order logic; the linear lambda calculus; and the Logic of Bunched Implications. And the relationship between the two notions of signature is non-trivial: in Plotto's finite product setting, his signatures are included among the Max et al ones; but in the more general situation, they are not, I think in an interesting way.