What's the difference between these 2 ways of generating sequences?

Question

I'm learning about F#, and there are 2 ways of generating sequences that i came across so far, and i'm curious about the differences between them if any.

First way:

Seq.unfold(fun x -> Some(x, x + 1)) 1 |> printfn "%A"

Second way:

Seq.initInfinite (fun x -> x + 1) |> printfn "%A"

Answer 1

There are two key differences between the two:

• First, unfold lets you keep some state between steps while initInfinite only gives you the index of the item that you are generating, so you need to have a way of producing a value based on the index.

• Second, unfold lets you create sequences that are finite (by returning None ) while initInfinite only creates infinite sequences (as the name suggests)

The unfold function is more general than initInfinite . To see this, we can easily implement initInfinite using unfold :

let initInfinite f = 
  Seq.unfold (fun n -> Some(f n, n + 1)) 0

In the other direction, the following example using unfold creates a sequence where each element is larger than the previous one by some random number. It ends once the number gets above 100:

let rnd = System.Random()
Seq.unfold (fun last -> 
  let next = last + rnd.Next(10)
  if last + next > 100 then None 
  else Some(last + next, last + next) ) 0

You cannot do this using initInfinite - because you do not know what the previous value was and you cannot end the sequence.