-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | QuickCheck common typeclasses -- -- This library provides quickcheck properties to ensure that typeclass -- instances the set of laws that they are supposed to. There are other -- libraries that do similar things, such as `genvalidity-hspec` and -- checkers. This library differs from other solutions by not -- introducing any new typeclasses that the user needs to learn. @package quickcheck-classes @version 0.4.2 -- | This library provides lists of properties that should hold for common -- typeclasses. All of these take a Proxy argument that is used to -- nail down the type for which the typeclass dictionaries should be -- tested. For example, at GHCi: -- --

--   >>> lawsCheck (monoidLaws (Proxy :: Proxy Ordering))
--   Monoid: Associative +++ OK, passed 100 tests.
--   Monoid: Left Identity +++ OK, passed 100 tests.
--   Monoid: Right Identity +++ OK, passed 100 tests.
--

-- -- Assuming that the Arbitrary instance for Ordering is -- good, we now have confidence that the Monoid instance for -- Ordering satisfies the monoid laws. We can check multiple -- typeclasses with: -- --

--   >>> foldMap (lawsCheck . ($ (Proxy :: Proxy Word))) [jsonLaws,showReadLaws]
--   ToJSON/FromJSON: Encoding Equals Value +++ OK, passed 100 tests.
--   ToJSON/FromJSON: Partial Isomorphism +++ OK, passed 100 tests.
--   Show/Read: Partial Isomorphism +++ OK, passed 100 tests.
--

module Test.QuickCheck.Classes -- | A convenience function for working testing properties in GHCi. See the -- test suite of this library for an example of how to integrate multiple -- properties into larger test suite. lawsCheck :: Laws -> IO () -- | A convenience function for checking multiple typeclass instances of -- multiple types. lawsCheckMany :: [(String, [Laws])] -> IO () -- | Tests everything from monoidProps plus the following: -- --

Commutative mappend a b ≡ mappend b a

commutativeMonoidLaws :: (Monoid a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws -- | Tests the following properties: -- --

Transitive a == b ∧ b == c ⇒ a == c
Symmetric a == b ⇒ b == a
Reflexive a == a

-- -- Some of these properties involve implication. In the case that the -- left hand side of the implication arrow does not hold, we do not -- retry. Consequently, these properties only end up being useful when -- the data type has a small number of inhabitants. eqLaws :: (Eq a, Arbitrary a, Show a) => Proxy a -> Laws -- | Tests the following properties: -- --

Antisymmetry @a ≤ b ∧ b ≤ a ⇒ a = b
Transitivity a ≤ b ∧ b ≤ c ⇒ a ≤ c
Totality a ≤ b ∨ a > b

ordLaws :: (Ord a, Arbitrary a, Show a) => Proxy a -> Laws showReadLaws :: (Show a, Read a, Eq a, Arbitrary a) => Proxy a -> Laws -- | Tests the following properties: -- --

Partial Isomorphism decode . encode ≡ -- Just
Encoding Equals Value decode . encode ≡ Just . -- toJSON

-- -- Note that in the second propertiy, the type of decode is -- ByteString -> Value, not ByteString -> a jsonLaws :: (ToJSON a, FromJSON a, Show a, Arbitrary a, Eq a) => Proxy a -> Laws -- | Tests the following properties: -- --

Quotient Remainder (quot x y) * y + (rem x y) ≡ -- x
Division Modulus (div x y) * y + (mod x y) ≡ -- x
Integer Roundtrip fromInteger (toInteger x) ≡ -- x

integralLaws :: (Integral a, Arbitrary a, Show a) => Proxy a -> Laws -- | Tests the following properties: -- --

Partial Isomorphism decode . encode ≡ -- Just
Encoding Equals Value decode . encode ≡ Just . -- toJSON

Associative mappend a (mappend b c) ≡ mappend -- (mappend a b) c
Left Identity mappend mempty a ≡ a
Right Identity mappend a mempty ≡ a

monoidLaws :: (Monoid a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws -- | Tests the following properties: -- --

Antisymmetry @a ≤ b ∧ b ≤ a ⇒ a = b
Transitivity a ≤ b ∧ b ≤ c ⇒ a ≤ c
Totality a ≤ b ∨ a > b

ordLaws :: (Ord a, Arbitrary a, Show a) => Proxy a -> Laws -- | Test that a Prim instance obey the several laws. primLaws :: (Prim a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws -- | Tests the following properties: -- --

Associative a <> (b <> c) ≡ (a -- <> b) <> c

semigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws showReadLaws :: (Show a, Read a, Eq a, Arbitrary a) => Proxy a -> Laws storableLaws :: (Storable a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws -- | Tests the following properties: -- --

Quotient Remainder (quot x y) * y + (rem x y) ≡ -- x
Division Modulus (div x y) * y + (mod x y) ≡ -- x
Integer Roundtrip fromInteger (toInteger x) ≡ -- x

integralLaws :: (Integral a, Arbitrary a, Show a) => Proxy a -> Laws -- | Tests the following properties: -- --

Conjunction Idempotence n .&. n ≡ -- n
Disjunction Idempotence n .|. n ≡ n
Double Complement complement (complement n) ≡ -- n
Set Bit setBit n i ≡ n .|. bit i
Clear Bit clearBit n i ≡ n .&. complement -- (bit i)
Complement Bit complementBit n i ≡ xor n (bit -- i)
Clear Zero clearBit zeroBits i ≡ -- zeroBits
Set Zero setBit zeroBits i ≡ bit i
Test Zero testBit zeroBits i ≡ False
Pop Zero popCount zeroBits ≡ 0
Count Leading Zeros of Zero countLeadingZeros -- zeroBits ≡ finiteBitSize ⊥
Count Trailing Zeros of Zero countTrailingZeros -- zeroBits ≡ finiteBitSize ⊥

-- -- All of the useful instances of the Bits typeclass also have -- FiniteBits instances, so these property tests actually require -- that instance as well. -- -- Note: This property test is only available when using -- base-4.7 or newer. bitsLaws :: (FiniteBits a, Arbitrary a, Show a) => Proxy a -> Laws -- | Tests the following properties: -- --

Partial Isomorphism fromList . toList ≡ -- id
Length Preservation fromList xs ≡ fromListN -- (length xs) xs

-- -- Note: This property test is only available when using -- base-4.7 or newer. isListLaws :: (IsList a, Show a, Show (Item a), Arbitrary a, Arbitrary (Item a), Eq a) => Proxy a -> Laws -- | Tests the following alt properties: -- --

Associativity (a <!> b) -- <!> c ≡ a <!> (b <!> -- c)
Left Distributivity @f <$> (a -- <!> b) = (f <$> a) <!> (f -- <$> b)

altLaws :: (Alt f, Eq1 f, Show1 f, Arbitrary1 f) => proxy f -> Laws -- | Tests the following alternative properties: -- --

Identity empty <|> x ≡ -- x x <|> empty ≡ x
Associativity a <|> (b -- <|> c) ≡ (a <|> b) <|> -- c)

alternativeLaws :: (Alternative f, Eq1 f, Show1 f, Arbitrary1 f) => proxy f -> Laws -- | Tests the following applicative properties: -- --

Identity pure id <*> -- v ≡ v
Composition pure (.) <*> u -- <*> v <*> w ≡ u <*> (v -- <*> w)
Homomorphism pure f <*> -- pure x ≡ pure (f x)
Interchange u <*> pure y ≡ -- pure ($ y) <*> u
LiftA2 (1) (<*>) ≡ liftA2 -- id

applicativeLaws :: (Applicative f, Eq1 f, Show1 f, Arbitrary1 f) => proxy f -> Laws -- | Tests the following Foldable properties: -- --

fold fold ≡ foldMap -- id
foldMap foldMap f ≡ foldr -- (mappend . f) mempty
foldr foldr f z t ≡ appEndo -- (foldMap (Endo . f) t ) z
foldr' foldr' f z0 xs = let f' k x z = -- k $! f x z in foldl f' id xs z0
foldl foldl f z t ≡ appEndo -- (getDual (foldMap (Dual . Endo . -- flip f) t)) z
foldl' foldl' f z0 xs = let f' x k z = -- k $! f z x in foldr f' id xs z0
toList toList ≡ foldr (:) -- []
null null ≡ foldr (const -- (const False)) True
length length ≡ getSum . foldMap -- (const (Sum 1))

-- -- Note that this checks to ensure that foldl' and -- foldr' are suitably strict. foldableLaws :: (Foldable f, Eq1 f, Show1 f, Arbitrary1 f) => proxy f -> Laws -- | Tests the following functor properties: -- --

Identity fmap id ≡ -- id
Composition fmap (f . g) ≡ fmap f . -- fmap g
Const (<$) ≡ fmap -- const

functorLaws :: (Functor f, Eq1 f, Show1 f, Arbitrary1 f) => proxy f -> Laws -- | Tests the following monadic properties: -- --

Left Identity return a >>= k -- ≡ k a
Right Identity m >>= return -- ≡ m
Associativity m >>= (\x -> k x -- >>= h) ≡ (m >>= k) >>= -- h
Return pure ≡ return
Ap (<*>) ≡ ap

monadLaws :: (Monad f, Applicative f, Eq1 f, Show1 f, Arbitrary1 f) => proxy f -> Laws -- | Tests the following Bifunctor properties: -- --

Identity bimap id id ≡ -- id
First Identity first id ≡ -- id
Second Identity second id ≡ -- id
Bifunctor Composition bimap f g ≡ -- first f . second g

-- -- Note: This property test is only available when this package is -- built with base-4.9+ or transformers-0.5+. bifunctorLaws :: (Bifunctor f, Eq2 f, Show2 f, Arbitrary2 f) => proxy f -> Laws -- | A set of laws associated with a typeclass. data Laws Laws :: String -> [(String, Property)] -> Laws -- | Name of the typeclass whose laws are tested [lawsTypeclass] :: Laws -> String -- | Pairs of law name and property [lawsProperties] :: Laws -> [(String, Property)] instance GHC.Classes.Eq Test.QuickCheck.Classes.EquationTwo instance GHC.Classes.Eq Test.QuickCheck.Classes.Equation instance GHC.Classes.Eq Test.QuickCheck.Classes.LinearEquation instance GHC.Classes.Eq a => GHC.Classes.Eq (Test.QuickCheck.Classes.Bottom a) instance GHC.Classes.Eq Test.QuickCheck.Classes.LastNothing instance GHC.Classes.Eq Test.QuickCheck.Classes.ChooseFirst instance GHC.Classes.Eq Test.QuickCheck.Classes.ChooseSecond instance (GHC.Classes.Eq a, Data.Primitive.Types.Prim a) => GHC.Classes.Eq (Test.QuickCheck.Classes.PrimArray a) instance Data.Primitive.Types.Prim a => GHC.Exts.IsList (Test.QuickCheck.Classes.PrimArray a) instance Data.Bits.FiniteBits a => Test.QuickCheck.Arbitrary.Arbitrary (Test.QuickCheck.Classes.BitIndex a) instance GHC.Show.Show Test.QuickCheck.Classes.EquationTwo instance Test.QuickCheck.Arbitrary.Arbitrary Test.QuickCheck.Classes.EquationTwo instance GHC.Show.Show Test.QuickCheck.Classes.Equation instance Test.QuickCheck.Arbitrary.Arbitrary Test.QuickCheck.Classes.Equation instance Data.Functor.Classes.Eq1 m => GHC.Classes.Eq (Test.QuickCheck.Classes.LinearEquationM m) instance Data.Functor.Classes.Show1 m => GHC.Show.Show (Test.QuickCheck.Classes.LinearEquationM m) instance Test.QuickCheck.Arbitrary.Arbitrary1 m => Test.QuickCheck.Arbitrary.Arbitrary (Test.QuickCheck.Classes.LinearEquationM m) instance GHC.Show.Show Test.QuickCheck.Classes.LinearEquation instance Test.QuickCheck.Arbitrary.Arbitrary Test.QuickCheck.Classes.LinearEquation instance (Data.Functor.Classes.Eq2 f, GHC.Classes.Eq a, GHC.Classes.Eq b) => GHC.Classes.Eq (Test.QuickCheck.Classes.Apply2 f a b) instance (Data.Functor.Classes.Show2 f, GHC.Show.Show a, GHC.Show.Show b) => GHC.Show.Show (Test.QuickCheck.Classes.Apply2 f a b) instance (Test.QuickCheck.Arbitrary.Arbitrary2 f, Test.QuickCheck.Arbitrary.Arbitrary a, Test.QuickCheck.Arbitrary.Arbitrary b) => Test.QuickCheck.Arbitrary.Arbitrary (Test.QuickCheck.Classes.Apply2 f a b) instance (Data.Functor.Classes.Eq1 f, GHC.Classes.Eq a) => GHC.Classes.Eq (Test.QuickCheck.Classes.Apply f a) instance (GHC.Base.Applicative f, GHC.Base.Monoid a) => Data.Semigroup.Semigroup (Test.QuickCheck.Classes.Apply f a) instance (GHC.Base.Applicative f, GHC.Base.Monoid a) => GHC.Base.Monoid (Test.QuickCheck.Classes.Apply f a) instance (Data.Functor.Classes.Show1 f, GHC.Show.Show a) => GHC.Show.Show (Test.QuickCheck.Classes.Apply f a) instance (Test.QuickCheck.Arbitrary.Arbitrary1 f, Test.QuickCheck.Arbitrary.Arbitrary a) => Test.QuickCheck.Arbitrary.Arbitrary (Test.QuickCheck.Classes.Apply f a) instance GHC.Show.Show a => GHC.Show.Show (Test.QuickCheck.Classes.Bottom a) instance Test.QuickCheck.Arbitrary.Arbitrary a => Test.QuickCheck.Arbitrary.Arbitrary (Test.QuickCheck.Classes.Bottom a) instance GHC.Show.Show Test.QuickCheck.Classes.LastNothing instance Test.QuickCheck.Arbitrary.Arbitrary Test.QuickCheck.Classes.LastNothing instance GHC.Show.Show Test.QuickCheck.Classes.ChooseFirst instance Test.QuickCheck.Arbitrary.Arbitrary Test.QuickCheck.Classes.ChooseFirst instance GHC.Show.Show Test.QuickCheck.Classes.ChooseSecond instance Test.QuickCheck.Arbitrary.Arbitrary Test.QuickCheck.Classes.ChooseSecond instance (GHC.Base.Applicative f, Data.Semigroup.Semigroup a) => Data.Semigroup.Semigroup (Test.QuickCheck.Classes.Ap f a) instance (GHC.Base.Applicative f, GHC.Base.Monoid a, Data.Semigroup.Semigroup a) => GHC.Base.Monoid (Test.QuickCheck.Classes.Ap f a) instance Data.Semigroup.Semigroup Test.QuickCheck.Classes.Status instance GHC.Base.Monoid Test.QuickCheck.Classes.Status