Safe Haskell  None 

Language  Haskell2010 
Synopsis
 lawsCheck :: Laws > IO ()
 lawsCheckMany :: [(String, [Laws])] > IO ()
 lawsCheckOne :: Proxy a > [Proxy a > Laws] > IO ()
 bitsLaws :: (FiniteBits a, Arbitrary a, Show a) => Proxy a > Laws
 eqLaws :: (Eq a, Arbitrary a, Show a) => Proxy a > Laws
 substitutiveEqLaws :: (Eq a, Arbitrary a, CoArbitrary a, Function a, Show a) => Proxy a > Laws
 numLaws :: (Num a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 integralLaws :: (Integral a, Arbitrary a, Show a) => Proxy a > Laws
 ixLaws :: (Ix a, Arbitrary a, Show a) => Proxy a > Laws
 isListLaws :: (IsList a, Show a, Show (Item a), Arbitrary a, Arbitrary (Item a), Eq a) => Proxy a > Laws
 jsonLaws :: (ToJSON a, FromJSON a, Show a, Arbitrary a, Eq a) => Proxy a > Laws
 monoidLaws :: (Monoid a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 commutativeMonoidLaws :: (Monoid a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 semigroupMonoidLaws :: (Semigroup a, Monoid a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 ordLaws :: (Ord a, Arbitrary a, Show a) => Proxy a > Laws
 enumLaws :: (Enum a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 boundedEnumLaws :: (Enum a, Bounded a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 primLaws :: (Prim a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 semigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 commutativeSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 exponentialSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 idempotentSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 rectangularBandSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 semiringLaws :: (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 ringLaws :: (Ring a, Eq a, Arbitrary a, Show a) => Proxy a > Laws
 gcdDomainLaws :: (Eq a, GcdDomain a, Arbitrary a, Show a) => Proxy a > Laws
 euclideanLaws :: (Eq a, Euclidean a, Arbitrary a, Show a) => Proxy a > Laws
 showLaws :: (Show a, Arbitrary 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
 genericLaws :: (Generic a, Eq a, Arbitrary a, Show a, Show (Rep a ()), Arbitrary (Rep a ()), Eq (Rep a ())) => Proxy a > Laws
 generic1Laws :: forall (f :: Type > Type) proxy. (Generic1 f, Eq1 f, Arbitrary1 f, Show1 f, Eq1 (Rep1 f), Show1 (Rep1 f), Arbitrary1 (Rep1 f)) => proxy f > Laws
 alternativeLaws :: forall (f :: Type > Type) proxy. (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
 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
 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
 applicativeLaws :: forall (f :: Type > Type) proxy. (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
 contravariantLaws :: forall (f :: Type > Type) proxy. (Contravariant 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
 foldableLaws :: forall proxy (f :: Type > Type). (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
 functorLaws :: forall (f :: Type > Type) proxy. (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
 monadLaws :: forall (f :: Type > Type) proxy. (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
 monadPlusLaws :: forall (f :: Type > Type) proxy. (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
 monadZipLaws :: forall (f :: Type > Type) proxy. (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
 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
 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
 traversableLaws :: forall (f :: Type > Type) proxy. (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
 bifoldableLaws :: forall proxy (f :: Type > Type > Type). (Bifoldable 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
 bifunctorLaws :: forall proxy (f :: Type > Type > Type). (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
 bitraversableLaws :: forall proxy (f :: Type > Type > Type). (Bitraversable 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
 categoryLaws :: forall proxy (c :: Type > Type > Type). (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
 commutativeCategoryLaws :: forall proxy (c :: Type > Type > Type). (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
 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
 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
 muvectorLaws :: (Eq a, Unbox a, Arbitrary a, Show a) => Proxy a > Laws
 data Laws = Laws {
 lawsTypeclass :: String
 lawsProperties :: [(String, Property)]
 data Proxy1 (f :: Type > Type) = Proxy1
 data Proxy2 (f :: Type > Type > Type) = Proxy2
Running
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.
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)  AProxy
forSet
Int
. setInt :: Proxy (Set Int) setInt = Proxy  AProxy
forMap
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
 Right Rotation
no sign extension → (rotateR n i ≡ (shiftR n i) .. (shiftL n (finiteBitSize ⊥  i)))
 Left Rotation
no sign extension → (rotateL n i ≡ (shiftL n i) .. (shiftR n (finiteBitSize ⊥  i)))
 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 base4.7
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 Negation
x
/=
y==
not
(x==
y)
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.
substitutiveEqLaws :: (Eq a, Arbitrary a, CoArbitrary a, Function a, Show a) => Proxy a > Laws #
numLaws :: (Num 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
 Additive Inverse
negate
a+
a ≡ 0 Subtraction
a
+
negate
b ≡ a
b Abs Is Idempotent
 @
abs
(abs
a) ≡abs
a  Signum Is Idempotent
 @
signum
(signum
a) ≡signum
a  Product Of Abs And Signum Is Id
abs
a *signum
a ≡ a
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
 QuotRem is (Quot, Rem)
quotRem x y ≡ (quot x y, rem x y)
 DivMod is (Div, Mod)
divMod x y ≡ (div x y, mod x y)
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 base4.7
or newer.
jsonLaws :: (ToJSON a, FromJSON a, Show a, Arbitrary a, Eq a) => Proxy a > Laws Source #
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:
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.
primLaws :: (Prim a, Eq a, Arbitrary a, Show a) => Proxy a > Laws Source #
Test that a Prim
instance obey the several laws.
commutativeSemigroupLaws :: (Semigroup a, Eq a, Arbitrary a, Show a) => Proxy a > Laws #
Tests the following properties:
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:
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 Source #
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
Also tests that fromNatural
is a homomorphism of semirings:
 FromNatural Maps Zero
fromNatural
0 =zero
 FromNatural Maps One
fromNatural
1 =one
 FromNatural Maps Plus
fromNatural
(a
+b
) =fromNatural
a
+fromNatural
b
 FromNatural Maps Times
fromNatural
(a
*b
) =fromNatural
a
*fromNatural
b
ringLaws :: (Ring a, Eq a, Arbitrary a, Show a) => Proxy a > Laws Source #
Tests the following properties:
Note that this does not test any of the laws tested by semiringLaws
.
gcdDomainLaws :: (Eq a, GcdDomain a, Arbitrary a, Show a) => Proxy a > Laws Source #
Test that a GcdDomain
instance obey several laws.
Check that divide
is an inverse of times:
y /= 0 => (x * y) `divide` y == Just x
,y /= 0, x `divide` y == Just z => x == z * y
.
Check that gcd
is a common divisor and is a multiple of any common divisor:
x /= 0, y /= 0 => isJust (x `divide` gcd x y) && isJust (y `divide` gcd x y)
,z /= 0 => isJust (gcd (x * z) (y * z) `divide` z)
.
Check that lcm
is a common multiple and is a factor of any common multiple:
x /= 0, y /= 0 => isJust (lcm x y `divide` x) && isJust (lcm x y `divide` y)
,x /= 0, y /= 0, isJust (z `divide` x), isJust (z `divide` y) => isJust (z `divide` lcm x y)
.
Check that gcd
of coprime
numbers is a unit of the semiring (has an inverse):
y /= 0, coprime x y => isJust (1 `divide` gcd x y)
.
euclideanLaws :: (Eq a, Euclidean a, Arbitrary a, Show a) => Proxy a > Laws Source #
Test that a Euclidean
instance obey laws of a Euclidean domain.
y /= 0, r == x `rem` y => r == 0  degree r < degree y
,y /= 0, (q, r) == x `quotRem` y => x == q * y + r
,y /= 0 => x `quot` x y == fst (x `quotRem` y)
,y /= 0 => x `rem` x y == snd (x `quotRem` y)
.
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 base4.5
or older, a shim implementation
of readMaybe
is used.
storableLaws :: (Storable a, Eq a, Arbitrary a, Show a) => Proxy a > Laws #
Tests the following Storable
properties:
 SetGet
(
pokeElemOff
ptr ix a >>peekElemOff
ptr ix') ≡pure
a GetSet
(
peekElemOff
ptr ix >>pokeElemOff
ptr ix a) ≡pure
a
genericLaws :: (Generic a, Eq a, Arbitrary a, Show a, Show (Rep a ()), Arbitrary (Rep a ()), Eq (Rep a ())) => Proxy a > Laws #
Tests the following properties:
Note: This property test is only available when
using base4.5
or newer.
Note: from
and to
don't actually care about
the type variable x
in
, so here we instantiate
it to Rep
a x
by default. If you would like to instantiate ()
x
as something else, please file a bug report.
generic1Laws :: forall (f :: Type > Type) proxy. (Generic1 f, Eq1 f, Arbitrary1 f, Show1 f, Eq1 (Rep1 f), Show1 (Rep1 f), Arbitrary1 (Rep1 f)) => proxy f > Laws #
Unary type constructors
alternativeLaws :: forall (f :: Type > Type) proxy. (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 #
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 Source #
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 Source #
applicativeLaws :: forall (f :: Type > Type) proxy. (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 #
contravariantLaws :: forall (f :: Type > Type) proxy. (Contravariant 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 #
foldableLaws :: forall proxy (f :: Type > Type). (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$!
f x z infoldl
f'id
xs z0 foldr1
foldr1
f t ≡ letJust
(xs,x) =unsnoc
(toList
t) infoldr
f x xs foldl
foldl
f z t ≡appEndo
(getDual
(foldMap
(Dual
.Endo
.flip
f) t)) z foldl'
foldl'
f z0 xs ≡ let f' x k z = k$!
f z x infoldr
f'id
xs z0 foldl1
foldl1
f t ≡ let x : xs =toList
t infoldl
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 :: forall (f :: Type > Type) proxy. (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 #
monadLaws :: forall (f :: Type > Type) proxy. (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 #
monadPlusLaws :: forall (f :: Type > Type) proxy. (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 #
monadZipLaws :: forall (f :: Type > Type) proxy. (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 #
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 Source #
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 Source #
traversableLaws :: forall (f :: Type > Type) proxy. (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
for every applicative transformation.
traverse
f ≡traverse
(t.
f)t
 Identity
traverse
Identity
≡Identity
 Composition
traverse
(Compose
.
fmap
g.
f) ≡Compose
.
fmap
(traverse
g).
traverse
f Sequence Naturality
t
for every applicative transformation.
sequenceA
≡sequenceA
.
fmap
tt
 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.
Binary type constructors
bifoldableLaws :: forall proxy (f :: Type > Type > Type). (Bifoldable 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:
 Bifold Identity
bifold
≡bifoldMap
id
id
 BifoldMap Identity
bifoldMap
f g ≡bifoldr
(mappend
.
f) (mappend
.
g)mempty
 Bifoldr Identity
bifoldr
f g z t ≡appEndo
(bifoldMap
(Endo
.
f) (Endo
.
g) t) z
Note: This property test is only available when this package is built with
base4.10+
or transformers0.5+
.
bifunctorLaws :: forall proxy (f :: Type > Type > Type). (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 #
bitraversableLaws :: forall proxy (f :: Type > Type > Type). (Bitraversable 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 Bitraversable
properties:
 Naturality
for every applicative transformationbitraverse
(t.
f) (t.
g) ≡ t.
bitraverse
f gt
 Identity
bitraverse
Identity
Identity
≡Identity
 Composition
Compose
.
fmap
(bitraverse
g1 g2).
bitraverse
f1 f2 ≡bitraverse
(Compose
.
fmap
g1 g2.
f1) (Compose
.
fmap
g2.
f2)
Note: This property test is only available when this package is built with
base4.9+
or transformers0.5+
.
categoryLaws :: forall proxy (c :: Type > Type > Type). (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 #
commutativeCategoryLaws :: forall proxy (c :: Type > Type > Type). (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:
Note: This property test is only available when this package is built with
base4.9+
or transformers0.5+
.
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 Source #
Tests the following Semigroupoid
properties:
Note: This property test is only available when this package is built with
base4.9+
or transformers0.5+
.
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 Source #
Tests everything from semigroupoidLaws
plus the following:
Note: This property test is only available when this package is built with
base4.9+
or transformers0.5+
.
muvectorLaws :: (Eq a, Unbox a, Arbitrary a, Show a) => Proxy a > Laws Source #
Test that a MVector
instance obey several laws.
Types
A set of laws associated with a typeclass.
Note: Most of the toplevel functions provided
by this library have the shape
`forall a. (Ctx a) => Proxy a > Laws`. You can just
as easily provide your own Laws
in libraries/test suites
using regular QuickCheck machinery.
Laws  
