Modulepartial-order-0.2.0.0Haskell2010

Data.PartialOrd

This module provides the PartialOrd typeclass suitable for types admitting a partial order.

Along with the PartialOrd typeclass and some utility functions for working with partially ordered types, it exports implementations for the numeric types several numeric types, lists and sets.

Synopsis

class PartialOrd
value maxima
value minima
value elem
value notElem
value nub

Packagepartial-order-0.2.0.0
Exports6
LanguageHaskell2010
LicenceBSD-3-Clause
SourcePartialOrd.hs

classclass PartialOrd a where

Methods

(<=) :: a -> a -> Bool
Less-than-or-equal relation.
(>=) :: a -> a -> Bool
Bigger-than-or-equal relation. Defined in terms of <=.
(==) :: a -> a -> Bool
Equality relation. Defined in terms of <=.
(/=) :: a -> a -> Bool
Inequality relation. Defined in terms of ==.
(<) :: a -> a -> Bool
Less-than relation relation. Defined in terms of <= and /=.
(>) :: a -> a -> Bool
Bigger-than relation. Defined in terms of <= and /=.
compare :: a -> a -> Maybe Ordering
Compare function, returning either Just an Ordering or Nothing.

Instances6PartialOrd

PartialOrd IntegerDefined in partial-order-0.2.0.0 · Data.PartialOrd
PartialOrd DoubleDefined in partial-order-0.2.0.0 · Data.PartialOrd
PartialOrd FloatDefined in partial-order-0.2.0.0 · Data.PartialOrd
PartialOrd IntDefined in partial-order-0.2.0.0 · Data.PartialOrd
Derive the partial order from the total order for the following types:
Ord a => PartialOrd (Set a)Defined in partial-order-0.2.0.0 · Data.PartialOrd
Define the partial order in terms of the subset relation.
PartialOrd a => PartialOrd [a]Defined in partial-order-0.2.0.0 · Data.PartialOrd
Define the partial order in terms of the sublist relation.

valuemaxima :: PartialOrd a => [a] -> [a]

Source#

Compute the list of all elements that are not less than any other element in the list.

valueminima :: PartialOrd a => [a] -> [a]

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Compute the list of all elements that are not bigger than any other element in the list.

valueelem :: (PartialOrd a, Foldable t) => a -> t a -> Bool

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Version of the traditional elem function using the PartialOrd notion of equality.

valuenotElem :: (PartialOrd a, Foldable t) => a -> t a -> Bool

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Version of the traditional notElem function using the PartialOrd notion of equality.

valuenub :: PartialOrd a => [a] -> [a]

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Version of the traditional nub function using the PartialOrd notion of equality.