[Haskell-beginners] Re: Real world example of Typeclasses > Interfaces

[Ertugrul Soeylemez]

Alec Benzer <alecbenzer at gmail.com> wrote:

> I was speaking more generally, not specifically about the Haskell
> typeclasses Num and Enum (although actually irrational numbers aren't
> enumerable now that I think of it, but I also guess that's a
> relatively moot point since you can't really represent irrational
> numbers in a programming language)

There is a Num instance, which doesn't make sense to be an Enum
instance:

  instance Num a => Num (a -> a) where
    f + g = \x -> f x + g x
    -- ...

This makes some formulas look much nicer and more convenient to write:

  constOne :: Floating a => a -> a
  constOne = sin^2 + cos^2

Unfortunately Eq and Show are superclasses of Num, so you need a few
bogus instances:

  instance Eq (a -> a) where
    (==) = undefined

  instance Show (a -> a) where
    show = const "<function>"

As an alternative you can do this with the reader functor, too, although
it doesn't look nearly as nice for the above formula:

  constOne :: Floating a => a -> a
  constOne = (+) <$> (^2) . sin <*> (^2) . cos

It looks great for other formulas, though, and is more general:

  splits :: [a] -> [([a], [a])]
  splits = zip <$> inits <*> tails


Greets,
Ertugrul


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