[Haskell-cafe] Families of type classes

[Klaus Ostermann]

Hi all,

I am not a Haskell expert, and I am currently exploring type classes and need 
some advice.

I want to define a family of mutually recursive types
as a collection of type classes and then I want to be able
to map these collections of types to a set of other types
using instance declarations.

For example, I have a type family for graphs, consisting of
the types "Node" and "Edge". In another part of my application
I have the types "Person" and "Likes" (a pair of persons), and
I want to map the roles "Node" and "Edge" to "Person" and "Likes",
respectively.

It seems to me that functional dependencies could be a way to
model it (maybe it can also be done much simpler, but I don't know how).

Here is what I tried:

class (Node n, Edge e) => Graph g n e | g -> n, g -> e where

class Node n where
   isConnectedTo :: Graph g n e => g -> n -> e -> Bool

class Edge e where
  n1 :: Graph g n e  => g -> e -> n
  n2 :: Graph g n e  => g -> e -> n

type Person = String
type Likes = (Person, Person)

data DummyGraph = DummyGraph String

instance Graph DummyGraph Person Likes where

instance Node Person where
   isConnectedTo g n (p1,p2) = (p1 == n) || (p2 == n)

instance Edge Likes where
   n1 g (p1,p2) = p1
   n2 g (p1,p2) = p2

This "DummyGraph" thing is supposed to be used as a kind of "family object"
which stands for a particular type class family. However, this is not yet quite 
right because I get the error message

  Couldn't match the rigid variable `e' against `(a, b)'
    `e' is bound by the type signature for `isConnectedTo'
    Expected type: e
    Inferred type: (a, b)
  When checking the pattern: (p1, p2)
  In the definition of `isConnectedTo':
      isConnectedTo g n (p1, p2) = (p1 == n) || (p2 == n)

Similar error messages occur in the instance declaration for Edge/Likes.

I don't understand exactly what my error is. Maybe I would need a completely 
different strategy to model this.

Any help would be appreciated!

Regards,
Klaus