Data.Poset

Description

Partially ordered data types. The standard Ord class is for total orders and therefore not suitable for floating point. However, we can still define meaningful max and sort functions for these types.

We define a PosetOrd class which extends Ord by adding a NComp constructor representing that two elements are incomparable.

Synopsis

Documentation

class Eq a => Poset a whereSource

Class for partially ordered data types. Instances should satisfy the following laws for all values a, b and c:

a leq a.
a leq b and b leq a implies a == b.
a leq b and b leq c implies a leq c.

But note that the floating point instances don't satisfy the first rule.

Minimal definition: posetCmp or leq.

Methods

posetCmp :: a -> a -> PosetOrd Source

(<==>) :: a -> a -> Bool Source

Is comparable to.

(</=>) :: a -> a -> Bool Source

Is not comparable to.

leq :: a -> a -> Bool Source

Less than or equal.

geq :: a -> a -> Bool Source

Greater than or equal.

lt :: a -> a -> Bool Source

Strict less than.

gt :: a -> a -> Bool Source

Strict greater than.

Instances

Poset Bool
Poset Char
Poset Int
Poset Int8
Poset Int16
Poset Int32
Poset Int64
Poset Integer
Poset Word
Poset Word8
Poset Word16
Poset Word32
Poset Word64
Poset a => Poset [a]
Integral a => Poset (Ratio a)
Poset a => Poset (Maybe a)

data PosetOrd Source

Are two elements of the underlying comparabale or not; if they are, then Ordering tell the relation between them.

Constructors

Comp Ordering
NComp

Instances

Bounded PosetOrd
Enum PosetOrd
Eq PosetOrd
Read PosetOrd
Show PosetOrd
Monoid PosetOrd

comparing :: Poset b => (a -> b) -> a -> a -> PosetOrd Source

Apply a function to values before comparing.