Safe Haskell | None |
---|---|
Language | Haskell2010 |
Properties of relations
Synopsis
- reflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
- reflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
- reflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
- reflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
- reflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
- transitiveOnElems :: (a -> a -> Bool) -> a -> a -> a -> Bool
- transitivityOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property
- transitivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
- transitivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
- transitivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
- antisymmetricOnElemsWithEquality :: (a -> a -> Bool) -> (a -> a -> Bool) -> a -> a -> Bool
- 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
- antisymmetry :: (Show a, Eq a, GenUnchecked a) => (a -> a -> Bool) -> Property
- antisymmetryOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> Bool) -> Property
- antireflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
- antireflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
- antireflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
- antireflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
- antireflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
- symmetricOnElems :: (a -> a -> Bool) -> a -> a -> Bool
- symmetryOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property
- symmetryOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
- symmetry :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
- symmetryOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
Documentation
\[ Reflexive(\prec) \quad\equiv\quad \forall a: (a \prec a) \]
reflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property Source #
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 Source #
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 Source #
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)
\[ Transitive(\prec) \quad\equiv\quad \forall a, b, c: ((a \prec b) \wedge (b \prec c)) \Rightarrow (a \prec c) \]
transitivityOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property Source #
transitivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property Source #
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 Source #
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 Source #
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 Source #
\[ Antisymmetric(\prec, \doteq) \quad\equiv\quad \forall a, b: ((a \prec b) \wedge (b \prec a)) \Rightarrow (a \doteq b) \]
antisymmetryOnGensWithEquality :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> a -> Bool) -> (a -> [a]) -> Property Source #
antisymmetryOnGens :: (Show a, Eq a) => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property Source #
antisymmetryOnValid :: (Show a, Eq a, GenValid a) => (a -> a -> Bool) -> Property Source #
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 Source #
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 Source #
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)
\[ Antireflexive(\prec) \quad\equiv\quad \forall a: \neg (a \prec a) \]
antireflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property Source #
antireflexivityOnValid ((<) :: Double -> Double -> Bool)
antireflexivityOnValid ((/=) :: Double -> Double -> Bool)
antireflexivityOnValid ((>) :: Double -> Double -> Bool)
antireflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property Source #
antireflexivity ((<) :: Int -> Int -> Bool)
antireflexivity ((/=) :: Int -> Int -> Bool)
antireflexivity ((>) :: Int -> Int -> Bool)
antireflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property Source #
antireflexivityOnArbitrary ((<) :: Int -> Int -> Bool)
antireflexivityOnArbitrary ((/=) :: Int -> Int -> Bool)
antireflexivityOnArbitrary ((>) :: Int -> Int -> Bool)
\[ Symmetric(\prec) \quad\equiv\quad \forall a, b: (a \prec b) \Leftrightarrow (b \prec a) \]
symmetryOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property Source #
symmetryOnValid ((==) :: Double -> Double -> Bool)
symmetryOnValid ((/=) :: Double -> Double -> Bool)