Test.QuickCheck.Classes

This library provides sets of properties that should hold for common typeclasses.

Note: on GHC < 8.5, this library uses the higher-kinded typeclasses (Show1, Eq1, Ord1, etc.), but on GHC >= 8.5, it uses `-XQuantifiedConstraints` to express these constraints more cleanly.

Running

lawsCheck :: Laws -> IO ()

A convenience function for testing properties in GHCi. 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.

lawsCheckMany

Arguments

:: [(String, [Laws])]

Element is type name paired with typeclass laws

-> IO ()

A convenience function for checking multiple typeclass instances of multiple types. Consider the following Haskell source file:

import Data.Proxy (Proxy(..))
import Data.Map (Map)
import Data.Set (Set)

-- A Proxy for Set Int. 
setInt :: Proxy (Set Int)
setInt = Proxy

-- A Proxy for Map Int Int.
mapInt :: Proxy (Map Int Int)
mapInt = Proxy

myLaws :: Proxy a -> [Laws]
myLaws p = [eqLaws p, monoidLaws p]

namedTests :: [(String, [Laws])]
namedTests =
  [ ("Set Int", myLaws setInt)
  , ("Map Int Int", myLaws mapInt)
  ]

Now, in GHCi:

>>> lawsCheckMany namedTests

Testing properties for common typeclasses
-------------
-- Set Int --
-------------

Eq: Transitive +++ OK, passed 100 tests.
Eq: Symmetric +++ OK, passed 100 tests.
Eq: Reflexive +++ OK, passed 100 tests.
Monoid: Associative +++ OK, passed 100 tests.
Monoid: Left Identity +++ OK, passed 100 tests.
Monoid: Right Identity +++ OK, passed 100 tests.
Monoid: Concatenation +++ OK, passed 100 tests.

-----------------
-- Map Int Int --
-----------------

Eq: Transitive +++ OK, passed 100 tests.
Eq: Symmetric +++ OK, passed 100 tests.
Eq: Reflexive +++ OK, passed 100 tests.
Monoid: Associative +++ OK, passed 100 tests.
Monoid: Left Identity +++ OK, passed 100 tests.
Monoid: Right Identity +++ OK, passed 100 tests.
Monoid: Concatenation +++ OK, passed 100 tests.

In the case of a failing test, the program terminates with exit code 1.

lawsCheckOne :: Proxy a -> [Proxy a -> Laws] -> IO ()

A convenience function that allows one to check many typeclass instances of the same type.

>>> specialisedLawsCheckMany (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.

Properties

Ground types

bitsLaws :: (FiniteBits 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.

eqLaws :: (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.

integralLaws :: (Integral 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

isListLaws :: (IsList a, Show a, Show (Item a), Arbitrary a, Arbitrary (Item a), Eq 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.

jsonLaws :: (ToJSON a, FromJSON a, Show a, Arbitrary a, Eq 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 property, the type of decode is ByteString -> Value, not ByteString -> a

monoidLaws :: (Monoid a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Associative

mappend a (mappend b c) ≡ mappend (mappend a b) c

Left Identity

mappend mempty a ≡ a

Right Identity

mappend a mempty ≡ a

Concatenation

mconcat as ≡ foldr mappend mempty as

commutativeMonoidLaws :: (Monoid a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Commutative

mappend a b ≡ mappend b a

Note that this does not test associativity or identity. Make sure to use monoidLaws in addition to this set of laws.

ordLaws :: (Ord 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

enumLaws :: (Enum a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Succ Pred Identity

succ (pred x) ≡ x

Pred Succ Identity

pred (succ x) ≡ x

This only works for Enum types that are not bounded, meaning that succ and pred must be total. This means that these property tests work correctly for types like Integer but not for Int.

Sadly, there is not a good way to test fromEnum and toEnum, since many types that have reasonable implementations for succ and pred have more inhabitants than Int does.

boundedEnumLaws :: (Enum a, Bounded a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the same properties as enumLaws except that it requires the type to have a Bounded instance. These tests avoid taking the successor of the maximum element or the predecessor of the minimal element.

primLaws :: (Prim a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Test that a Prim instance obey the several laws.

semigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Associative

a <> (b <> c) ≡ (a <> b) <> c

Concatenation

sconcat as ≡ foldr1 (<>) as

Times

stimes n a ≡ foldr1 (<>) (replicate n a)

commutativeSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Commutative

a <> b ≡ b <> a

Note that this does not test associativity. Make sure to use semigroupLaws in addition to this set of laws.

exponentialSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Exponential

stimes n (a <> b) ≡ stimes n a <> stimes n b

Note that this does not test associativity. Make sure to use semigroupLaws in addition to this set of laws.

idempotentSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Idempotent

a <> a ≡ a

Note that this does not test associativity. Make sure to use semigroupLaws in addition to this set of laws. In literature, this class of semigroup is known as a band.

rectangularBandSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Rectangular Band

a <> b <> a ≡ a

Note that this does not test associativity. Make sure to use semigroupLaws in addition to this set of laws.

semiringLaws :: (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following properties:

Additive Commutativity

a + b ≡ b + a

Additive Left Identity

0 + a ≡ a

Additive Right Identity

a + 0 ≡ a

Multiplicative Associativity

a * (b * c) ≡ (a * b) * c

Multiplicative Left Identity

1 * a ≡ a

Multiplicative Right Identity

a * 1 ≡ a

Multiplication Left Distributes Over Addition

a * (b + c) ≡ (a * b) + (a * c)

Multiplication Right Distributes Over Addition

(a + b) * c ≡ (a * c) + (b * c)

Multiplicative Left Annihilation

0 * a ≡ 0

Multiplicative Right Annihilation

a * 0 ≡ 0

showLaws :: (Show a, Arbitrary a) => Proxy a -> Laws

Tests the following properties:

Show

show a ≡ showsPrec 0 a ""

Equivariance: showsPrec

showsPrec p a r ++ s ≡ showsPrec p a (r ++ s)

Equivariance: showList

showList as r ++ s ≡ showList as (r ++ s)

showReadLaws :: (Show a, Read a, Eq a, Arbitrary a) => Proxy a -> Laws

Tests the following properties:

Partial Isomorphism: show / read

readMaybe (show a) ≡ Just a

Partial Isomorphism: show / read with initial space

readMaybe (" " ++ show a) ≡ Just a

Partial Isomorphism: showsPrec / readsPrec

(a,"") `elem` readsPrec p (showsPrec p a "")

Partial Isomorphism: showList / readList

(as,"") `elem` readList (showList as "")

Partial Isomorphism: showListWith shows / readListDefault

(as,"") `elem` readListDefault (showListWith shows as "")

Note: When using base-4.5 or older, a shim implementation of readMaybe is used.

storableLaws :: (Storable a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws

Tests the following alternative properties:

Set-Get

(pokeElemOff ptr ix a >> peekElemOff ptr ix') ≡ pure a

Get-Set

(peekElemOff ptr ix >> pokeElemOff ptr ix a) ≡ pure a

Unary type constructors

alternativeLaws :: (Alternative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests the following alternative properties:

Left Identity

empty <|> x ≡ x

Right Identity

x <|> empty ≡ x

Associativity

a <|> (b <|> c) ≡ (a <|> b) <|> c)

altLaws :: forall proxy f. (Alt f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests the following alt properties:

Associativity

(a <!> b) <!> c ≡ a <!> (b <!> c)

Left Distributivity

f <$> (a <!> b) ≡ (f <$> a) <!> (f <$> b)

applyLaws :: (Apply f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests the following alt properties:

LiftF2 (1)

(<.>) ≡ liftF2 id

applicativeLaws :: (Applicative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => 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

foldableLaws :: forall proxy f. (Foldable f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => 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

foldr1

foldr1 f t ≡ let Just (xs,x) = unsnoc (toList t) in foldr f x xs

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

foldl1

foldl1 f t ≡ let x : xs = toList t in foldl f x xs

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.

functorLaws :: (Functor f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests the following functor properties:

Identity

fmap id ≡ id

Composition

fmap (f . g) ≡ fmap f . fmap g

Const

(<$) ≡ fmap const

monadLaws :: (Monad f, Applicative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => 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

monadPlusLaws :: (MonadPlus f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests the following monad plus properties:

Left Identity

mplus empty x ≡ x

Right Identity

mplus x empty ≡ x

Associativity

mplus a (mplus b c) ≡ mplus (mplus a b) c)

Left Zero

mzero >>= f ≡ mzero

Right Zero

m >> mzero ≡ mzero

monadZipLaws :: (MonadZip f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests the following monadic zipping properties:

Naturality

liftM (f *** g) (mzip ma mb) = mzip (liftM f ma) (liftM g mb)

In the laws above, the infix function *** refers to a typeclass method of Arrow.

plusLaws :: forall proxy f. (Plus f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests the following alt properties:

Left Identity

zero <!> m ≡ m

Right Identity

m <!> zero ≡ m

extendedPlusLaws :: forall proxy f. (Plus f, Alternative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests everything from altLaws, plus the following:

Congruency

zero ≡ empty

traversableLaws :: (Traversable f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a)) => proxy f -> Laws

Tests the following Traversable properties:

Naturality

t . traverse f ≡ traverse (t . f) for every applicative transformation t

Identity

traverse Identity ≡ Identity

Composition

traverse (Compose . fmap g . f) ≡ Compose . fmap (traverse g) . traverse f

Sequence Naturality

t . sequenceA ≡ sequenceA . fmap t for every applicative transformation t

Sequence Identity

sequenceA . fmap Identity ≡ Identity

Sequence Composition

sequenceA . fmap Compose ≡ Compose . fmap sequenceA . sequenceA

foldMap

foldMap ≡ foldMapDefault

fmap

fmap ≡ fmapDefault

Where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

• Identity: t (pure x) ≡ pure x
• Distributivity: t (x <*> y) ≡ t x <*> t y

Binary type constructors

bifunctorLaws :: forall proxy f. (Bifunctor f, forall a b. (Eq a, Eq b) => Eq (f a b), forall a b. (Show a, Show b) => Show (f a b), forall a b. (Arbitrary a, Arbitrary b) => Arbitrary (f a b)) => 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+.

categoryLaws :: forall proxy c. (Category c, forall a b. (Eq a, Eq b) => Eq (c a b), forall a b. (Show a, Show b) => Show (c a b), forall a b. (Arbitrary a, Arbitrary b) => Arbitrary (c a b)) => proxy c -> Laws

Tests the following Category properties:

Right Identity

f . id ≡ f

Left Identity

id . f ≡ f

Associativity

f . (g . h) ≡ (f . g) . h

Note: This property test is only available when this package is built with base-4.9+ or transformers-0.5+.

commutativeCategoryLaws :: forall proxy c. (Category c, forall a b. (Eq a, Eq b) => Eq (c a b), forall a b. (Show a, Show b) => Show (c a b), forall a b. (Arbitrary a, Arbitrary b) => Arbitrary (c a b)) => proxy c -> Laws

Test everything from categoryLaws plus the following:

Commutative

f . g ≡ g . f

Note: This property test is only available when this package is built with base-4.9+ or transformers-0.5+.

semigroupoidLaws :: forall proxy s. (Semigroupoid s, forall a b. (Eq a, Eq b) => Eq (s a b), forall a b. (Show a, Show b) => Show (s a b), forall a b. (Arbitrary a, Arbitrary b) => Arbitrary (s a b)) => proxy s -> Laws

Tests the following Semigroupoid properties:

Associativity

f `o' (g `o' h) ≡ (f `o' g) `o' h

Note: This property test is only available when this package is built with base-4.9+ or transformers-0.5+.

commutativeSemigroupoidLaws :: forall proxy s. (Semigroupoid s, forall a b. (Eq a, Eq b) => Eq (s a b), forall a b. (Show a, Show b) => Show (s a b), forall a b. (Arbitrary a, Arbitrary b) => Arbitrary (s a b)) => proxy s -> Laws

Tests everything from semigroupoidLaws plus the following:

Commutative

f `o' g ≡ g `o' f

Note: This property test is only available when this package is built with base-4.9+ or transformers-0.5+.

Types

data Laws

A set of laws associated with a typeclass.

Constructors

Laws

Fields

• lawsTypeclass :: String

  Name of the typeclass whose laws are tested

• lawsProperties :: [(String, Property)]

  Pairs of law name and property

data Proxy1 (f :: * -> *)

In older versions of GHC, Proxy is not poly-kinded, so we provide Proxy1.

Constructors

Proxy1

data Proxy2 (f :: * -> * -> *)

In older versions of GHC, Proxy is not poly-kinded, so we provide Proxy2.

Constructors

Proxy2