Test.Validity.Relations.Antisymmetry

Documentation

antisymmetricOnElemsWithEquality

Arguments

:: (a -> a -> Bool)

A relation

-> (a -> a -> Bool)

An equivalence relation

-> a

-> a

Two elements

-> Bool

\[ Antisymmetric(\prec, \doteq) \quad\equiv\quad \forall a, b: ((a \prec b) \wedge (b \prec a)) \Rightarrow (a \doteq b) \]

antisymmetryOnGensWithEquality :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> a -> Bool) -> (a -> [a]) -> Property

antisymmetryOnGens :: (Show a, Eq a) => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property

antisymmetryOnValid :: (Show a, Eq a, GenValid a) => (a -> a -> Bool) -> Property

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

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

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

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

antisymmetryOnValid (Data.List.isPrefixOf :: [Double] -> [Double] -> Bool)

antisymmetryOnValid (Data.List.isSuffixOf :: [Double] -> [Double] -> Bool)

antisymmetryOnValid (Data.List.isInfixOf :: [Double] -> [Double] -> Bool)

antisymmetry :: (Show a, Eq a, GenUnchecked a) => (a -> a -> Bool) -> Property

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

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

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

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

antisymmetry (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)

antisymmetry (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)

antisymmetry (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)

antisymmetry ((\x y -> even x && odd y) :: Int -> Int -> Bool)

antisymmetryOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> Bool) -> Property

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

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

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

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

antisymmetryOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)

antisymmetryOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)

antisymmetryOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)

antisymmetryOnArbitrary ((\x y -> even x && odd y) :: Int -> Int -> Bool)