type system problems with type families and classes

fail.hs

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}

import Data.Bits
import Data.Word

class (Bits (T c)) => C c where
  type T c :: *
  
  f1 ::  (T c, T c) -> (T c, T c)
  f1 (a, b) =
    let x = a .&. b
        y = x .|. complement b
    in (x, y)

  f2 :: (T c, T c) -> T c
  f2 = fst . f1

data D

instance C D where
  type T D = Word32

{-
fail.hs:18:14:
    Could not deduce (T c0 ~ T c)
    from the context (C c)
      bound by the class declaration for `C'
      at /home/alios/src/lab/fail.hs:(8,1)-(18,15)
    NB: `T' is a type function, and may not be injective
    Expected type: (T c, T c) -> (T c, T c)
      Actual type: (T c0, T c0) -> (T c0, T c0)
    In the second argument of `(.)', namely `f1'
    In the expression: fst . f1
Failed, modules loaded: none.
-}


{-
The code above was a reduced form. To get the idea what I was really trying to express is the code below.
The first thing I wrote down was the instance declaration below, which looked pretty nice and expressiv to me...
-}

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}

import Data.Word
import Data.Bits
import Data.Text (Text)
 
type Netmask f = Address f    

class (Bits (Address f)) => AddressFamily f where
  type Address f :: *

  network :: (Address f, Address f) -> Address f
  network = fst . networkRange
  
  networkRange ::  (Address f) -> (Address f, Address f)
  networkRange (a, m) =
    let nwAddr = a .&. m
        bcAddr = nwAddr .|. complement m
    in (nwAddr, bcAddr)

data IPv4

instance AddressFamily IPv4 where
  type Address IPv4 = Word32

It is not realy about getting the problem solved, its more that I need to come uppon a real use for language feature, to have the feeling that I realy understood what the possiblities and use cases of that lang feature are... TypeFamilies are still open at the moment on my list ;-)

So what I realy liked here were two things:

• a data type with a signature like Address IPv4
• the way to write the class implementation and say f.e.: the type Address IPv4 = Word32