Test.Validity.Relations

Properties of relations

Documentation

reflexiveOnElem

Arguments

:: (a -> a -> Bool)

A relation

-> a

An element

-> Bool

\[ Reflexive(\prec) \quad\equiv\quad \forall a: (a \prec a) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

transitiveOnElems

Arguments

:: (a -> a -> Bool)

A relation

-> a

-> a

-> a

Three elements

-> Bool

\[ Transitive(\prec) \quad\equiv\quad \forall a, b, c: ((a \prec b) \wedge (b \prec c)) \Rightarrow (a \prec c) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

antireflexiveOnElem

Arguments

:: (a -> a -> Bool)

A relation

-> a

An element

-> Bool

\[ Antireflexive(\prec) \quad\equiv\quad \forall a: \neg (a \prec a) \]

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

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

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

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

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

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

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

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

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

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

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

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

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

symmetricOnElems

Arguments

:: (a -> a -> Bool)

A relation

-> a

-> a

Two elements

-> Bool

\[ Symmetric(\prec) \quad\equiv\quad \forall a, b: (a \prec b) \Leftrightarrow (b \prec a) \]

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

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

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

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

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

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

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

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

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

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