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GHC 9.10.3 · lts/ghc-9.10.x · 248f8f0 · 2026-10-05

Modulegenvalidity-property-1.0.0.0Haskell2010

Test.Validity.Operations.Identity

  • 13 values
valueleftIdentityOnElemWithEquality
  1. :: (b -> a -> a)

    A binary operation

  2. -> (a -> a -> Bool)

    An equality

  3. -> b

    A candidate left-identity

  4. -> a

    An element

  5. -> Bool
#

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

valuerightIdentityOnElemWithEquality
  1. :: (a -> b -> a)

    A binary operation

  2. -> (a -> a -> Bool)

    An equality

  3. -> b

    A candidate right-identity

  4. -> a

    An element

  5. -> Bool
#

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

valueidentityOnGen
  1. :: (Show a, Eq a)
  2. => a -> a -> a
  3. -> a
  4. -> Gen a
  5. -> a -> [a]
  6. -> Property
#

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

valueidentity :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> a -> Property
#
Property
identity ((*) :: Int -> Int -> Int) 1
Property
identity ((+) :: Int -> Int -> Int) 0