Question

If i have a function f and a stream s . How can I apply this function to the stream. Similiar to how a List.map would work.

It is an infinite stream of any type:

type 'a stream = Cons of 'a * (unit -> 'a stream)

I have come up with this, which is surely wrong but at least it reperesents what i am trying to do

type 'a stream = Cons of 'a * (unit -> 'a stream) 

let rec map f (cons(x,xsf)) = f x then map f (xsf)

Answer 1

Something like this ought to work:

module Stream =
    let rec map f (Cons(x,xs)) =
        Cons(f x,fun () -> xs() |> map f)

This defines a Stream module where we can keep helpful functions for dealing with streams (analogous to the List module), with just a single map function in it. The map function takes a function f and a stream made by consing x to the function xs, and maps f over the stream, returning a new stream whose head is f x and whose tail is gotten by mapping f over the stream that results from calling xs.