Why does a partial application have value restriction?

Question

I can understand that allowing mutable is the reason for value restriction and weakly polymorphism. Basically a mutable ref inside a function may change the type in

Answer 1

Partial application doesn't preclude mutation. For example, here is a refactored version of your code that would also be incorrect without value restriction:

let aux cache x =
    match !cache with
    | Some y -> y
    | None -> cache := Some x; x

let remember = aux (ref None)