Curry–Howard applies when there’s a computational interpretation of proofs — like in AL, which encodes computation and abstraction in a logic. You don’t get to

Curry–Howard applies when there’s a computational interpretation of proofs — like in AL, which encodes computation and abstraction in a logic. You don’t get to do type-like work, then deny the structural analogy just because you renamed the machinery. It’s a type system built while insisting type systems are obsolete.