Data.POrder

This module provides the POrder and related classes

Documentation

class POrder a where

This class indicates that the type a is partially ordered by some relation ⊑.

The class does not actually have a method for ⊑, because we do not need it at runtime. Nevertheless the order better exists for the safety of this API.

This order may be unrelated to the total order given by Ord.

Methods

eqOfLe :: a -> a -> Bool

The eqOfLe method checks _related_ elements for equality.

Formally: For all x ⊑ y, eqOfLe x y == True iff x == y.

This can be more efficient than testing for equality. For example for sets, (==) needs to compare the elements, but eqOfLe only needs to compare sizes. It is always ok to use (==) here.

Instances

POrder Natural

Ordered by '(<=)f'

Defined in Data.POrder

Methods

eqOfLe :: Natural -> Natural -> Bool

POrder Bool

Arbitrary using the False < True order

Defined in Data.POrder

Methods

eqOfLe :: Bool -> Bool -> Bool

POrder a => POrder (Dual a)

The dual order

Defined in Data.POrder

Methods

eqOfLe :: Dual a -> Dual a -> Bool

POrder (Set a)

Ordered by subsetOf

Defined in Data.POrder

Methods

eqOfLe :: Set a -> Set a -> Bool

POrder a => POrder (Maybe a)

Adds Nothing as a least element to an existing partial order

Defined in Data.POrder

Methods

eqOfLe :: Maybe a -> Maybe a -> Bool

class Bottom a where

A class indicating that the type a is has a bottom element.

Methods

bottom :: a

Instances

Bottom Natural

Bottom is 0

Defined in Data.POrder

Methods

bottom :: Natural

Bottom Bool

Bottom is False

Defined in Data.POrder

Methods

bottom :: Bool

Top a => Bottom (Dual a)

Bottom is the top of a

Defined in Data.POrder

Methods

bottom :: Dual a

Bottom (Set a)

Bottom is empty

Defined in Data.POrder

Methods

bottom :: Set a

POrder a => Bottom (Maybe a)

Bottom is Nothing

Defined in Data.POrder

Methods

bottom :: Maybe a

class POrder a => Top a where

A class indicating that the type a is has a top element.

Methods

top :: a

Instances

Top Bool

Top is True

Defined in Data.POrder

Methods

top :: Bool