Test.Validity.Operations

Properties of operations

Documentation

leftIdentityOnElemWithEquality

Arguments

:: (b -> a -> a)

A binary operation

-> (a -> a -> Bool)

An equality

-> b

A candidate left-identity

-> a

An element

-> Bool

\[ LeftIdentity(\star, \doteq, b) \quad\equiv\quad \forall a: (b \star a) \doteq a \]

leftIdentityOnGenWithEquality

Arguments

:: Show a

=> (b -> a -> a)

A binary operation

-> (a -> a -> Bool)

An equality

-> b

A candidate left-identity

-> Gen a

-> (a -> [a])

-> Property

leftIdentityOnGen

Arguments

:: (Show a, Eq a)

=> (b -> a -> a)

A binary operation

-> b

A candidate left-identity

-> Gen a

-> (a -> [a])

-> Property

leftIdentityOnValid :: (Show a, Eq a, GenValid a) => (b -> a -> a) -> b -> Property

leftIdentityOnValid (flip ((^) :: Rational -> Int -> Rational)) 1

leftIdentity :: (Show a, Eq a, GenUnchecked a) => (b -> a -> a) -> b -> Property

leftIdentity (flip ((^) :: Int -> Int -> Int)) 1

leftIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (b -> a -> a) -> b -> Property

leftIdentityOnArbitrary (flip ((^) :: Int -> Int -> Int)) 1

rightIdentityOnElemWithEquality

Arguments

:: (a -> b -> a)

A binary operation

-> (a -> a -> Bool)

An equality

-> b

A candidate right-identity

-> a

An element

-> Bool

\[ RightIdentity(\star, \doteq, b) \quad\equiv\quad \forall a: (a \star b) \doteq a \]

rightIdentityOnGenWithEquality

Arguments

:: Show a

=> (a -> b -> a)

A binary operation

-> (a -> a -> Bool)

An equality

-> b

A candidate right-identity

-> Gen a

-> (a -> [a])

-> Property

rightIdentityOnGen

Arguments

:: (Show a, Eq a)

=> (a -> b -> a)

A binary operation

-> b

A candidate right-identity

-> Gen a

-> (a -> [a])

-> Property

rightIdentityOnValid :: (Show a, Eq a, GenValid a) => (a -> b -> a) -> b -> Property

rightIdentityOnValid ((^) :: Rational -> Int -> Rational) 1

rightIdentity :: (Show a, Eq a, GenUnchecked a) => (a -> b -> a) -> b -> Property

rightIdentity ((^) :: Int -> Int -> Int) 1

rightIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b -> a) -> b -> Property

rightIdentityOnArbitrary ((^) :: Int -> Int -> Int) 1

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

\[ Identity(\star, \doteq, b) \quad\equiv\quad LeftIdentity(\star, \doteq, b) \wedge RightIdentity(\star, \doteq, b) \]

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

identityOnValid ((*) :: Rational -> Rational -> Rational) 1

identityOnValid ((+) :: Rational -> Rational -> Rational) 0

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

identity ((*) :: Int -> Int -> Int) 1

identity ((+) :: Int -> Int -> Int) 0

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

identityOnArbitrary ((*) :: Int -> Int -> Int) 1

identityOnArbitrary ((+) :: Int -> Int -> Int) 0

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

\[ Associative(\star) \quad\equiv\quad \forall a, b, c: (a \star b) \star c = a \star (b \star c) \]

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

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

associative ((*) :: Int -> Int -> Int)

associative ((+) :: Int -> Int -> Int)

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

associativeOnArbitrary ((*) :: Int -> Int -> Int)

associativeOnArbitrary ((+) :: Int -> Int -> Int)

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

\[ Commutative(\star) \quad\equiv\quad \forall a, b: a \star b = b \star a \]

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

commutativeOnValids ((+) :: Rational -> Rational -> Rational)

commutativeOnValids ((*) :: Rational -> Rational -> Rational)

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

commutative ((+) :: Int -> Int -> Int)

commutative ((*) :: Int -> Int -> Int)

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

commutativeOnArbitrary ((+) :: Int -> Int -> Int)

commutativeOnArbitrary ((*) :: Int -> Int -> Int)