What is the role of `while`-loops in computation expressions in F#?

Question

If you define a While method of the builder-object, you can use while-loops in your computation expressions. The signature of the While

Answer 1

If you look at how computation expressions are evaluated, you'll see that

while foo() do
  printfn "step"
  yield bar()

is translated to something like

builder.While(fun () -> foo(), 
              builder.Delay(fun () -> 
                              printfn "step"
                              builder.Yield(bar()))))

This translation allows the body of the while loop to be evaluated multiple times. While your type signatures are accurate for some computation expressions (such as seq or async), note that the insertion of the call to Delay may result in a different signature. For instance, you could define a list builder like this:

type ListBuilder() =
  member x.Delay f = f
  member x.While(f, l) = if f() then l() @ (x.While(f, l)) else []
  member x.Yield(i) = [i]
  member x.Combine(l1,l2) = l1 @ l2()
  member x.Zero() = []
  member x.Run f = f()

let list = ListBuilder()

Now you can evaluate an expression like:

list {
  let x = ref 0
  while !x < 10 do
    yield !x
    x := !x + 1
}

to get the equivalent of [0 .. 9].

Here, our While method has the signature (unit -> bool) * (unit -> 'a list) -> 'a list, rather than (unit -> bool) * 'a list -> 'a list. In general, when the Delay operation has type (unit -> M<'a>) -> D<M<'a>>, the While method's signature will be (unit -> bool) * D<M<'a>> -> M<'a>.