Any applicative functor can be given numeric instances in a boilerplate way. The applicative-numbers package provides an include file that makes it a snap to define these instances. See Data.Numeric.Function for an example.

Project wiki page: http://haskell.org/haskellwiki/applicative-numbers

Copyright 2009-2013 Conal Elliott; BSD3 license.

Instances of Num classes for applicative functors. To be #include 'd after defining APPLICATIVE as the applicative functor name and CONSTRAINTS as a list of constraints, which must carry its own trailing comma if non-empty. The APPLICATIVE symbol gets #undef 'd at the end of the include file, so that multiple includes are convenient.

For instance,

#define INSTANCE_Ord #define INSTANCE_Enum #define APPLICATIVE Vec2 #include "ApplicativeNumeric-inc.hs" #define APPLICATIVE Vec3 #include "ApplicativeNumeric-inc.hs" #define APPLICATIVE Vec4 #include "ApplicativeNumeric-inc.hs"

You'll also have to import pure and liftA2 from Control.Applicative and specify the FlexibleContexts language extension (due to an implementation hack).