Question

I was playing around with typeclasses and made this:

class Firstable f where
  fst :: f a -> a

class Secondable f where
  snd :: f a -> a

I then tried to add an implementation for (,) and realized that I could do:

instance Secondable ((,) a) where
  snd (x,y) = y

I’m pretty sure this works because Secondable should have kind (* -> *) where ((,) a) has that type, however, I don’t know how to implement Firstable for ((,) * a) where * is the bound variable, In my interpretation I am trying to do the equivalent of:

instance Firstable (flip (,) a) where ...

Is there a way to do this in Haskell? Preferably without extensions?

Answer 1

A version with worse parametricity guarantees can be had with MPTCS and Fundeps or with TypeFamilies.

type family Fst p
type instance Fst (a,b) = a
type instance Fst (a,b,c) = a

…

class First p where
   fst :: p -> Fst p

instance Fst (a,b) where
   fst (a,_) = a

instance Fst (a,b,c) where
   fst (a,_,_) = a

…

but ultimately, you’ll need to use some extensions.