| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Test.Validity.Relations
- reflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
- reflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> Property
- reflexivityOnValid :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property
- reflexivity :: (Show a, GenValidity 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) -> Property
- transitivityOnValid :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property
- transitivity :: (Show a, GenValidity 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) -> Property
- antisymmetryOnGensEq :: (Show a, Eq a) => (a -> a -> Bool) -> Gen (a, a) -> Property
- antisymmetryOnValid :: (Show a, Eq a, GenValidity a) => (a -> a -> Bool) -> Property
- antisymmetry :: (Show a, Eq a, GenValidity a) => (a -> a -> Bool) -> Property
- antisymmetryOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> Bool) -> Property
- symmetricOnElems :: (a -> a -> Bool) -> a -> a -> Bool
- symmetryOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a) -> Property
- symmetryOnValid :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property
- symmetry :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property
- symmetryOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
Properties of relations
Reflexivity
\[ Reflexive(prec) \quad\equiv\quad \forall a: (a \prec a) \]
reflexivityOnValid :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property Source #
reflexivity :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property Source #
reflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property Source #
reflexivityOnArbitrary ((==) :: Int -> Int -> Bool)
Transitivity
\[ Transitive(\prec) \quad\equiv\quad \forall a, b, c: ((a \prec b) \wedge (b \prec c)) \Rightarrow (a \prec c) \]
transitivityOnValid :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property Source #
transitivity :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property Source #
transitivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property Source #
transitivityOnArbitrary ((==) :: Int -> Int -> Bool)
Antisymmetry
antisymmetricOnElemsWithEquality Source #
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 Source #
antisymmetryOnValid :: (Show a, Eq a, GenValidity a) => (a -> a -> Bool) -> Property Source #
antisymmetry :: (Show a, Eq a, GenValidity a) => (a -> a -> Bool) -> Property Source #
antisymmetryOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> Bool) -> Property Source #
antisymmetryOnArbitrary ((<=) :: Int -> Int -> Bool)
Symmetry
\[ Symmetric(\prec) \quad\equiv\quad \forall a, b: (a \prec b) \Leftrightarrow (b \prec a) \]
symmetryOnValid :: (Show a, GenValidity a) => (a -> a -> Bool) -> Property Source #