Question

Let’s say I have:

data MyType
myToDouble :: MyType -> Double

Let’s say I want MyType to be an instance of Num or Real or something that Double is already an instance of.

Is there a simple way to accomplish that without having to manually writing out all the methods in Num/Real for it?

So… is there some way of just saying:

instance Real MyType by way of myToDouble

Answer 1

Definitely not; Real depends on Num, and Num has methods which return a (or more accurately, are covariant in a). How are you going to implement:

(+) :: MyType -> MyType -> MyType

given just MyType and myToDouble?

Now maybe you already have all the other instances and are just wondering about Real. Well, the only method Real has is of its own toRational, so:

instance Real MyType where
    toRational = toRational . myToDouble

As for your more general question: unfortunately not. If you have a class whose methods are all contravariant (only take as arguments) in the type variable, then you should be able to automatically define a typeclass on a projection like this. But Haskell has no mechanism to do so. (You could write one yourself using Template Haskell).

You can “forward” a newtype’s instances to its underlying type using GeneralizedNewtypeDeriving. Eg.

{-# LANGUAGE GeneralizedNewtypeDeriving #-}

newtype MyType = MyType Double
    deriving (Eq,Ord,Show,Num,Real)

But you can’t use any old isomorphism. It’s a shame.