[Haskell-cafe] class default method proposal

[ajb at spamcop.net]

G'day all.

Quoting David Menendez <dave at zednenem.com>:

> This is pretty much how I define Functor and Applicative instances for my
> monads. It is admittedly irritating to have to write out the boilerplate,
> but  it doesn't seem irritating enough to require a language extension to
> eliminate.

In the case of Functor and Applicative, that's true.  Cases where it's
likely to be more useful involve absurdly fine-grained class hierarchies,
like the numeric prelude.  Getting fanciful for a moment, and not claiming
that this is a good structure:

class Plus a b c | a b -> c where
     (+) :: a -> b -> c

class Minus a b c | a b -> c where
     (-) :: a -> b -> c

class Times a b c | a b -> c where
     (*) :: a -< b -> c

class Zero a where
     zero :: a

class One a where
     one :: a

class (Zero a, Plus a a a, Minus a a a) => Additive a where
     negate :: a -> a

     negate a = zero - a
     a - b = a + negate b

class (Mul a a a, One a) => Multiplicative a where
     (^) :: a -> Integer -> a

class (Multiplicative a, Additive a) => Ring a where
     fromInteger :: Integer -> a

     zero = fromInteger 0
     one = fromInteger 1

class (Ring a, Ord a) => OrderedRing a where
     abs :: a -> a
     abs x = x `max` negate x

     signum :: a -> a
     -- etc

class (OrderedRing a, Show a) => Num a

You can imagine how unwieldy this would now get if you just wanted to
declare an instance for Num a.

Cheers,
Andrew Bromage