open System

// Question 1.
type Stack<'a> = 
    | Elem of 'a * Stack<'a>
    | Empty
    member this.Push a = Elem (a, this)
    member this.Top = 
        match this with
        | Elem (a, _) -> a
        | Empty -> failwith "Empty stack!"
    member this.Pop = 
        match this with
        | Elem (_, rest) -> rest
        | Empty -> failwith "Empty stack!"
    override this.ToString () =
        match this with
        | Elem (e, rest) -> e.ToString() + "," + rest.ToString()
        | Empty -> "Empty"

type Foo () = class end
type Bar () = inherit Foo ()

let question1 () = 
    printfn "Question 1"
    let a = (((Empty.Push "hello").Push "world").Push "it's fun").Pop
    printfn "a: %O" a
    assert (a.ToString () = "world,hello,Empty")

    let b = ((Empty.Push 1).Push 3)
    printfn "b.Top: %O" b.Top
    assert (b.Top = 3)

    let c : Stack<Bar> = (Empty.Push <| Bar ()).Push <| Bar ()
    c.Top :> Bar |> ignore
    c.Top :> Foo |> ignore

    let d : Stack<#Foo> = (Empty.Push <| Bar ()).Push <| Bar ()
    d.Top :> Bar |> ignore

// Question 4.
let question4 () =
    let rec sieve sequence =
        seq {
            let h = Seq.head sequence
            yield h
            yield! sieve <| Seq.filter (fun m -> m % h <> 0) sequence
        }
    let primes = sieve <| (Seq.initInfinite id |> Seq.skip 2)
    printfn "first primes: %A" <| (Seq.take 100 primes |> Seq.toList)

[<EntryPoint>]
let main argv = 
    question1 ()
    question4 ()
    0