DavidA wrote:
Now, what I'd like to do is have Lex and Glex, and any further monomial orderings I define later, automatically derive Show and Num instances from Monomial (because it seems like boilerplate to have to define Show and Num instances by hand). Something like the following (not valid Haskell):
class OrdMonomial m where fromRaw :: Monomial -> m toRaw :: m -> Monomial
instance OrdMonomial Lex where fromRaw m = Lex m toRaw (Lex m) = m
instance OrdMonomial Glex where fromRaw m = Glex m toRaw (Glex m) = m
derive OrdMonomial m => Show m where show m = show (toRaw m)
derive OrdMonomial m => Num m where m * m' = fromRaw (toRaw m * toRaw m')
Change "derive" to "instance" and enable some GHC extensions by passing -fglasgow-exts -fallow-overlapping-instances -fallow-undecidable-instances to it (or use a GHC_OPTIONS pragma at the top of your source file) to make your code work with GHC. To go a step further, using functional dependencies, you can write a small framework: -- the class of wrapper types class Wrapper w a | w -> a where wrap :: a -> w unwrap :: w -> a -- the class of types with "derived" show instances class Wrapper w => DeriveShow w -- actual "deriving" of show instances instance (Wrapper w a, Show a, DeriveShow w) => Show w where show = show . unwrap and use it for your situation: -- the inner type to be wrapped and it's instances newtype Monomial = Monomial (Map String Int) deriving (Eq) instance Show Monomial where show (Monomial a) = ... -- some wrappers around this inner type newtype Lex = Lex Monomial deriving (Eq) newtype Glex = Glex Monomial deriving (Eq) instance Wrapper Lex Monomial where wrap x = Lex x unwrap (Lex x) = x instance Wrapper Glex Monomial where wrap x = Glex x unwrap (Glex x) = x -- specialised instances for the wrappers instance Ord Lex where Lex (Monomial m) <= Lex (Monomial m') = ... instance Ord Glex where Glex (Monomial m) <= Glex (Monomial m') = ... -- "derived" instances for the wrappers instance DeriveShow Lex instance DeriveShow Glex But given newtype deriving, wich should work for you for everything except Show and Read, this may well be overkill. Tillmann