Convert from type `T a` to `T b` without boilerpla

Question

So, I have an AST data type with a large number of cases, which is parameterized by an "annotation" type

data Expr a = Plus a Int Int
    | ...
    | Times a Int Int

I have annotation types S and T, and some function f :: S -> T. I want to take an Expr S and convert it to an Expr T using my conversion f on each S which occurs within an Expr value.

Is there a way to do this using SYB or generics and avoid having to pattern match on every case? It seems like the type of thing that this is suited for. I just am not familiar enough with SYB to know the specific way to do it.

Answer 1

It sounds like you want a Functor instance. This can be automatically derived by GHC using the DeriveFunctor extension.

Answer 2

Based on your follow-up question, it seems that a generics library is more appropriate to your situation than Functor. I'd recommend just using the function given on SYB's wiki page:

{-# LANGUAGE DeriveDataTypeable, ScopedTypeVariables, FlexibleContexts #-}
import Data.Generics
import Unsafe.Coerce

newtype C a = C a deriving (Data,Typeable)

fmapData :: forall t a b. (Typeable a, Data (t (C a)), Data (t a)) =>
    (a -> b) -> t a -> t b
fmapData f input = uc . everywhere (mkT $ \(x::C a) -> uc (f (uc x)))
                    $ (uc input :: t (C a))
    where uc = unsafeCoerce

The reason for the extra C type is to avoid a problematic corner case where there are occurrences of fields at the same type as a (more details on the wiki). The caller of fmapData doesn't need to ever see it.

This function does have a few extra requirements compared to the real fmap: there must be instances of Typeable for a, and Data for t a. In your case t a is Expr a, which means that you'll need to add a deriving Data to the definition of Expr, as well as have a Data instance in scope for whatever a you're using.