Haskell newtype, but keep old functions

Question

I want to define a type of "Ideal" which is a list but with some structure. Numeric prelude already defines instances of Ring for lists, but they're not using the definitions of addition and multiplication I want. So I think in this instance I should say

newtype Ideal a = Ideal [a]

This works fine, but now it gives me an error if I try to do, say take 5 $ Ideal [0..].

Is there a way that I can keep the functions I want and only override the definitions I explicitly override?

Answer 1

If you're not too set on things being completely automatic, you could use the utility functions in the newtype package, e.g. something like over Ideal $ take 5.

Edit: Also, as an aside, it's not too hard to extend the functions from the newtype package to handle other cases. For example, I had these definitions lying around:

infixl 3 ./
(./) :: (Newtype n o) => (o -> t) -> (n -> t)
(./) fx = fx . unpack

liftN f x = pack $ f ./ x
liftN2 f x y = pack $ f ./ x ./ y
liftN3 f x y z = pack $ f ./ x ./ y ./ z

Not actually the best design for such combinators, I suspect, but you get the idea.

Answer 2

For plain functions, no. You'll have to provide your own definitions.

However, for functions that belong to a type class, you can use the GeneralizedNewtypeDeriving extension to expose the type classes you want from the underlying type of a newtype.

{-# LANGUAGE GeneralizedNewtypeDeriving #-}
newtype MyState a = MyState (State Int a)
    deriving (Monad)