fun with f#

// Learn more about F# at http://fsharp.net
// See the 'F# Tutorial' project for more help.
exception Empty

let hd list =
    match list with
    |   [] -> raise Empty
    |   hd::tl -> hd

let tl list =
    match list with
    |   [] -> raise Empty
    |   hd::tl -> tl

let zero x y z =
    x + y + z

let one x y =
    (y,x)

let two (a, b) (c, d) =
    (a, b, c, d)

let three f g (a : int, b : int, c : int) =
    (f a |> g, f b |> g, f c |> g)

let four =
    fun a b c -> a + b + c

let five =
    ()

let six arr =
     (arr |> Array.min, arr |> Array.averageBy (fun elem -> float elem), arr |> Array.max)

let seven arr =
    arr |> Array.sumBy (fun elem -> float elem)

let rec eight n =
    match n with
    | 0 -> 1
    | _ -> n * eight (n - 1)

let rec eightSimple n =
    List.fold (fun acc elem -> acc * elem) 1 [1 .. n]

let nine list index =
    List.nth list index

let rec nineRecursive list index =
    let rec foo list index i =
        match i = index with
            |   false -> foo (tl list) index (i + 1)
            |   true -> hd list
    foo list index 0

let ten list n =
    let rec foo array n i =
        match i < n with
            |   true -> hd array + foo (tl array) n (i + 1)
            |   false -> 0
    foo list n 0

let tenWithCheats list n =
    Seq.fold (fun acc elem -> (acc + elem)) 0 (list |> Seq.take(n))

let eleven list n =
    ten (List.rev list) n

[<EntryPoint>]
let main argv =
    printfn "zero 2 3 5 = %i" (zero 2 3 5)
    printfn "one 3 5 = %A" (one 3 5)
    printfn "two (2 3) (5 4) = %A" (two (2,3) (5, 4))
    printfn "three fn x => x + 1 fm x => x * 2 (1, 2, 3) = %A" (three (fun x -> x + 1) (fun x -> x * 2) (1, 2, 3))
    printfn "eight 3 = %i" (eightSimple 3)
    printfn "nine [1 .. 25] 15 = %A" (nineRecursive [1 .. 25] 15)
    printfn "tenRetared [1 .. 10] 5 = %i" (tenWithCheats [1 .. 10] 5)
    printfn "eleven [1 .. 10] 5 = %i " (eleven [1 .. 10] 5)
    System.Console.ReadLine()
    0 // return an integer exit code