sure of course one does not need types to do natural deduction… if you throw what you showed me to your average maths undergrad in the US they will get confused — I truly don’t see how proofs are simple
It is a matter of presentation and what people are used to. In particular, in abstraction logic, in the simplest (and most general!) case, you only have these proof rules: Axiom, Assume, AddAnte, BindAnte, FreeAnte, InferAnte. If we just focus on this case, we can choose simpler names for these rules: Axiom, Assume, Add, Bind, Free, Infer. That's it. That is all there is to proof.
auggierose|5 months ago