Wednesday, December 12, 2012

Error management with state monads

The Maybe, Option in F#, monad returns only Nothing/None when "things go bad".
In real life we want to return details of what when wrong.

The other day someone asked me: how do I choose if something should go in the return part of the state monad, or in the state itself? Last post I showed you how to combine the Maybe and State monad. The natural next step is to extend things further in order to allow some form of error management; This provides more comfort than the  "all or nothing" standard behavior of the Maybe monad;  And, is exactly a case where we can choose either to return error information, or to augment the state to store error state.

Returning the error seems the natural thing to do. The idea is to use an Either like type, which either returns what you want normally, or the error status.  In F#, the Maybe monad is either returning "Some value" or "None",  the idea would be instead to return something like "Ok value" or "Failed error" based on a type declaration like:

type ReturnWithErr<'t,'err> =
| Ok     of  't
| Failed of  'err

 The problem with this, is that it brings you back to programming with return errors. One of the reasons why exception were invented is that it is a painful effort to decide what to do with each of these returned error.

The magic of functional programming is that we can "swivel" between a functional and state view. (I'll need to make a post on this concept, very important). Therefore we can "decide" that our error management is stateful. And as this is a local state that is caried around by the monad (it is "local" enough that it is ok to put things in it like the current error state).

We need to do better than using the basic state monad because it removes failed states, and therefore would remove any "state of error" that we might try to keep. The idea is then to split the state into two parts:
  • the "transactional" state that is lost on failure
  • the "error" state that is kept on failure
Normally the "error" state is only updated in case of error. Although you could imagine having a "not" like operator that clears the error state.

We know enough to write some code. In the previous post, I showed you how the bind operator of the stateful Maybe monad needs to track one state. Now we write a bind works with the two states instead of one. From the orginal state monad perspective there is still only one state but it is a tuplet transactionalState*errorState :

let bindOpt m g =
    SM(fun ((s,err) as sr) ->
    let (rf, ((s2,err2) as sr2)) = run m sr
    match rf with
    | Some rfv ->
        let (rg, ((s3,err3) as sr3)) = run (g rfv) sr2
        match rg with
        | Some _ ->
            (rg, sr3)
        | None ->
            (None, (s,err3))
    | None ->
        (None, (s,err2)))

It pretty much does what I mentioned above: the transactional state follows the "ok" path (states s, s2, and s3), the error state follow the failed path (state err, err2, and err3)

We want a few helper functions:

let getState f = SM (fun ((s,err) as sr) -> (Some(f s), sr))
let mapState f = SM (fun(s,err) -> (Some(), (f s,err)))
let ret x = SM (fun s -> (Some x,s))
let retSome mapErr optX = SM (fun((s,err) as sr) ->
    match optX with
    | Some _ -> (optX, sr)
    | None ->(None, (s, mapErr err)))
let retNone mapErr = SM (fun(s,err) -> (None, (s, mapErr err)))

And now we can wrap our monad in the "do" notation semantic of F#:

type OptState() =
    member inline b.Bind (m, f) =  bindOpt m f
    member inline b.Combine(m1, m2) = bindOpt m1 (fun _ ->m2)
    member inline b.Return x = ret x
    member inline b.ReturnFrom m = m

To demontrate the concept, I assume my error state is just a list of strings. So I need a little helper function to add to this list:

let cons x t = x :: t
And now I can refactor the "get" function (see previous post):
let get7 key =
    optState {
        let! kv = getState getKeyValues
        let! value = retSome (cons (sprintf "key %A not found" key)) (Map.tryFind key kv)
        return value
If the get function fails, the error state will hold a list of string where the failure is reported. In this next example, the get fails because "x" is not part of the state map (again see last post the map only has keys "a" and "b"):
let test15 =
    optState {
        let! a = get7 "a"
        let! b = get7 "x"
        do! set7 ("c",(a+b))
        let! counter = increment8
        return counter
Running this, run test15 (testState1,[]), gives:
(null, ({keyValues = map [("a", 1.0); ("b", 2.0)];
           counter = 100;}, ["key "x" not found"]))
And it has the error message in the error state! One of the key concept of the arrow is that a flow of information gets modified, while the other part stays the same. Augmenting state monads as shown above is really about applying the same idea. Next time I'll talk above higher order monadic constructions. We can again use our simple example for that. 

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