[Haskell-cafe] free vs. operational vs. free-operational

Heinrich Apfelmus apfelmus at quantentunnel.de
Sat Nov 30 21:39:13 UTC 2013

Nickolay Kudasov wrote:
>> ​In the 'free' approach, I find it unpleasant that some laws are
>> automatic from the functor type, while others have to be ensured by the
>> interpreter. That's why 'operational' offers only one way to implement
>> monads: everything has to be done in the interpreter.
>> As far as I know these instances are heavily used in practice, though they
> are inconvenient in a way. Perhaps they could be moved in a separate
> module. On the other hand one could use `FreeT` which derives instances in
> a different manner.

Well, that they are heavily used in practice does not mean that they are 
actually useful in practice. The thing is that as soon as your functor 
is a monad, I don't think you really need the Free type anymore -- your 
instruction type is already a monad.

>> If you look at the transformer version  Control.Monad.Trans.Free , you
>> will see that there are no MonadState instances -- as expected, because you
>> have to specify the interaction of effects.
> Some instances​​ are present in HEAD [1], just not on hackage yet. Some
> other instances (MonadCont [2], MonadWriter [3]) are waiting for Edward
> Kmett's approval.

Ah, I see now. Yes, it is possible for all classes that don't have 
control operations. (But I think it will be impossible for MonadCont).

And looking at my 'operational' package, it appears that  ProgramT 
already includes the desired  MonadState  and  MonadIO  instances! In 
other words, 'operational' had always included proper support for monad 
transformer stacks.

(The  MonadReader  class has a control operation, local , but looking at 
the source for  FreeT , it appears that it can actually be lifted. Amazing!)

> Note that `Free` does not have "the true" set of mtl instances. While these
> instances (derived from underlying functor) are heavily used in practice
> for `Free`, `FreeT` suggests deriving instances from the transformed monad
> (not underlying functor). It turns out the latter can be done for the most
> part of MonadX instances (MonadWriter instance is somewhat questionable).
> See some comments in [4].
> That said, as we saw, Free can give you some laws automatically. However,
>> this also has a drawback: Program has an optimization that Free can never
>> have. Namely, Program gives you a (>>=) that can be used in a
>> left-associative way (Think (((x ++ y) ++ z) ++ w) ) while still allowing
>> pattern matching.
> As far as I can tell, this corresponds to church encoded versions of `Free`
> and `FreeT`, namely `F` and `FT`​​.
> This is possible due to the work "Asymptotic Improvement of Computations
> over Free Monads" by Janis Voightländer [5] and based on Edward Kmett's "Free
> Monads for Less" series of articles [6,7]. `F` is on hackage already and
> `FT` is in HEAD.

Almost, but not quite. The key qualification is "while still allowing 
pattern matching". The church encoding is akin to difference lists: you 
get O(1) (++), but now  head  and  tail  are  O(n) .

In contrast, Program represents lists of instructions in a way similar to

    data List a = Nil | One a | Concat (List a) (List a)

This gives you O(1) append and head / tail if used in an ephemeral 
fashion. (It is actually possible to turn this into a genuine O(1) head 
and tail, but it's not worth it.) You can't do this optimization in Free.

To summarize, I currently don't see what 'free' offers that the 
'operational' package can't do equally well with only 11 exported symbols.

Best regards,
Heinrich Apfelmus


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