Haskell Language Type Classes Type class inheritance: Ord type class
Example
Haskell supports a notion of class extension. For example, the class Ord inherits all of the operations in Eq, but in addition has a compare function that returns an Ordering between values. Ord may also contain the common order comparison operators, as well as a min method and a max method.
The => notation has the same meaning as it does in a function signature and requires type a to implement Eq, in order to implement Ord.
data Ordering = EQ | LT | GT
class Eq a => Ord a where
compare :: Ord a => a -> a -> Ordering
(<) :: Ord a => a -> a -> Bool
(<=) :: Ord a => a -> a -> Bool
(>) :: Ord a => a -> a -> Bool
(>=) :: Ord a => a -> a -> Bool
min :: Ord a => a -> a -> a
max :: Ord a => a -> a -> a
All of the methods following compare can be derived from it in a number of ways:
x < y = compare x y == LT
x <= y = x < y || x == y -- Note the use of (==) inherited from Eq
x > y = not (x <= y)
x >= y = not (x < y)
min x y = case compare x y of
EQ -> x
LT -> x
GT -> y
max x y = case compare x y of
EQ -> x
LT -> y
GT -> x
Type classes that themselves extend Ord must implement at least either the compare method or the (<=) method themselves, which builds up the directed inheritance lattice.
