open System.Collections.Generic

let memoize (f : 'a -> 'b) =
    let cache = new Dictionary<'a, 'b>()

    let memoizedF x =
        match cache.TryGetValue(x) with
        | true, y -> y
        | false, _ ->
            printfn "computing..."
            let y = f x
            cache.Add(x, y)
            y

    memoizedF

let rec y f x = f (y f) x

let inc1 =
    let f = memoize (fun x -> x + 1)
    fun x -> f x

let add2 =
    let f = memoize (fun (x, y) -> x + y)
    fun x y -> f(x, y)

let mul3 : 'a -> 'a -> 'a -> 'a =
    let f = memoize (fun (x, y, z) -> x * y * z)
    fun x y z -> f(x, y, z)