[Haskell-cafe] Functional dependencies with Type Classes
Manuel M T Chakravarty
chak at cse.unsw.edu.au
Sun Mar 30 22:49:13 EDT 2008
Henning Günther:
> suppose there are two (identical) classes:
>
>> class Res a b | a -> b where
>> getRes :: a -> b
>
> and
>
>> class Res2 t where
>> type Member t
>> getRes2 :: t -> Member t
>
> It is easy to automatically make every instance of Res2 an instance of
> res:
>
>> instance Res2 a => Res a (Member a) where
>> getRes x = getRes2 x
>
> However, declaring every instance of Res an instance of Res2 seems
> impossible, as the following doesn't compile
>
>> instance Res a b => Res2 a where
>> type Member a = b
>> getRes2 x = getRes x
>
> Question is: How to do this? The reason I need it is because I use a
> library which uses functional dependencies, but my classes shall be
> type
> families.
The last definition is invalid as the right-hand side of a type family
instance can only depend on its parameters. However, in
type Member a = b
you pull 'b' out of thin air. Remember that associated types (ie,
type families as part of classes) are only syntactic sugar for sparate
type family and class declarations. Obviously, it would be imposible
to pull the type instance out of the class in your definition. (The
mismatch between FDs and TFs here really is due to FDs being tied to
classes and TFs being separable - in that sense TFs are more general
than FDs, and hence, you cannot always simulate TFs with FDs.)
However, you can wrap an FD library into a TF interface with some
additional effort. Using your example for illustration, define the
type family and class separately:
type family Member a
class Res2 a where
getRes2 :: a -> Member a
Then, implement the catch all class instance as follows:
instance Res a (Member a) => Res2 a where
getRes2 x = getRes x
(This needs -fundecidable-instances. It is perfectly decidable if
your FD class is, but GHC doesn't know that.)
Now, the additional overhead is that you need to define the type
family instances separately; ie, for every class instance of the FD
class, such as
instance Res Int Bool where
getRes x = x == 0
you need to repeat the type mapping:
type instance Member Int = Bool
I hope this is not too much of a burden in your application.
Manuel
PS: Hmm, maybe this should go onto the wiki...
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