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
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