-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Standard properties for functions on `Validity` types
--   
--   Standard properties for functions on Validity types
@package genvalidity-property
@version 1.0.0.0

-- | Standard tests involving validity
module Test.Validity.Functions.Idempotence
idempotentOnGen :: (Show a, Eq a) => (a -> a) -> Gen a -> (a -> [a]) -> Property
idempotent :: (Show a, Eq a, GenValid a) => (a -> a) -> Property

-- | id is idempotent for any type:
--   
--   
--   idempotentOnArbitrary (id :: Int -> Int)
--   
--   
--   const, given any input, is idempotent for any type as well:
--   
--   
--   \int -> idempotentOnArbitrary (const int :: Int -> Int)
--   
idempotentOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a) -> Property

module Test.Validity.Operations.Associativity

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

-- | 
--   associative ((*) :: Int -> Int -> Int)
--   
--   
--   
--   associative ((+) :: Int -> Int -> Int)
--   
associative :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> Property

-- | 
--   associativeOnArbitrary ((*) :: Int -> Int -> Int)
--   
--   
--   
--   associativeOnArbitrary ((+) :: Int -> Int -> Int)
--   
associativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> Property

module Test.Validity.Operations.Commutativity

-- | <math>
commutativeOnGens :: (Show a, Show b, Eq b) => (a -> a -> b) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property

-- | 
--   commutative ((+) :: Int -> Int -> Int)
--   
--   
--   
--   commutative ((*) :: Int -> Int -> Int)
--   
commutative :: (Show a, Show b, Eq b, GenValid a) => (a -> a -> b) -> Property

-- | 
--   commutativeOnArbitrary ((+) :: Int -> Int -> Int)
--   
--   
--   
--   commutativeOnArbitrary ((*) :: Int -> Int -> Int)
--   
--   
--   commutativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a
--   -> a) -> Property
commutativeOnArbitrary :: (Show a, Show b, Eq b, Arbitrary a) => (a -> a -> b) -> Property

module Test.Validity.Operations.Identity

-- | <math>
leftIdentityOnElemWithEquality :: (b -> a -> a) -> (a -> a -> Bool) -> b -> a -> Bool
leftIdentityOnGenWithEquality :: Show a => (b -> a -> a) -> (a -> a -> Bool) -> b -> Gen a -> (a -> [a]) -> Property
leftIdentityOnGen :: (Show a, Eq a) => (b -> a -> a) -> b -> Gen a -> (a -> [a]) -> Property

-- | 
--   leftIdentity (flip ((^) :: Int -> Int -> Int)) 1
--   
leftIdentity :: (Show a, Eq a, GenValid a) => (b -> a -> a) -> b -> Property

-- | 
--   leftIdentityOnArbitrary (flip ((^) :: Int -> Int -> Int)) 1
--   
leftIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (b -> a -> a) -> b -> Property

-- | <math>
rightIdentityOnElemWithEquality :: (a -> b -> a) -> (a -> a -> Bool) -> b -> a -> Bool
rightIdentityOnGenWithEquality :: Show a => (a -> b -> a) -> (a -> a -> Bool) -> b -> Gen a -> (a -> [a]) -> Property
rightIdentityOnGen :: (Show a, Eq a) => (a -> b -> a) -> b -> Gen a -> (a -> [a]) -> Property

-- | 
--   rightIdentity ((^) :: Int -> Int -> Int) 1
--   
rightIdentity :: (Show a, Eq a, GenValid a) => (a -> b -> a) -> b -> Property

-- | 
--   rightIdentityOnArbitrary ((^) :: Int -> Int -> Int) 1
--   
rightIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b -> a) -> b -> Property

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

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

-- | 
--   identityOnArbitrary ((*) :: Int -> Int -> Int) 1
--   
--   
--   
--   identityOnArbitrary ((+) :: Int -> Int -> Int) 0
--   
identityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> a -> Property

-- | Properties of operations
module Test.Validity.Operations

module Test.Validity.Property.Utils
forAllValid :: (Show a, GenValid a, Testable prop) => (a -> prop) -> Property
shouldBeValid :: (Show a, Validity a) => a -> Expectation
shouldBeInvalid :: (Show a, Validity a) => a -> Expectation
(<==>) :: Bool -> Bool -> Bool
(===>) :: Bool -> Bool -> Bool

-- | Tests for GenValidity instances
module Test.Validity.GenValidity.Property

-- | The given generator generates only valid data points
genGeneratesValid :: (Show a, Validity a) => Gen a -> Property

-- | The given generator generates only invalid data points
genGeneratesInvalid :: (Show a, Validity a) => Gen a -> Property

-- | Standard tests involving validity
module Test.Validity.Functions.Validity

-- | The function produces valid output when the input is generated as
--   specified by the given generator.
producesValidsOnGen :: (Show a, Show b, Validity b) => (a -> b) -> Gen a -> (a -> [a]) -> Property

-- | The function produces valid output when the input is generated by
--   genValid
producesValid :: (Show a, Show b, GenValid a, Validity b) => (a -> b) -> Property

-- | The function produces valid output when the input is generated by
--   arbitrary
producesValidsOnArbitrary :: (Show a, Show b, Arbitrary a, Validity b) => (a -> b) -> Property
producesValidsOnGens2 :: (Show a, Show b, Show c, Validity c) => (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
producesValid2 :: (Show a, Show b, Show c, GenValid a, GenValid b, Validity c) => (a -> b -> c) -> Property
producesValidsOnArbitrary2 :: (Show a, Show b, Show c, Arbitrary a, Arbitrary b, Validity c) => (a -> b -> c) -> Property
producesValidsOnGens3 :: (Show a, Show b, Show c, Show d, Validity d) => (a -> b -> c -> d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property
producesValid3 :: (Show a, Show b, Show c, Show d, GenValid a, GenValid b, GenValid c, Validity d) => (a -> b -> c -> d) -> Property
producesValidsOnArbitrary3 :: (Show a, Show b, Show c, Show d, Arbitrary a, Arbitrary b, Arbitrary c, Validity d) => (a -> b -> c -> d) -> Property

module Test.Validity.Relations.Antireflexivity

-- | <math>
antireflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
antireflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property

-- | 
--   antireflexivity ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   antireflexivity ((/=) :: Int -> Int -> Bool)
--   
--   
--   
--   antireflexivity ((>) :: Int -> Int -> Bool)
--   
antireflexivity :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   antireflexivityOnArbitrary ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   antireflexivityOnArbitrary ((/=) :: Int -> Int -> Bool)
--   
--   
--   
--   antireflexivityOnArbitrary ((>) :: Int -> Int -> Bool)
--   
antireflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

module Test.Validity.Relations.Antisymmetry

-- | <math>
antisymmetricOnElemsWithEquality :: (a -> a -> Bool) -> (a -> a -> Bool) -> a -> a -> Bool
antisymmetryOnGensWithEquality :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> a -> Bool) -> (a -> [a]) -> Property
antisymmetryOnGens :: (Show a, Eq a) => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property

-- | 
--   antisymmetry ((>) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetry ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetry ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetry ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetry (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetry (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetry (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetry ((\x y -> even x && odd y) :: Int -> Int -> Bool)
--   
antisymmetry :: (Show a, Eq a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   antisymmetryOnArbitrary ((>) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary ((\x y -> even x && odd y) :: Int -> Int -> Bool)
--   
antisymmetryOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> Bool) -> Property

module Test.Validity.Relations.Reflexivity

-- | <math>
reflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
reflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property

-- | 
--   reflexivity ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivity ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivity ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivity (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   reflexivity (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   reflexivity (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
reflexivity :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   reflexivityOnArbitrary ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
reflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

module Test.Validity.Relations.Symmetry

-- | <math>
symmetricOnElems :: (a -> a -> Bool) -> a -> a -> Bool
symmetryOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property

-- | 
--   symmetry ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   symmetry ((/=) :: Int -> Int -> Bool)
--   
symmetry :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   symmetryOnArbitrary ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   symmetryOnArbitrary ((/=) :: Int -> Int -> Bool)
--   
symmetryOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

module Test.Validity.Relations.Transitivity

-- | <math>
transitiveOnElems :: (a -> a -> Bool) -> a -> a -> a -> Bool
transitivityOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property

-- | 
--   transitivity ((>) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   transitivity (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   transitivity (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
transitivity :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   transitivityOnArbitrary ((>) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   transitivityOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   transitivityOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
transitivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

-- | Properties of relations
module Test.Validity.Relations

-- | Tests for shrinking functions
module Test.Validity.Shrinking.Property

-- | 
--   shrinkPreservesValidOnGenValid ((:[]) :: Int -> [Int])
--   
shrinkPreservesValidOnGenValid :: (Show a, GenValid a) => (a -> [a]) -> Property

-- | 
--   shrinkValidPreservesValid (pure 5 :: Gen Rational)
--   
shrinkValidPreservesValid :: (Show a, GenValid a) => Gen a -> Property

-- | 
--   shrinkingStaysValid (pure 5 :: Gen Double) (\d -> [d - 1, d - 2])
--   
shrinkingStaysValid :: (Show a, Validity a) => Gen a -> (a -> [a]) -> Property

-- | 
--   shrinkingStaysValidWithLimit (pure 5 :: Gen Double) (\d -> [d - 1, read "NaN"]) 1
--   
shrinkingStaysValidWithLimit :: (Show a, Validity a) => Gen a -> (a -> [a]) -> Int -> Property

-- | 
--   shrinkingPreserves (pure 5 :: Gen Int) (:[]) (== 5)
--   
shrinkingPreserves :: Show a => Gen a -> (a -> [a]) -> (a -> Bool) -> Property

-- | 
--   shrinkingPreservesWithLimit (pure 4) (:[]) 100 (== 4)
--   
shrinkingPreservesWithLimit :: Show a => Gen a -> (a -> [a]) -> Int -> (a -> Bool) -> Property

-- | 
--   shrinkDoesNotShrinkToItself (shrinkValid :: Double -> [Double])
--   
shrinkDoesNotShrinkToItself :: (Show a, Eq a, GenValid a) => (a -> [a]) -> Property

-- | 
--   shrinkDoesNotShrinkToItselfWithLimit (shrinkValid :: Double -> [Double]) 100
--   
shrinkDoesNotShrinkToItselfWithLimit :: (Show a, Eq a, GenValid a) => (a -> [a]) -> Int -> Property

-- | 
--   shrinkDoesNotShrinkToItselfOnValid (shrinkValid ::  Rational -> [Rational])
--   
shrinkDoesNotShrinkToItselfOnValid :: (Show a, Eq a, GenValid a) => (a -> [a]) -> Property

-- | 
--   shrinkDoesNotShrinkToItselfOnValidWithLimit (shrinkValid :: Rational -> [Rational]) 100
--   
shrinkDoesNotShrinkToItselfOnValidWithLimit :: (Show a, Eq a, GenValid a) => (a -> [a]) -> Int -> Property

-- | 
--   doesNotShrinkToItself (pure 5 :: Gen Double) shrinkValid
--   
doesNotShrinkToItself :: (Show a, Eq a) => Gen a -> (a -> [a]) -> Property

-- | 
--   doesNotShrinkToItselfWithLimit (pure 5 :: Gen Double) shrinkValid 100
--   
doesNotShrinkToItselfWithLimit :: (Show a, Eq a) => Gen a -> (a -> [a]) -> Int -> Property

module Test.Validity.Types

-- | A class of types that are the result of functions that can fail
class CanFail (f :: Type -> Type)
hasFailed :: CanFail f => f a -> Bool
resultIfSucceeded :: CanFail f => f a -> Maybe a
instance Test.Validity.Types.CanFail (GHC.Internal.Data.Either.Either e)
instance Test.Validity.Types.CanFail GHC.Internal.Maybe.Maybe

-- | Standard tests involving inverse functions
module Test.Validity.Functions.Inverse
inverseFunctionsOnGen :: (Show a, Eq a) => (a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctions :: (Show a, Eq a, GenValid a) => (a -> b) -> (b -> a) -> Property

-- | id is its own inverse function for every type: prop>
--   inverseFunctionsOnArbitrary id (id :: Int -> Int)
inverseFunctionsOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b) -> (b -> a) -> Property
inverseFunctionsIfFirstSucceedsOnGen :: (Show a, Eq a, CanFail f) => (a -> f b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfFirstSucceeds :: (Show a, Eq a, GenValid a, CanFail f) => (a -> f b) -> (b -> a) -> Property
inverseFunctionsIfFirstSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f) => (a -> f b) -> (b -> a) -> Property
inverseFunctionsIfSecondSucceedsOnGen :: (Show a, Eq a, CanFail f) => (a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSecondSucceeds :: (Show a, Eq a, GenValid a, CanFail f) => (a -> b) -> (b -> f a) -> Property
inverseFunctionsIfSecondSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f) => (a -> b) -> (b -> f a) -> Property
inverseFunctionsIfSucceedOnGen :: (Show a, Eq a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSucceed :: (Show a, Eq a, GenValid a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property
inverseFunctionsIfSucceedOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property

module Test.Validity.Functions.Equivalence
equivalentOnGen :: (Show a, Show b, Eq b) => (a -> b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property
equivalent :: (Show a, GenValid a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property

-- | 
--   equivalentOnArbitrary ((* 2) . (+ 1)) ((+ 2) . (* 2) :: Int -> Int)
--   
equivalentOnArbitrary :: (Show a, Arbitrary a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property
equivalentOnGens2 :: (Show a, Show b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalent2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property

-- | 
--   equivalentOnArbitrary2 (+) ((+) :: Int -> Int -> Int)
--   
equivalentOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property
equivalentWhenFirstSucceedsOnGen :: (Show a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property
equivalentWhenFirstSucceeds :: (Show a, GenValid a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property
equivalentWhenFirstSucceedsOnArbitrary :: (Show a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property
equivalentWhenFirstSucceedsOnGens2 :: (Show a, Show b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentWhenFirstSucceeds2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Property
equivalentWhenFirstSucceedsOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Property
equivalentWhenSecondSucceedsOnGen :: (Show a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Gen a -> (a -> [a]) -> Property
equivalentWhenSecondSucceeds :: (Show a, GenValid a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property
equivalentWhenSecondSucceedsOnArbitrary :: (Show a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property
equivalentWhenSecondSucceedsOnGens2 :: (Show a, Show b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentWhenSecondSucceeds2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Property
equivalentWhenSecondSucceedsOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Property
equivalentWhenSucceedOnGen :: (Show a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Gen a -> (a -> [a]) -> Property
equivalentWhenSucceed :: (Show a, GenValid a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property
equivalentWhenSucceedOnArbitrary :: (Show a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property
equivalentWhenSucceedOnGens2 :: (Show a, Show b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentWhenSucceed2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Property
equivalentWhenSucceedOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Property
equivalentOnGens3 :: (Show a, Show b, Show c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property
equivalent3 :: (Show a, GenValid a, Show b, GenValid b, Show c, GenValid c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Property
equivalentOnArbitrary3 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Arbitrary c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Property

module Test.Validity.Functions.CanFail

-- | The function succeeds if the input is generated by the given generator
succeedsOnGen :: (Show a, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property

-- | The function succeeds if the input is generated by genValid
succeeds :: (Show a, Show (f b), GenValid a, CanFail f) => (a -> f b) -> Property

-- | The function succeeds if the input is generated by arbitrary
succeedsOnArbitrary :: (Show a, Show (f b), Arbitrary a, CanFail f) => (a -> f b) -> Property
succeedsOnGens2 :: (Show a, Show b, Show (f c), CanFail f) => (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
succeeds2 :: (Show a, Show b, Show (f c), GenValid a, GenValid b, CanFail f) => (a -> b -> f c) -> Property
succeedsOnArbitrary2 :: (Show a, Show b, Show (f c), Arbitrary a, Arbitrary b, CanFail f) => (a -> b -> f c) -> Property

-- | The function fails if the input is generated by the given generator
failsOnGen :: (Show a, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property
failsOnGens2 :: (Show a, Show b, Show (f c), CanFail f) => (a -> b -> f c) -> Gen a -> (a -> [a]) -> Gen b -> (b -> [b]) -> Property

-- | The function produces output that satisfies isValid if it is
--   given input that is generated by the given generator.
validIfSucceedsOnGen :: (Show a, Show b, Validity b, CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property

-- | The function produces output that satisfies isValid if it is
--   given input that is generated by arbitrary.
validIfSucceedsOnArbitrary :: (Show a, Show b, Arbitrary a, Validity b, CanFail f) => (a -> f b) -> Property

-- | The function produces output that satisfies isValid if it is
--   given input that is generated by genValid.
validIfSucceeds :: (Show a, Show b, GenValid a, Validity b, CanFail f) => (a -> f b) -> Property
validIfSucceedsOnGens2 :: (Show a, Show b, Show c, Validity c, CanFail f) => (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
validIfSucceeds2 :: (Show a, Show b, Show c, GenValid a, GenValid b, Validity c, CanFail f) => (a -> b -> f c) -> Property
validIfSucceedsOnArbitrary2 :: (Show a, Show b, Show c, Arbitrary a, Arbitrary b, Validity c, CanFail f) => (a -> b -> f c) -> Property
validIfSucceedsOnGens3 :: (Show a, Show b, Show c, Show d, Validity d, CanFail f) => (a -> b -> c -> f d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property
validIfSucceeds3 :: (Show a, Show b, Show c, Show d, GenValid a, GenValid b, GenValid c, Validity d, CanFail f) => (a -> b -> c -> f d) -> Property
validIfSucceedsOnArbitrary3 :: (Show a, Show b, Show c, Show d, Arbitrary a, Arbitrary b, Arbitrary c, Validity d, CanFail f) => (a -> b -> c -> f d) -> Property

-- | Validity tests involving functions
module Test.Validity.Functions

module Test.Validity.Property
forAllValid :: (Show a, GenValid a, Testable prop) => (a -> prop) -> Property

-- | The given generator generates only valid data points
genGeneratesValid :: (Show a, Validity a) => Gen a -> Property

-- | The function produces valid output when the input is generated as
--   specified by the given generator.
producesValidsOnGen :: (Show a, Show b, Validity b) => (a -> b) -> Gen a -> (a -> [a]) -> Property

-- | The function produces valid output when the input is generated by
--   genValid
producesValid :: (Show a, Show b, GenValid a, Validity b) => (a -> b) -> Property

-- | The function produces valid output when the input is generated by
--   arbitrary
producesValidsOnArbitrary :: (Show a, Show b, Arbitrary a, Validity b) => (a -> b) -> Property
producesValidsOnGens2 :: (Show a, Show b, Show c, Validity c) => (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
producesValid2 :: (Show a, Show b, Show c, GenValid a, GenValid b, Validity c) => (a -> b -> c) -> Property
producesValidsOnArbitrary2 :: (Show a, Show b, Show c, Arbitrary a, Arbitrary b, Validity c) => (a -> b -> c) -> Property
producesValidsOnGens3 :: (Show a, Show b, Show c, Show d, Validity d) => (a -> b -> c -> d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property
producesValid3 :: (Show a, Show b, Show c, Show d, GenValid a, GenValid b, GenValid c, Validity d) => (a -> b -> c -> d) -> Property
producesValidsOnArbitrary3 :: (Show a, Show b, Show c, Show d, Arbitrary a, Arbitrary b, Arbitrary c, Validity d) => (a -> b -> c -> d) -> Property

-- | A class of types that are the result of functions that can fail
class CanFail (f :: Type -> Type)
hasFailed :: CanFail f => f a -> Bool
resultIfSucceeded :: CanFail f => f a -> Maybe a

-- | The function succeeds if the input is generated by the given generator
succeedsOnGen :: (Show a, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property

-- | The function succeeds if the input is generated by genValid
succeeds :: (Show a, Show (f b), GenValid a, CanFail f) => (a -> f b) -> Property

-- | The function succeeds if the input is generated by arbitrary
succeedsOnArbitrary :: (Show a, Show (f b), Arbitrary a, CanFail f) => (a -> f b) -> Property
succeedsOnGens2 :: (Show a, Show b, Show (f c), CanFail f) => (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
succeeds2 :: (Show a, Show b, Show (f c), GenValid a, GenValid b, CanFail f) => (a -> b -> f c) -> Property
succeedsOnArbitrary2 :: (Show a, Show b, Show (f c), Arbitrary a, Arbitrary b, CanFail f) => (a -> b -> f c) -> Property

-- | The function fails if the input is generated by the given generator
failsOnGen :: (Show a, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property
failsOnGens2 :: (Show a, Show b, Show (f c), CanFail f) => (a -> b -> f c) -> Gen a -> (a -> [a]) -> Gen b -> (b -> [b]) -> Property

-- | The function produces output that satisfies isValid if it is
--   given input that is generated by the given generator.
validIfSucceedsOnGen :: (Show a, Show b, Validity b, CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property

-- | The function produces output that satisfies isValid if it is
--   given input that is generated by arbitrary.
validIfSucceedsOnArbitrary :: (Show a, Show b, Arbitrary a, Validity b, CanFail f) => (a -> f b) -> Property

-- | The function produces output that satisfies isValid if it is
--   given input that is generated by genValid.
validIfSucceeds :: (Show a, Show b, GenValid a, Validity b, CanFail f) => (a -> f b) -> Property
validIfSucceedsOnGens2 :: (Show a, Show b, Show c, Validity c, CanFail f) => (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
validIfSucceeds2 :: (Show a, Show b, Show c, GenValid a, GenValid b, Validity c, CanFail f) => (a -> b -> f c) -> Property
validIfSucceedsOnArbitrary2 :: (Show a, Show b, Show c, Arbitrary a, Arbitrary b, Validity c, CanFail f) => (a -> b -> f c) -> Property
validIfSucceedsOnGens3 :: (Show a, Show b, Show c, Show d, Validity d, CanFail f) => (a -> b -> c -> f d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property
validIfSucceeds3 :: (Show a, Show b, Show c, Show d, GenValid a, GenValid b, GenValid c, Validity d, CanFail f) => (a -> b -> c -> f d) -> Property
validIfSucceedsOnArbitrary3 :: (Show a, Show b, Show c, Show d, Arbitrary a, Arbitrary b, Arbitrary c, Validity d, CanFail f) => (a -> b -> c -> f d) -> Property
equivalentOnGen :: (Show a, Show b, Eq b) => (a -> b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property
equivalent :: (Show a, GenValid a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property

-- | 
--   equivalentOnArbitrary ((* 2) . (+ 1)) ((+ 2) . (* 2) :: Int -> Int)
--   
equivalentOnArbitrary :: (Show a, Arbitrary a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property
equivalentOnGens2 :: (Show a, Show b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalent2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property

-- | 
--   equivalentOnArbitrary2 (+) ((+) :: Int -> Int -> Int)
--   
equivalentOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property
equivalentOnGens3 :: (Show a, Show b, Show c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property
equivalent3 :: (Show a, GenValid a, Show b, GenValid b, Show c, GenValid c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Property
equivalentOnArbitrary3 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Arbitrary c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Property
equivalentWhenFirstSucceedsOnGen :: (Show a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property
equivalentWhenFirstSucceeds :: (Show a, GenValid a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property
equivalentWhenFirstSucceedsOnArbitrary :: (Show a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property
equivalentWhenFirstSucceedsOnGens2 :: (Show a, Show b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentWhenFirstSucceeds2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Property
equivalentWhenFirstSucceedsOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Property
equivalentWhenSecondSucceedsOnGen :: (Show a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Gen a -> (a -> [a]) -> Property
equivalentWhenSecondSucceeds :: (Show a, GenValid a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property
equivalentWhenSecondSucceedsOnArbitrary :: (Show a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property
equivalentWhenSecondSucceedsOnGens2 :: (Show a, Show b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentWhenSecondSucceeds2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Property
equivalentWhenSecondSucceedsOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Property
equivalentWhenSucceedOnGen :: (Show a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Gen a -> (a -> [a]) -> Property
equivalentWhenSucceed :: (Show a, GenValid a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property
equivalentWhenSucceedOnArbitrary :: (Show a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property
equivalentWhenSucceedOnGens2 :: (Show a, Show b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentWhenSucceed2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Property
equivalentWhenSucceedOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Property
inverseFunctionsOnGen :: (Show a, Eq a) => (a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctions :: (Show a, Eq a, GenValid a) => (a -> b) -> (b -> a) -> Property

-- | id is its own inverse function for every type: prop>
--   inverseFunctionsOnArbitrary id (id :: Int -> Int)
inverseFunctionsOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b) -> (b -> a) -> Property
inverseFunctionsIfFirstSucceedsOnGen :: (Show a, Eq a, CanFail f) => (a -> f b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfFirstSucceeds :: (Show a, Eq a, GenValid a, CanFail f) => (a -> f b) -> (b -> a) -> Property
inverseFunctionsIfFirstSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f) => (a -> f b) -> (b -> a) -> Property
inverseFunctionsIfSecondSucceedsOnGen :: (Show a, Eq a, CanFail f) => (a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSecondSucceeds :: (Show a, Eq a, GenValid a, CanFail f) => (a -> b) -> (b -> f a) -> Property
inverseFunctionsIfSecondSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f) => (a -> b) -> (b -> f a) -> Property
inverseFunctionsIfSucceedOnGen :: (Show a, Eq a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSucceed :: (Show a, Eq a, GenValid a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property
inverseFunctionsIfSucceedOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property
idempotentOnGen :: (Show a, Eq a) => (a -> a) -> Gen a -> (a -> [a]) -> Property
idempotent :: (Show a, Eq a, GenValid a) => (a -> a) -> Property

-- | id is idempotent for any type:
--   
--   
--   idempotentOnArbitrary (id :: Int -> Int)
--   
--   
--   const, given any input, is idempotent for any type as well:
--   
--   
--   \int -> idempotentOnArbitrary (const int :: Int -> Int)
--   
idempotentOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a) -> Property

-- | <math>
reflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
reflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property

-- | 
--   reflexivity ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivity ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivity ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivity (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   reflexivity (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   reflexivity (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
reflexivity :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   reflexivityOnArbitrary ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   reflexivityOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
reflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

-- | <math>
transitiveOnElems :: (a -> a -> Bool) -> a -> a -> a -> Bool
transitivityOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property

-- | 
--   transitivity ((>) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivity (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   transitivity (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   transitivity (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
transitivity :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   transitivityOnArbitrary ((>) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   transitivityOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   transitivityOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   transitivityOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
transitivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

-- | <math>
antisymmetricOnElemsWithEquality :: (a -> a -> Bool) -> (a -> a -> Bool) -> a -> a -> Bool
antisymmetryOnGensWithEquality :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> a -> Bool) -> (a -> [a]) -> Property
antisymmetryOnGens :: (Show a, Eq a) => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property

-- | 
--   antisymmetry ((>) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetry ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetry ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetry ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetry (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetry (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetry (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetry ((\x y -> even x && odd y) :: Int -> Int -> Bool)
--   
antisymmetry :: (Show a, Eq a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   antisymmetryOnArbitrary ((>) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary ((>=) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary ((<=) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)
--   
--   
--   
--   antisymmetryOnArbitrary ((\x y -> even x && odd y) :: Int -> Int -> Bool)
--   
antisymmetryOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> Bool) -> Property

-- | <math>
antireflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
antireflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property

-- | 
--   antireflexivity ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   antireflexivity ((/=) :: Int -> Int -> Bool)
--   
--   
--   
--   antireflexivity ((>) :: Int -> Int -> Bool)
--   
antireflexivity :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   antireflexivityOnArbitrary ((<) :: Int -> Int -> Bool)
--   
--   
--   
--   antireflexivityOnArbitrary ((/=) :: Int -> Int -> Bool)
--   
--   
--   
--   antireflexivityOnArbitrary ((>) :: Int -> Int -> Bool)
--   
antireflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

-- | <math>
symmetricOnElems :: (a -> a -> Bool) -> a -> a -> Bool
symmetryOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property

-- | 
--   symmetry ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   symmetry ((/=) :: Int -> Int -> Bool)
--   
symmetry :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

-- | 
--   symmetryOnArbitrary ((==) :: Int -> Int -> Bool)
--   
--   
--   
--   symmetryOnArbitrary ((/=) :: Int -> Int -> Bool)
--   
symmetryOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

-- | <math>
leftIdentityOnElemWithEquality :: (b -> a -> a) -> (a -> a -> Bool) -> b -> a -> Bool
leftIdentityOnGenWithEquality :: Show a => (b -> a -> a) -> (a -> a -> Bool) -> b -> Gen a -> (a -> [a]) -> Property
leftIdentityOnGen :: (Show a, Eq a) => (b -> a -> a) -> b -> Gen a -> (a -> [a]) -> Property

-- | 
--   leftIdentity (flip ((^) :: Int -> Int -> Int)) 1
--   
leftIdentity :: (Show a, Eq a, GenValid a) => (b -> a -> a) -> b -> Property

-- | 
--   leftIdentityOnArbitrary (flip ((^) :: Int -> Int -> Int)) 1
--   
leftIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (b -> a -> a) -> b -> Property

-- | <math>
rightIdentityOnElemWithEquality :: (a -> b -> a) -> (a -> a -> Bool) -> b -> a -> Bool
rightIdentityOnGenWithEquality :: Show a => (a -> b -> a) -> (a -> a -> Bool) -> b -> Gen a -> (a -> [a]) -> Property
rightIdentityOnGen :: (Show a, Eq a) => (a -> b -> a) -> b -> Gen a -> (a -> [a]) -> Property

-- | 
--   rightIdentity ((^) :: Int -> Int -> Int) 1
--   
rightIdentity :: (Show a, Eq a, GenValid a) => (a -> b -> a) -> b -> Property

-- | 
--   rightIdentityOnArbitrary ((^) :: Int -> Int -> Int) 1
--   
rightIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b -> a) -> b -> Property

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

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

-- | 
--   identityOnArbitrary ((*) :: Int -> Int -> Int) 1
--   
--   
--   
--   identityOnArbitrary ((+) :: Int -> Int -> Int) 0
--   
identityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> a -> Property

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

-- | 
--   associative ((*) :: Int -> Int -> Int)
--   
--   
--   
--   associative ((+) :: Int -> Int -> Int)
--   
associative :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> Property

-- | 
--   associativeOnArbitrary ((*) :: Int -> Int -> Int)
--   
--   
--   
--   associativeOnArbitrary ((+) :: Int -> Int -> Int)
--   
associativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> Property

-- | <math>
commutativeOnGens :: (Show a, Show b, Eq b) => (a -> a -> b) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property

-- | 
--   commutative ((+) :: Int -> Int -> Int)
--   
--   
--   
--   commutative ((*) :: Int -> Int -> Int)
--   
commutative :: (Show a, Show b, Eq b, GenValid a) => (a -> a -> b) -> Property

-- | 
--   commutativeOnArbitrary ((+) :: Int -> Int -> Int)
--   
--   
--   
--   commutativeOnArbitrary ((*) :: Int -> Int -> Int)
--   
--   
--   commutativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a
--   -> a) -> Property
commutativeOnArbitrary :: (Show a, Show b, Eq b, Arbitrary a) => (a -> a -> b) -> Property
