(int, float, bool, string)

(a) Consider a function with polymorphic type f : a -> a -> a.

What is the type of f 0 ?

What is the type of fun x -> (f f) x ? Briefly explain your reasoning.

(b) Consider a function with polymorphic type f : (a * b) -> (b -> a) -> a

What is the type of f (0, true) ?

What is the type of fun x y -> f (x, y) ? Does it have the same type as f ? Briefly explain your reasoning.

(c) Consider a function with polymorphic type g : (a -> b > b) -> b -> a.

What is the type of g (+)?

What is the type of fun x -> (g g) x ? Briefly explain your reasoning.

(d) Consider the following function.

Is it well typed? Briefly explain your reasoning.

let f (x : int list) : bool list match x with | [] -> x | hd :: tl -> true :: [] let f (x : int list) : bool list match x with | [] -> x | hd :: tl -> true :: []