[Haskell-cafe] a problem defining a monad instance

[Miguel Mitrofanov]

The usual continuation trick:

fromDistrib :: Ord a => Distrib a -> Cont (Distrib r) a
fromDistrib da = Cont (\c -> dcompose da c)
toDistrib :: Cont (Distrib r) r -> Distrib r
toDistrib (Cont f) = f dreturn

"Cont anything" is a monad.

On 6 Nov 2009, at 21:08, Petr Pudlak wrote:

>   Hi all,
>
> (This is a literate Haskell post.)
>
> I've encountered a small problem when trying to define a specialized
> monad instance. Maybe someone will able to help me or to tell me that
> it's impossible :-).
>
> To elaborate: I wanted to define a data type which is a little bit
> similar to the [] monad. Instead of just having a list of possible
> outcomes of a computation, I wanted to have a probability associated
> with each possible outcome.
>
> A natural way to define such a structure is to use a map from possible
> values to numbers, let's say Floats:
>
>> module Distribution where
>>
>> import qualified Data.Map as M
>>
>> newtype Distrib a = Distrib { undistrib :: M.Map a Float }
>
> Defining functions to get a monad instance is not difficult.
> "return" is just a singleton:
>
>> dreturn :: a -> Distrib a
>> dreturn k = Distrib (M.singleton k 1)
>
> Composition is a little bit more difficult, but the functionality is
> quite natural. (I welcome suggestions how to make the code nicer /  
> more
> readable.) However, the exact definition is not so important.
>
>> dcompose :: (Ord b) => Distrib a -> (a -> Distrib b) -> Distrib b
>> dcompose (Distrib m) f = Distrib $ M.foldWithKey foldFn M.empty m
>>  where
>>     foldFn a prob umap = M.unionWith (\psum p -> psum + prob * p)  
>> umap (undistrib $ f a)
>
> The problem is the (Ord b) condition, which is required for the Map
> functions.  When I try to define the monad instance as
>
>> instance Monad Distrib where
>>    return = dreturn
>>    (>>=)  = dcompose
>
> obviously, I get an error at (>>=):
>    Could not deduce (Ord b) from the context.
>
> Is there some way around? Either to somehow define the monad, or to
> achieve the same functionality without using Map, which requires Ord
> instances?
>
>    Thanks a lot,
>    Petr
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