genvalidity-property-0.0.0.0: Standard properties for functions on `Validity` types

Safe HaskellNone
LanguageHaskell2010

Test.Validity.Operations

Description

Properties of operations

Synopsis

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 
-> 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 -> Double)) 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 
-> 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 -> Int -> Double) 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 -> Property #

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

identityOnValid ((*) :: Double -> Double -> Double) 1
identityOnValid ((+) :: Double -> Double -> Double) 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) -> 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 -> 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) -> Property #

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

commutative ((+) :: Double -> Double -> Double)
commutative ((*) :: Double -> Double -> Double)

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)