Data.POrder

This module provides the POrder and related classes

Documentation

class Eq a => POrder a

This (empty) class indicates that the type a is partially ordered. The class is empty because we do not need any of the operations on runtime. Nevertheless the order better exists for the safety of this API.

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

Instances

POrder Natural

Ordered by '(<=)f'

Defined in Data.POrder

POrder Bool

Arbitrary using the False < True order

Defined in Data.POrder

POrder a => POrder (Dual a)

The dual order

Defined in Data.POrder

Eq a => POrder (Set a)

Ordered by subsetOf

Defined in Data.POrder

POrder a => POrder (Maybe a)

Adds Nothing as a least element to an existing partial order

Defined in Data.POrder

class POrder a => Bottom a where

A class indicating that the type a is partially ordered and 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

Eq 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 partially ordered and has a top element.

Methods

top :: a

Instances

Top Bool

Top is True

Defined in Data.POrder

Methods

top :: Bool