06_TypeClasses.md

Type Class

[ToC]

Introduction

A type class defines some types related by their operations. This is saying that typeclasses are usually defined in terms of those operations, and these operations group those types together.

For example, we can put all types that can be converted to a String in the same type class called Show .

We can introduce this Show type class by:

class Show a where
  show :: a -> String

Then we can give an instance to the type class.

instance Show String where
  show s = s

instance Show Boolean where
  show true = "true"
  show false = "false"

Functor

We have seen how map is defined for [], and we can also map on other types. We call these types Functor if they can be mapped and can satistify the Functor law at the same time.

Functor laws: map id = id | map (compose g f) = map g . map f

class Functor f where
  map :: forall a b. (a -> b) -> f a -> f b

instance Functor Maybe where
  map f (Just x) = Just (f x)
  map f  Nothing = Nothing

Common type classes

class Eq a where
  eq :: a -> a -> Boolean

-- data Ordering = LT | GT | EQ
class Eq a => Ord a where
  compare :: a -> a -> Ordering

class Foldable f where
  foldl :: forall a b. (b -> a -> b) -> b -> f a -> b
  foldr :: forall a b. (a -> b -> b) -> b -> f a -> b
  foldMap :: forall a m. Monoid m => (a -> m) -> f a -> m