Camfort.Specification.Stencils.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.

Documentation

class PartialOrd a where

Minimal complete definition

(<=)

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.

Instances

PartialOrd Offsets

Defined in Camfort.Specification.Stencils.Model

Methods

(<=) :: Offsets -> Offsets -> Bool

(>=) :: Offsets -> Offsets -> Bool

(==) :: Offsets -> Offsets -> Bool

(/=) :: Offsets -> Offsets -> Bool

(<) :: Offsets -> Offsets -> Bool

(>) :: Offsets -> Offsets -> Bool

compare :: Offsets -> Offsets -> Maybe Ordering

PartialOrd Integer

Defined in Camfort.Specification.Stencils.PartialOrd

Methods

(<=) :: Integer -> Integer -> Bool

(>=) :: Integer -> Integer -> Bool

(==) :: Integer -> Integer -> Bool

(/=) :: Integer -> Integer -> Bool

(<) :: Integer -> Integer -> Bool

(>) :: Integer -> Integer -> Bool

compare :: Integer -> Integer -> Maybe Ordering

PartialOrd Double

Defined in Camfort.Specification.Stencils.PartialOrd

Methods

(<=) :: Double -> Double -> Bool

(>=) :: Double -> Double -> Bool

(==) :: Double -> Double -> Bool

(/=) :: Double -> Double -> Bool

(<) :: Double -> Double -> Bool

(>) :: Double -> Double -> Bool

compare :: Double -> Double -> Maybe Ordering

PartialOrd Float

Defined in Camfort.Specification.Stencils.PartialOrd

Methods

(<=) :: Float -> Float -> Bool

(>=) :: Float -> Float -> Bool

(==) :: Float -> Float -> Bool

(/=) :: Float -> Float -> Bool

(<) :: Float -> Float -> Bool

(>) :: Float -> Float -> Bool

compare :: Float -> Float -> Maybe Ordering

PartialOrd Int

Derive the partial order from the total order for the following types:

Defined in Camfort.Specification.Stencils.PartialOrd

Methods

(<=) :: Int -> Int -> Bool

(>=) :: Int -> Int -> Bool

(==) :: Int -> Int -> Bool

(/=) :: Int -> Int -> Bool

(<) :: Int -> Int -> Bool

(>) :: Int -> Int -> Bool

compare :: Int -> Int -> Maybe Ordering

PartialOrd (Interval 'Standard)

Defined in Camfort.Specification.Stencils.Model

Methods

(<=) :: Interval 'Standard -> Interval 'Standard -> Bool

(>=) :: Interval 'Standard -> Interval 'Standard -> Bool

(==) :: Interval 'Standard -> Interval 'Standard -> Bool

(/=) :: Interval 'Standard -> Interval 'Standard -> Bool

(<) :: Interval 'Standard -> Interval 'Standard -> Bool

(>) :: Interval 'Standard -> Interval 'Standard -> Bool

compare :: Interval 'Standard -> Interval 'Standard -> Maybe Ordering

Ord a => PartialOrd (Set a)

Define the partial order in terms of the subset relation.

Defined in Camfort.Specification.Stencils.PartialOrd

Methods

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

(>=) :: Set a -> Set a -> Bool

(==) :: Set a -> Set a -> Bool

(/=) :: Set a -> Set a -> Bool

(<) :: Set a -> Set a -> Bool

(>) :: Set a -> Set a -> Bool

compare :: Set a -> Set a -> Maybe Ordering

PartialOrd a => PartialOrd [a]

Define the partial order in terms of the sublist relation.

Defined in Camfort.Specification.Stencils.PartialOrd

Methods

(<=) :: [a] -> [a] -> Bool

(>=) :: [a] -> [a] -> Bool

(==) :: [a] -> [a] -> Bool

(/=) :: [a] -> [a] -> Bool

(<) :: [a] -> [a] -> Bool

(>) :: [a] -> [a] -> Bool

compare :: [a] -> [a] -> Maybe Ordering

PartialOrd a => PartialOrd (Vec n a)

Defined in Camfort.Specification.Stencils.Model

Methods

(<=) :: Vec n a -> Vec n a -> Bool

(>=) :: Vec n a -> Vec n a -> Bool

(==) :: Vec n a -> Vec n a -> Bool

(/=) :: Vec n a -> Vec n a -> Bool

(<) :: Vec n a -> Vec n a -> Bool

(>) :: Vec n a -> Vec n a -> Bool

compare :: Vec n a -> Vec n a -> Maybe Ordering

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

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

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

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

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

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

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

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

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

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