What is the purpose of the Zero member when defining F# computation expressions?

Question

I am trying to learn F# computation expressions. In general, what is the purpose of the Zero member?

What is its definition for sequences?

What is its definition for async workflows?

Answer 1

The Zero member is used, for example, when you omit the else branch in an if expression:

comp { if b then return 1
       return 2 }

... would be translated to something like this:

comp.Combine
  ( if b then comp.Return(1) else comp.Zero(),
    comp.Return(2) )

How is it defined for standard computation types?

• For asynchronous workflows, it is defined as asynchronous workflow that immediately returns a unit value - essentially equivalent to writing: async { return () }.

• For sequences (where you use yield instead of return) the Zero member returns a sequence that does not return anything, corresponding to the standard Seq.empty value.

If you want to read about some more theoretical background, then you can check out this paper. In a more theoretical terms, it says that Zero is either going to be return () (when the computation is a monad) or it is going to be the unit of a monoid (when the computation is monoidal) which is something that Haskellers call mzero.