Lifting class instance in Haskell

Question

Is there a way to "lift" a class instance in Haskell easily?

I've been frequently needing to create, e.g., Num instances for some classes that are just "lifting" the Num structure through the type constructor like this:

data SomeType a = SomeCons a

instance (Num a)=>Num SomeCons a where
    (SomeCons x) + (SomeCons y) = SomeCons (x+y)
    negate (SomeCons x) = SomeCons (negate x)
    -- similarly for other functions.

Is there a way to avoid this boilerplate and "lift" this Num structure automatically? I usually have to do this with Show and other classes also when I was trying to learn existencials and the compiler wouldn't let me use deriving(Show).

Answer 1

The generalized newtype deriving extension is what you want here:

{-# LANGUAGE GeneralizedNewtypeDeriving #-}

module Main where

newtype SomeType a = SomeCons a deriving (Num, Show, Eq)

main = do
  let a = SomeCons 2
      b = SomeCons 3
  print $ a + b

Output:

*Main> main
SomeCons 5

Answer 2

GHC implements what you want : Extensions to the deriving mecanism. These modifications are often shown for future standard language extension (As seen on haskell' wiki)

To Enable this extension, you must use the following pragma

{-# GeneralizedNewtypeDeriving #-}

and then use a deriving on your newtype declaration, as usual

data SomeType a = SomeCons a deriving (Num)

Answer 3

GeneralizedNewtypeDeriving