[Haskell-cafe] collection monads

Matthias Fischmann fis at wiwi.hu-berlin.de
Thu Oct 5 08:05:43 EDT 2006

On Thu, Oct 05, 2006 at 10:34:19AM +1300, tpledger at ihug.co.nz wrote:
> To: haskell-cafe at haskell.org, fis at wiwi.hu-berlin.de
> From: tpledger at ihug.co.nz
> Date: Thu, 05 Oct 2006 10:34:19 +1300
> Subject: [Haskell-cafe] collection monads
> Matthias Fischmann wrote:
> > another beginners question about monads: given the type
> >
> > | data (Ix x) => Permutation x = Permutation [x]
> >
> > i wanted to define
> >
> > | instance Monad Permutation where
> > |     return xs = Permutation xs
> >
> > but of course nothing about the monad class guarantees xs to be of
> > type list.  the monad class seems unsuitable for holding collections,
> > and i am inclined to not instantiate permutations.
> >
> > just to be sure: is there any easy way to do it that i missed?
> Do you expect the contained type x to change during a
> sequence of monadic actions?  e.g. would you ever use (>>=)
> at the type 'Permutation Int -> (Int -> Permutation Bool) ->
> Permutation Bool'?

no, i don't need that.  but aside from the fact that

>     data Permutation k v = Permutation [(k, v)]
>     instance (Ix k) => Monad (Permutation k)

is redundant (i think of the permutation as a function applicable to
arbitrary lists): how would that change anything?  my definition of
return still doesn't work.  or how would you redefine 'return'?

you gave me an idea, though:

data Permutation a x = Permutation (Array x a -> Array x a)
instance Monad (Permutation a) where
  return _ = Permutation id
  (>>=) (Permutation f) g = g f

but this is dysfunctional for many reasons, too.  for a start, (>>=)
wouldn't really by good for anything, even if i could repair its type.
composition of permutations seems to be something profoundly different
from monadic binding.  perhaps permutations just don't have it in them
to become monads?

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