module Test.Validity.Operations.Identity
( leftIdentityOnElemWithEquality
, leftIdentityOnGenWithEquality
, leftIdentityOnGen
, leftIdentityOnValid
, leftIdentity
, leftIdentityOnArbitrary
, rightIdentityOnElemWithEquality
, rightIdentityOnGenWithEquality
, rightIdentityOnGen
, rightIdentityOnValid
, rightIdentity
, rightIdentityOnArbitrary
, identityOnGen
, identityOnValid
, identity
, identityOnArbitrary
) where
import Data.GenValidity
import Test.QuickCheck
leftIdentityOnElemWithEquality
:: (b -> a -> a)
-> (a -> a -> Bool)
-> b
-> a
-> Bool
leftIdentityOnElemWithEquality op eq b a = (b `op` a) `eq` a
leftIdentityOnGenWithEquality
:: Show a
=> (b -> a -> a)
-> (a -> a -> Bool)
-> b
-> Gen a
-> Property
leftIdentityOnGenWithEquality op eq b gen =
forAll gen $ leftIdentityOnElemWithEquality op eq b
leftIdentityOnGen
:: (Show a, Eq a)
=> (b -> a -> a)
-> b
-> Gen a
-> Property
leftIdentityOnGen op = leftIdentityOnGenWithEquality op (==)
leftIdentityOnValid
:: (Show a, Eq a, GenValid a)
=> (b -> a -> a) -> b -> Property
leftIdentityOnValid op b = leftIdentityOnGen op b genValid
leftIdentity
:: (Show a, Eq a, GenUnchecked a)
=> (b -> a -> a) -> b -> Property
leftIdentity op b = leftIdentityOnGen op b genUnchecked
leftIdentityOnArbitrary
:: (Show a, Eq a, Arbitrary a)
=> (b -> a -> a) -> b -> Property
leftIdentityOnArbitrary op b = leftIdentityOnGen op b arbitrary
rightIdentityOnElemWithEquality
:: (a -> b -> a)
-> (a -> a -> Bool)
-> b
-> a
-> Bool
rightIdentityOnElemWithEquality op eq b a = (a `op` b) `eq` a
rightIdentityOnGenWithEquality
:: Show a
=> (a -> b -> a)
-> (a -> a -> Bool)
-> b
-> Gen a
-> Property
rightIdentityOnGenWithEquality op eq b gen =
forAll gen $ rightIdentityOnElemWithEquality op eq b
rightIdentityOnGen
:: (Show a, Eq a)
=> (a -> b -> a)
-> b
-> Gen a
-> Property
rightIdentityOnGen op = rightIdentityOnGenWithEquality op (==)
rightIdentityOnValid
:: (Show a, Eq a, GenValid a)
=> (a -> b -> a) -> b -> Property
rightIdentityOnValid op b = rightIdentityOnGen op b genValid
rightIdentity
:: (Show a, Eq a, GenUnchecked a)
=> (a -> b -> a) -> b -> Property
rightIdentity op b = rightIdentityOnGen op b genUnchecked
rightIdentityOnArbitrary
:: (Show a, Eq a, Arbitrary a)
=> (a -> b -> a) -> b -> Property
rightIdentityOnArbitrary op b = rightIdentityOnGen op b arbitrary
identityOnGen
:: (Show a, Eq a)
=> (a -> a -> a) -> a -> Gen a -> Property
identityOnGen op e gen =
leftIdentityOnGen op e gen .&&. rightIdentityOnGen op e gen
identityOnValid
:: (Show a, Eq a, GenValid a)
=> (a -> a -> a) -> a -> Property
identityOnValid op a = identityOnGen op a genValid
identity
:: (Show a, Eq a, GenUnchecked a)
=> (a -> a -> a) -> a -> Property
identity op e = identityOnGen op e genUnchecked
identityOnArbitrary
:: (Show a, Eq a, Arbitrary a)
=> (a -> a -> a) -> a -> Property
identityOnArbitrary op a = identityOnGen op a arbitrary