Test.Validity.Operations

Properties of operations

Identity element

Left identity

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

-> Property

leftIdentityOnGen

Arguments

:: (Show a, Eq a)

=> (b -> a -> a)

A binary operation

-> b

A candidate left-identity

-> Gen a

-> Property

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

leftIdentityOnValid (flip ((^) @Double @Int)) 1

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

leftIdentity (flip ((^) @Int @Int)) 1

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

leftIdentityOnArbitrary (flip ((^) @Int @Int)) 1

Right identity

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

-> Property

rightIdentityOnGen

Arguments

:: (Show a, Eq a)

=> (a -> b -> a)

A binary operation

-> b

A candidate right-identity

-> Gen a

-> Property

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

rightIdentityOnValid ((^) @Double) 1

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

rightIdentity ((^) @Int) 1

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

rightIdentityOnArbitrary ((^) @Int) 1

Identity

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

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

identityOnValid ((*) @Double) 1

identityOnValid ((+) @Double) 0

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

identity ((*) @Int) 1

identity ((+) @Int) 0

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

identityOnArbitrary ((*) @Int) 1

identityOnArbitrary ((+) @Int) 0

Associativity

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

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

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

associative ((*) @Int)

associative ((+) @Int)

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

associativeOnArbitrary ((*) @Int)

associativeOnArbitrary ((+) @Int)

Commutativity

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

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

commutative ((+) @Double)

commutative ((*) @Double)

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

commutative ((+) @Int)

commutative ((*) @Int)

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

commutativeOnArbitrary ((+) @Int)

commutativeOnArbitrary ((*) @Int)