[Haskell] Re: Rebindable syntax for monads and arrows

[Ashley Yakeley]

In article <200501071653.j07GrHMu002630 at asterix.cs.indiana.edu>,
 Amr A Sabry <sabry at cs.indiana.edu> wrote:

> The type Vec below is almost a monad:
> - the operations vreturn and @>>= are almost of the right type 
>   (they have an additional constraint FinSet a =>)
> - the operations vreturn and @>>= satisfy the monad laws 
> 
>   class Eq a => FinSet a where enumerate :: [a]
> 
>   newtype Vec a = Vec (a -> Float)
>   unV (Vec f) = f
> 
>   vreturn :: FinSet a => a -> Vec a
>   vreturn a = Vec (\ b -> if a==b then 1 else 0)
> 
>   (@>>=) :: FinSet a => Vec a -> (a -> Vec b) -> Vec b
>   (Vec va) @>>= f = Vec (\ b -> sum [ (va a) * (unV (f a) b) | 
>                                       a <- enumerate])
> 
> Because of the additional type constraint (FinSet a =>) we cannot make the
> type Vec an instance of the class Monad, and hence we cannot use the
> do-notation to express our computations.

You can to do this with GADTs:

data MyVec a where
  MkMyVec :: (FinSet a) => Vec a -> MyVec a

instance Monad MyVec where
  return a = MkMyVec (vreturn a)
  etc.

GADTs are scheduled for version 6.4 of GHC. The version of GHC now in 
CVS does not currently allow this however, see GHC bug #1097046.

-- 
Ashley Yakeley, Seattle WA