Is Milner let polymorphism a rank 2 feature?

Question

let a = b in c can be thought as a syntactic sugar for (\\a -> c) b, but in a typed setting in general it\'s not the case. For example, in the Milne

Answer 1

I recall many years ago seeing in a book about lambda calculus (possibly Barendregt) a type system preserved by beta expansion. It had no quantification, but it had disjunction to express that a term needed to be of more than one type simultaneously, as well as a special type omega which every term inhabited. As I recall, the latter avoids Daniel Wagner's dead code objection. While every expression was well-typed, restricting the position of omega in the type allowed you to charactize which expressions had (weak?) head normal forms.

Also if I recall correctly, fully normal form expressions had principal types, which did not contain omega.

For example the principal type of \f x -> f (f x) (the Church numeral 2) would be something like ((A -> B) /\ (B -> C)) -> A -> C