Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.POrder

Description

This module provides the POrder and related classes

Synopsis

class POrder a where
- eqOfLe :: a -> a -> Bool
class Bottom a where
- bottom :: a
class POrder a => Top a where
- top :: a

Documentation

class POrder a where Source #

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 Source #

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

Instances details

POrder Natural Source #	Ordered by '(<=)f'
Instance details Defined in Data.POrder Methods eqOfLe :: Natural -> Natural -> Bool Source #
POrder Bool Source #	Arbitrary using the `False < True` order
Instance details Defined in Data.POrder Methods eqOfLe :: Bool -> Bool -> Bool Source #
POrder a => POrder (Dual a) Source #	The dual order
Instance details Defined in Data.POrder Methods eqOfLe :: Dual a -> Dual a -> Bool Source #
POrder (Set a) Source #	Ordered by `subsetOf`
Instance details Defined in Data.POrder Methods eqOfLe :: Set a -> Set a -> Bool Source #
POrder a => POrder (Maybe a) Source #	Adds `Nothing` as a least element to an existing partial order
Instance details Defined in Data.POrder Methods eqOfLe :: Maybe a -> Maybe a -> Bool Source #

class Bottom a where Source #

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

Methods

bottom :: a Source #

Instances

Instances details

Bottom Natural Source #	Bottom is 0
Instance details Defined in Data.POrder Methods bottom :: Natural Source #
Bottom Bool Source #	Bottom is `False`
Instance details Defined in Data.POrder Methods bottom :: Bool Source #
Top a => Bottom (Dual a) Source #	Bottom is the `top` of `a`
Instance details Defined in Data.POrder Methods bottom :: Dual a Source #
Bottom (Set a) Source #	Bottom is `empty`
Instance details Defined in Data.POrder Methods bottom :: Set a Source #
POrder a => Bottom (Maybe a) Source #	Bottom is `Nothing`
Instance details Defined in Data.POrder Methods bottom :: Maybe a Source #

class POrder a => Top a where Source #

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

Methods

top :: a Source #

Instances

Instances details

Top Bool Source #	Top is `True`
Instance details Defined in Data.POrder Methods top :: Bool Source #