[Haskell-cafe] Multi-parameter Type Class

[Thomas DuBuisson]

I see Lennart answered your question.  For more fun you could also do this
with TypeFamilies, which are the new hot thing in Haskell type level logic.
Since you are just getting into MPTC, FunDeps etc I figured you'd be
interested.

------ START CODE ------
{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies,
TypeSynonymInstances, FlexibleInstances, TypeFamilies #-}

data Foo = Foo Bar    deriving(Show)
data Bar = Bar String deriving(Show)

-- A family of types will evaluate from one type to another.
-- Here, I chose the word 'Eval', which you could make more meaningful.
-- It is basically a function over types.
type family Eval b

-- This is three definitions for the type function 'Eval'
type instance Eval Foo = Integer
type instance Eval Bar = String
type instance Eval [x] = [Eval x]

-- And instead of a functional dependency
-- you have a type level function (Eval) that operates on the type 'a'.
class ZOT a where
  zot :: a -> Eval a

instance ZOT Foo where
  zot x = 17

instance ZOT Bar where
  zot x = "Eighteen"

-- And don't forget that x must be an instance of ZOT to apply zot.
instance (ZOT x) => ZOT [x] where
  zot xs = map zot xs

main = do print $ zot $ Foo $ Bar "Blah"
          print $ zot $ Bar "Blah"
          print $ zot $ [Bar "Blah", Bar "Blah"] -- No map here please
----

2008/12/11 Paul Keir <pkeir at dcs.gla.ac.uk>

>  Hi all,
>
> I've been trying to refactor my tree conversion code to make
> better use of type classes; and I've discovered multi-parameter
> type classes and functional dependencies. I have a class with a
> function a2b, and I'd like "map" to be used when it's a list of
> type a.
>
> I've created a simple failing example:
>
> data Foo = Foo Bar    deriving(Show)
> data Bar = Bar String deriving(Show)
>
> class ZOT a b | a -> b where
>   zot :: a -> b
>
> instance ZOT Foo Integer where
>   zot x = 17
>
> instance ZOT Bar String where
>   zot x = "Eighteen"
>
> instance ZOT [x] [y] where   -- This bit
>   zot xs = map zot xs        -- fails
>
> main = do print $ zot $ Foo $ Bar "Blah"
>           print $ zot $ Bar "Blah"
>           print $ zot $ [Bar "Blah", Bar "Blah"] -- No map here please
>
> I know this would work if the third instance of zot
> explicitly took [Bar] and [String]. Can I not instead generalise
> for all the ADTs in my tree in the way I've outlined? Must I
> instantiate for the type of each list pair?
>
> Cheers,
> Paul
>
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>
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