Concept:
Type class Ord
Headline
A Language:Haskell type class for ordering
Description
The type class is concerned with types that admit comparison.
class Eq a => Ord a where
compare :: a -> a -> Ordering
(<) :: a -> a -> Bool
(<=) :: a -> a -> Bool
(>) :: a -> a -> Bool
(>=) :: a -> a -> Bool
max :: a -> a -> a
min :: a -> a -> a
These are essentially familiar comparison operators.
compare returns a value of an enum type to describing ordering.
data Ordering = LT | EQ | GT
LT should be read as "less than", EQ as "equal", and GT as "greater than".
It is sufficient to either define compare or "<=". All the other operators can be derived in a regular manner. Here is important to notice that every instance of Ord must also be an instance of Eq; see the type-class constraint above. Thus, < ad <= can be easily distinguished with the help of Eq.
Illustration
Consider the following data type for natural numbers: the Zero constructor should be thought as representing "0"; the Succ constructor should be thought of as representing the successor function (i.e., addition of 1 or increment).
data Nat = Zero | Succ Nat
Equality and ordering could be reasonably defined for Nat as follows.
instance Eq Nat where
Zero == Zero = True
Zero == (Succ _) = False
(Succ _) == Zero = False
(Succ x) == (Succ y) = x == y
instance Ord Nat where
compare Zero Zero = EQ
compare Zero (Succ _) = LT
compare (Succ _) Zero = GT
compare (Succ x) (Succ y) = compare x y
Equality and ordering is exercised at the Haskell prompt as follows.
> Zero == Zero
True
> Zero == Succ Zero
False
> Succ Zero == Succ Zero
True
> Zero < Succ Zero
True
> Succ Zero < Succ Zero
False
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