Polymorphic lists...

[Hal Daume III]

Though I haven't tried it, the explicit 'Sat' dictionary representation
would probably work here, something like:

> data ShowD a = ShowD { showD :: a -> String }
>    -- our explicit dictionary for show, would need one of
>    -- these for each class we care about
>
> -- the satisfaction class:
> class Sat t where dict :: t
>
> -- an instance for show:
> instance Show a => Sat (ShowD a) where dict = ShowD { showD = show }
> instance Sat (ShowD a) => Show a where show = showD dict

manually generating datatypes and instances is tedious, but could easily 
be automated.  you should be able to use this to write:

> satFold :: forall c b . Sat c b =>
>            (forall a . Sat (c a) => a -> i -> i) ->
>            b -> r -> b

or something similar.  probably worth a shot.

On Tue, 9 Mar 2004, MR K P SCHUPKE wrote:

> 
> I have written a first attempt at a fold function for the heterogenious list: 
> 
> class RFold i r where
>    rFold :: (forall a . a -> i -> i) -> i -> r -> i
> instance RFold i RNil where
>    rFold f i RNil = i 
> instance RFold i r => RFold i (a `RCons` r) where
>    rFold f i (x `RCons` xs) = f x (rFold f i xs)
> 
> This works providing the folded 'op' has the type: forall a . a -> i -> i
> which means it does not work for functions like show :: forall a . Show a => a -> i -> i
> as the types are different. I have not figured out a way to make it accept a constraint 
> like Show for example. Here is an example:
> 
> length = rFold (\_ -> (+1)) 0 relation
> 
> The use of such a function seems limited, if constraints like Show cannot be used, as
> most useful applications of fold would require some kind of class membership for example:
> 
> string = rFold shows "" relation
> 
> This fails to compile because shows has type:
> 
> shows :: forall a . Show a => a -> i -> i
> 
> but fold expects
> 
> op :: forall a . a -> i -> i
> 
> 	Regards,
> 	Keean Schupke.
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> 

-- 
 Hal Daume III                                   | hdaume at isi.edu
 "Arrest this man, he talks in maths."           | www.isi.edu/~hdaume