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Complete idiot's guide to the Maybe monad
f#monad

I am sure I am royally misunderstanding something important, and am going to ask a pretty basic question. Still I have no idea how to go on. I am going to compose a trivial sample on which I am stuck. I need to do some computation, "exit" it with an error if something fails, or continue with the result, do some other checks, exit or continue again and so on. The AttemptBuilder sample covers pretty much that. However, I cannot figure out how to map a function to a list.

Suppose I define the Maybe monad like this:

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type Maybe<’a> = option<’a>
 
let succeed x = Some(x)
let fail = None
let bind p rest = match p with | None -> fail | Some r -> rest r
let delay f = f()

type MaybeBuilder() =
    member b.Return(x)  = succeed x
    member b.Bind(p, rest) = bind p rest
    member b.Delay(f)   = delay f
    member b.Let(p,rest) : Maybe<’a> = rest p

let maybe = MaybeBuilder()

// A computation that could fail
let maybeSquare n = maybe {if n > 1000 then return! fail else return n * n}

I can easily get the function that squares members of a tuple, in such a way that s2 is not computed if s1 fails:

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let maybeSquareBoth (n1, n2) : Maybe<int * int> =
    maybe { let! s1 = maybeSquare n1
            let! s2 = maybeSquare n2
            return (s1, s2) }

Now, suppose I have a list that I want to run this computation on, and get the list of results. I do not want to carry on computation as soon as the first function computation "fails."

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let maybeSquareEvery (nl : int list) : Maybe<int list> =
    maybe {
      // Magic!
    }

What is the idiomatic way to express that?

.

I think that LOST is right:

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let rec maybeSquareEvery l =
  maybe {
    match l with
    | [] -> return []
    | h::t ->
        let! h' = maybeSquare h
        let! t' = maybeSquareEvery t
        return h'::t'
  }

Also, note that if you add a 

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member b.Zero() = fail

to your 

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MaybeBuilder

, then you can express 

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maybeSquare

more naturally as

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let maybeSquare n = maybe {if n <= 1000 then return n * n}

or

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let maybeSquare n = maybe {if n > 1000 then () else return n * n}
By on 1/11/2011 7:18 AM ()

Thank you both. So, as far as I understand it, there is no standard, idiomatic way to sweeten that syntax. That was the essence of my question if you wish : )

As for your suggestion for b.Zero()--in real life, a failure carries data indicating what the failure was, so there is no sensible zero in my case of Maybe<_>.

By on 1/11/2011 12:27 PM ()

I don't quite understand what the problem is. I would use the maybe monad, and define a couple of maybe higher-order functions. Given that, you should be able to write nice iterative code that stops as soon as some iteration fails.
Note that you can also override the semantics of for and while loops using members For and While in your workflow builder. If you've got while, for, recursion and higher order functions covered, what more would you need?

By on 1/11/2011 9:41 PM ()

Thanks, that was what I did in the end.

By on 1/12/2011 4:39 AM ()

I've never used computation expressions in F#, but I think your maybeSquareEvery function must be recursive.
Supposing it is recursive, // Magic! can be that:

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match nl with
| [] -> []
| head:: tail ->
  let! h = maybeSquare head
  let! t = maybeSquareEvery tail
  h :: t

Note this is not tail recursive version.

By on 1/11/2011 6:06 AM ()

Thanks. The problem is that I need to perform many calculations, and not all of them are map-type applications of function to lists. This is why I am looking for a more expressive idiom, which maybe { } would allow -- except for iterative applications.

I perfectly understand how to write the whole thing without CE, but it becomes ugly -- and I mean ugly!

By on 1/11/2011 6:38 AM ()

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