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 -> Property

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

reflexivityOnValid ((<=) @Double)

reflexivityOnValid ((==) @Double)

reflexivityOnValid ((>=) @Double)

reflexivityOnValid (Data.List.isPrefixOf @Double)

reflexivityOnValid (Data.List.isSuffixOf @Double)

reflexivityOnValid (Data.List.isInfixOf @Double)

reflexivityOnValid (Data.List.isSubsequenceOf @Double)

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

reflexivity ((<=) @Int)

reflexivity ((==) @Int)

reflexivity ((>=) @Int)

reflexivity (Data.List.isPrefixOf @Int)

reflexivity (Data.List.isSuffixOf @Int)

reflexivity (Data.List.isInfixOf @Int)

reflexivity (Data.List.isSubsequenceOf @Int)

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

reflexivityOnArbitrary ((<=) @Int)

reflexivityOnArbitrary ((==) @Int)

reflexivityOnArbitrary ((>=) @Int)

reflexivityOnArbitrary (Data.List.isPrefixOf @Int)

reflexivityOnArbitrary (Data.List.isSuffixOf @Int)

reflexivityOnArbitrary (Data.List.isInfixOf @Int)

reflexivityOnArbitrary (Data.List.isSubsequenceOf @Int)

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) -> Property

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

transitivityOnValid ((>) @Double)

transitivityOnValid ((>=) @Double)

transitivityOnValid ((==) @Double)

transitivityOnValid ((<=) @Double)

transitivityOnValid ((<) @Double)

transitivityOnValid (Data.List.isPrefixOf @Double)

transitivityOnValid (Data.List.isSuffixOf @Double)

transitivityOnValid (Data.List.isInfixOf @Double)

transitivityOnValid (Data.List.isSubsequenceOf @Double)

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

transitivity ((>) @Int)

transitivity ((>=) @Int)

transitivity ((==) @Int)

transitivity ((<=) @Int)

transitivity ((<) @Int)

transitivity (Data.List.isPrefixOf @Int)

transitivity (Data.List.isSuffixOf @Int)

transitivity (Data.List.isInfixOf @Int)

transitivity (Data.List.isSubsequenceOf @Int)

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

transitivityOnArbitrary ((>) @Int)

transitivityOnArbitrary ((>=) @Int)

transitivityOnArbitrary ((==) @Int)

transitivityOnArbitrary ((<=) @Int)

transitivityOnArbitrary ((<) @Int)

transitivityOnArbitrary (Data.List.isPrefixOf @Int)

transitivityOnArbitrary (Data.List.isSuffixOf @Int)

transitivityOnArbitrary (Data.List.isInfixOf @Int)

transitivityOnArbitrary (Data.List.isSubsequenceOf @Int)

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) -> Property

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

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

antisymmetryOnValid ((>) @Double)

antisymmetryOnValid ((>=) @Double)

antisymmetryOnValid ((<=) @Double)

antisymmetryOnValid ((<) @Double)

antisymmetryOnValid (Data.List.isPrefixOf @Double)

antisymmetryOnValid (Data.List.isSuffixOf @Double)

antisymmetryOnValid (Data.List.isInfixOf @Double)

antisymmetryOnValid (Data.List.isSubsequenceOf @Double)

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

antisymmetry ((>) @Int)

antisymmetry ((>=) @Int)

antisymmetry ((<=) @Int)

antisymmetry ((<) @Int)

antisymmetry (Data.List.isPrefixOf @Int)

antisymmetry (Data.List.isSuffixOf @Int)

antisymmetry (Data.List.isInfixOf @Int)

antisymmetry (Data.List.isSubsequenceOf @Int)

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

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

antisymmetryOnArbitrary ((>) @Int)

antisymmetryOnArbitrary ((>=) @Int)

antisymmetryOnArbitrary ((<=) @Int)

antisymmetryOnArbitrary ((<) @Int)

antisymmetryOnArbitrary (Data.List.isPrefixOf @Int)

antisymmetryOnArbitrary (Data.List.isSuffixOf @Int)

antisymmetryOnArbitrary (Data.List.isInfixOf @Int)

antisymmetryOnArbitrary (Data.List.isSubsequenceOf @Int)

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 -> Property

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

antireflexivityOnValid ((<) @Double)

antireflexivityOnValid ((/=) @Double)

antireflexivityOnValid ((>) @Double)

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

antireflexivity ((<) @Int)

antireflexivity ((/=) @Int)

antireflexivity ((>) @Int)

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

antireflexivityOnArbitrary ((<) @Int)

antireflexivityOnArbitrary ((/=) @Int)

antireflexivityOnArbitrary ((>) @Int)

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) -> Property

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

symmetryOnValid ((==) @Double)

symmetryOnValid ((/=) @Double)

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

symmetry ((==) @Int)

symmetry ((/=) @Int)

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

symmetryOnArbitrary ((==) @Int)

symmetryOnArbitrary ((/=) @Int)