shift-stream-way.fs

type StreamCons<'a> = 
    | Nil
    | Cons of 'a * Stream<'a>
and Stream<'a> = Lazy<StreamCons<'a>>

let inline force (l: Lazy<_>) = l.Force()

let rec toStream l : Stream<_> =
    lazy match l with
         | [] -> Nil
         | h::t -> Cons(h, toStream t)

let makeInfinite s : Stream<_> =
    let rec inner s' =
        lazy match s' with
             | Lazy Nil -> inner s |> force
             | Lazy (Cons (x, xs)) -> Cons(x, inner xs)
    inner s

let rec skip n s : Stream<_> =
    lazy match n,s with
         | 0, s -> force s
         | _, Lazy Nil -> Nil
         | n, Lazy (Cons (_, xs)) -> skip (n-1) xs |> force

let rec take n s : Stream<_> = 
    lazy match n,s with
         | 0, _ | _, Lazy Nil -> Nil
         | n, Lazy (Cons (x, xs)) -> Cons(x, take (n-1) xs)

let rec toList s = 
    match s with
    | Lazy Nil -> []
    | Lazy (Cons (x, xs)) -> x :: toList xs

let shift n l =
    l
    |> toStream
    |> makeInfinite
    |> skip n
    |> take l.Length
    |> toList

shift 2 [1..5] // [3; 4; 5; 1; 2]