How to make same types with different behavior in Haskell?

Question

I use Haskell and Functional Graph Library to represents graphs. There are two ways to compare graphs, directly, over function equal, or over another function, i wrote, isIsomorph. I want to use hash map to collect graphs. To do so I have to create instance of class Eq for my graphs. But I need two hash maps, first for graphs that compared by function equal, and second for graphs that compated by function isIsomorph.

---

If I do

type Fragment = Gr Atom Bond {-- Gr is a type constructor from the Functional Graph Library}

    instance Eq (Gr Atom Bond) where    
        g == g1 = equal g g1

    instance Eq Fragment where  
        g == g1 = isIsomorph g g1

I have got an expected error

Duplicate instance declarations:
      instance [overlap ok] Eq (Gr Atom Bond) -- Defined at HLab.hs:45:10
      instance [overlap ok] Eq Fragment -- Defined at HLab.hs:48:10

Because of type decalration is only wrap.

I can use another way

data Fragment = Fragment {fgraph :: Gr Atom Bond}

instance Eq (Gr Atom Bond) where    
    g == g1 = equal g g1

instance Eq Fragment where  
    Fragment g ==  Fragment g1 = isIsomorph g g1

That is correct but I have used an "heavy" type constructor data, this way is also inconvenient, I have to got graphs from fragments by addtional function fgraph.

Is there any "beautiful" and "true" way to divide this types in various parts of code?

Answer 1

The "beautiful" and "true" way to divide this types in various parts of code? is to use newtype instead of data: For all type system purposes, they are different (in particular, you can define different type class instances), but they share the same run-time representation and there is no additional like with data:

newtype Fragment = Fragment {fgraph :: Gr Atom Bond}

instance Eq (Gr Atom Bond) where    
    g == g1 = equal g g1

instance Eq Fragment where  
    Fragment g == Fragment g1 = isIsomorph g g1

You will still need to convert between graphs and fragments when trying to use graph functions on fragments.