QuickSpec

The main QuickSpec module. Everything you need to run QuickSpec lives here.

To run QuickSpec, you need to tell it which functions to test. We call the list of functions the signature. Here is an example signature, which tells QuickSpec to test the ++, reverse and [] functions:

sig = [
  con "++"      ((++) :: [A] -> [A] -> [A]),
  con "reverse" (reverse :: [A] -> [A]),
  con "[]"      ([] :: [A]) ]

The con function, used above, adds a function to the signature, given its name and its value. When declaring polymorphic functions in the signature, we use the types A to E to represent type variables. Having defined this signature, we can say quickSpec sig to test it and see the discovered equations.

If you want to test functions over your own datatypes, those types need to implement Arbitrary and Ord (if the Ord instance is a problem, see Observe). You must also declare those instances to QuickSpec, by including them in the signature. For monomorphic types you can do this using monoType:

data T = ...
main = quickSpec [
  ...,
  `monoType` (Proxy :: Proxy T)]

You can only declare monomorphic types with monoType. If you want to test your own polymorphic types, you must explicitly declare Arbitrary and Ord instances using the inst function.

You can also use QuickSpec to find conditional equations. To do so, you need to include some predicates in the signature. These are functions returning Bool which can appear as conditions in other equations. Declaring a predicate works just like declaring a function, except that you declare it using predicate instead of con.

You can also put certain options in the signature. The most useful is withMaxTermSize, which you can use to tell QuickSpec to generate larger equations.

The examples directory contains many examples. Here are some interesting ones:

• Arith.hs: a simple arithmetic example. Demonstrates basic use of QuickSpec.
• Lists.hs: list functions. Demonstrates testing polymorphic functions.
• Sorted.hs: sorting. Demonstrates finding conditional equations.
• IntSet.hs: a few functions from Data.IntSet. Demonstrates testing user-defined datatypes and finding conditional equations.
• PrettyPrinting.hs: pretty printing combinators. Demonstrates testing user-defined datatypes and using observational equality.
• Parsing.hs: parser combinators. Demonstrates testing polymorphic datatypes and using observational equality.

You can also find some larger case studies in our paper, <http://www.cse.chalmers.se/~nicsma/papers/quickspec2.pdf Quick specifications for the busy programmer>.

Running QuickSpec

quickSpec :: Signature sig => sig -> IO ()

Run QuickSpec. See the documentation at the top of this file.

data Sig

A signature.

Instances

Monoid Sig

Methods

mempty :: Sig

mappend :: Sig -> Sig -> Sig

mconcat :: [Sig] -> Sig

Signature Sig

Methods

toSig :: Sig -> Sig

class Signature sig where

A class of things that can be used as a QuickSpec signature.

Minimal complete definition

toSig

Methods

toSig :: sig -> Sig

Convert the thing to a signature.

Instances

Signature Sig

Methods

toSig :: Sig -> Sig

Signature sig => Signature [sig]

Methods

toSig :: [sig] -> Sig

Declaring functions and predicates

con :: Typeable a => String -> a -> Sig

Declare a constant with a given name and value. If the constant you want to use is polymorphic, you can use the types A, B, C, D, E to monomorphise it, for example:

constant "reverse" (reverse :: [A] -> [A])

QuickSpec will then understand that the constant is really polymorphic.

predicate :: (Predicateable a, Typeable a, Typeable (TestCase a)) => String -> a -> Sig

Declare a predicate with a given name and value. The predicate should be a function which returns Bool. It will appear in equations just like any other constant, but will also be allowed to appear as a condition.

For example:

sig = [
  con "delete" (delete :: Int -> [Int] -> [Int]),
  con "insert" (insert :: Int -> [Int] -> [Int]),
  predicate "member" (member :: Int -> [Int] -> Bool) ]

Type variables for polymorphic functions

data A

data B

data C

data D

data E

Declaring types

monoType :: forall proxy a. (Ord a, Arbitrary a, Typeable a) => proxy a -> Sig

Declare a new monomorphic type. The type must implement Ord and Arbitrary.

vars :: forall proxy a. Typeable a => [String] -> proxy a -> Sig

Customize how variables of a particular type are named.

monoTypeWithVars :: forall proxy a. (Ord a, Arbitrary a, Typeable a) => [String] -> proxy a -> Sig

Declare a new monomorphic type, saying how you want variables of that type to be named.

inst :: (Typeable c1, Typeable c2) => (c1 :- c2) -> Sig

Declare a typeclass instance. QuickSpec needs to have an Ord and Arbitrary instance for each type you want it to test.

For example, if you are testing Map k v, you will need to add the following two declarations to your signature:

inst (Sub Dict :: (Ord A, Ord B) :- Ord (Map A B))
inst (Sub Dict :: (Arbitrary A, Arbitrary B) :- Arbitrary (Map A B))

class (Arbitrary test, Ord outcome) => Observe test outcome a | a -> test outcome where

A typeclass for types which support observational equality, typically used for types that have no Ord instance.

An instance Observe test outcome a declares that values of type a can be tested for equality by random testing. You supply a function observe :: test -> outcome -> a. Then, two values x and y are considered equal, if for many random values of type test, observe test x == observe test y.

For an example of using observational equality, see PrettyPrinting.hs.

You must use inst to add the Observe instance to your signature. Note that monoType requires an Ord instance, so this even applies for monomorphic types. Don't forget to add the Arbitrary instance too in that case.

Methods

observe :: test -> a -> outcome

Make an observation on a value. Should satisfy the following law: if x /= y, then there exists a value of test such that observe test x /= observe test y.

observe :: (test ~ (), outcome ~ a) => test -> a -> outcome

Make an observation on a value. Should satisfy the following law: if x /= y, then there exists a value of test such that observe test x /= observe test y.

Instances

(Arbitrary a, Observe test outcome b) => Observe (a, test) outcome (a -> b)

Methods

observe :: (a, test) -> (a -> b) -> outcome

Exploring functions in series

background :: Signature sig => sig -> Sig

Declare some functions as being background functions. These are functions which are not interesting on their own, but which may appear in interesting laws with non-background functions. Declaring background functions may improve the laws you get out.

Here is an example, which tests ++ and length, giving 0 and + as background functions:

main = quickSpec [
  con "++" ((++) :: [A] -> [A] -> [A]),
  con "length" (length :: [A] -> Int),

  background [
    con "0" (0 :: Int),
    con "+" ((+) :: Int -> Int -> Int) ] ]

series :: Signature sig => [sig] -> Sig

Run QuickCheck on a series of signatures. Tests the functions in the first signature, then adds the functions in the second signature, then adds the functions in the third signature, and so on.

This can be useful when you have a core API you want to test first, and a larger API you want to test later. The laws for the core API will be printed separately from the laws for the larger API.

Here is an example which first tests 0 and + and then adds ++ and length:

main = quickSpec [sig1, sig2]
  where
    sig1 = [
      con "0" (0 :: Int),
      con "+" ((+) :: Int -> Int -> Int) ]
    sig2 = [
      con "++" ((++) :: [A] -> [A] -> [A]),
      con "length" (length :: [A] -> Int) ]

Customising QuickSpec

withMaxTermSize :: Int -> Sig

Set the maximum size of terms to explore (default: 7).

withMaxTests :: Int -> Sig

Set how many times to test each discovered law (default: 1000).

withMaxTestSize :: Int -> Sig

Set the maximum value for QuickCheck's size parameter when generating test data (default: 20).

defaultTo :: Typeable a => proxy a -> Sig

Set which type polymorphic terms are tested at.

withPruningDepth :: Int -> Sig

Set how hard QuickSpec tries to filter out redundant equations (default: no limit).

If you experience long pauses when running QuickSpec, try setting this number to 2 or 3.

withPruningTermSize :: Int -> Sig

Set the maximum term size QuickSpec will reason about when it filters out redundant equations (default: same as maximum term size).

If you get laws you believe are redundant, try increasing this number to 1 or 2 more than the maximum term size.

withFixedSeed :: Int -> Sig

Set the random number seed used for test case generation. Useful if you want repeatable results.

Re-exported functionality

class Typeable k (a :: k)

The class Typeable allows a concrete representation of a type to be calculated.

Minimal complete definition

typeRep#

newtype a :- b :: Constraint -> Constraint -> * infixr 9

This is the type of entailment.

a :- b is read as a "entails" b.

With this we can actually build a category for Constraint resolution.

e.g.

Because Eq a is a superclass of Ord a, we can show that Ord a entails Eq a.

Because instance Ord a => Ord [a] exists, we can show that Ord a entails Ord [a] as well.

This relationship is captured in the :- entailment type here.

Since p :- p and entailment composes, :- forms the arrows of a Category of constraints. However, Category only became sufficiently general to support this instance in GHC 7.8, so prior to 7.8 this instance is unavailable.

But due to the coherence of instance resolution in Haskell, this Category has some very interesting properties. Notably, in the absence of IncoherentInstances, this category is "thin", which is to say that between any two objects (constraints) there is at most one distinguishable arrow.

This means that for instance, even though there are two ways to derive Ord a :- Eq [a], the answers from these two paths _must_ by construction be equal. This is a property that Haskell offers that is pretty much unique in the space of languages with things they call "type classes".

What are the two ways?

Well, we can go from Ord a :- Eq a via the superclass relationship, and then from Eq a :- Eq [a] via the instance, or we can go from Ord a :- Ord [a] via the instance then from Ord [a] :- Eq [a] through the superclass relationship and this diagram by definition must "commute".

Diagrammatically,

                   Ord a
               ins /     \ cls
                  v       v
            Ord [a]     Eq a
               cls \     / ins
                    v   v
                   Eq [a]

This safety net ensures that pretty much anything you can write with this library is sensible and can't break any assumptions on the behalf of library authors.

Constructors

Sub (a -> Dict b)

Instances

Category Constraint (:-)

Possible since GHC 7.8, when Category was made polykinded.

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

() :=> (Eq ((:-) a b))

Methods

ins :: () :- Eq (a :- b)

() :=> (Ord ((:-) a b))

Methods

ins :: () :- Ord (a :- b)

() :=> (Show ((:-) a b))

Methods

ins :: () :- Show (a :- b)

Eq ((:-) a b)

Assumes IncoherentInstances doesn't exist.

Methods

(==) :: (a :- b) -> (a :- b) -> Bool

(/=) :: (a :- b) -> (a :- b) -> Bool

(Typeable Constraint p, Typeable Constraint q, p, q) => Data ((:-) p q)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> (p :- q) -> c (p :- q)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (p :- q)

toConstr :: (p :- q) -> Constr

dataTypeOf :: (p :- q) -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (p :- q))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (p :- q))

gmapT :: (forall b. Data b => b -> b) -> (p :- q) -> p :- q

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (p :- q) -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (p :- q) -> r

gmapQ :: (forall d. Data d => d -> u) -> (p :- q) -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> (p :- q) -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> (p :- q) -> m (p :- q)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (p :- q) -> m (p :- q)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (p :- q) -> m (p :- q)

Ord ((:-) a b)

Assumes IncoherentInstances doesn't exist.

Methods

compare :: (a :- b) -> (a :- b) -> Ordering

(<) :: (a :- b) -> (a :- b) -> Bool

(<=) :: (a :- b) -> (a :- b) -> Bool

(>) :: (a :- b) -> (a :- b) -> Bool

(>=) :: (a :- b) -> (a :- b) -> Bool

max :: (a :- b) -> (a :- b) -> a :- b

min :: (a :- b) -> (a :- b) -> a :- b

Show ((:-) a b)

Methods

showsPrec :: Int -> (a :- b) -> ShowS

show :: (a :- b) -> String

showList :: [a :- b] -> ShowS

a => NFData ((:-) a b)

Methods

rnf :: (a :- b) -> ()

data Dict a :: Constraint -> * where

Values of type Dict p capture a dictionary for a constraint of type p.

e.g.

Dict :: Dict (Eq Int)

captures a dictionary that proves we have an:

instance Eq 'Int

Pattern matching on the Dict constructor will bring this instance into scope.

Constructors

Dict :: Dict a

Instances

a :=> (Read (Dict a))

Methods

ins :: a :- Read (Dict a)

a :=> (Monoid (Dict a))

Methods

ins :: a :- Monoid (Dict a)

a :=> (Enum (Dict a))

Methods

ins :: a :- Enum (Dict a)

a :=> (Bounded (Dict a))

Methods

ins :: a :- Bounded (Dict a)

() :=> (Eq (Dict a))

Methods

ins :: () :- Eq (Dict a)

() :=> (Ord (Dict a))

Methods

ins :: () :- Ord (Dict a)

() :=> (Show (Dict a))

Methods

ins :: () :- Show (Dict a)

() :=> (Semigroup (Dict a))

Methods

ins :: () :- Semigroup (Dict a)

a => Bounded (Dict a)

Methods

minBound :: Dict a

maxBound :: Dict a

a => Enum (Dict a)

Methods

succ :: Dict a -> Dict a

pred :: Dict a -> Dict a

toEnum :: Int -> Dict a

fromEnum :: Dict a -> Int

enumFrom :: Dict a -> [Dict a]

enumFromThen :: Dict a -> Dict a -> [Dict a]

enumFromTo :: Dict a -> Dict a -> [Dict a]

enumFromThenTo :: Dict a -> Dict a -> Dict a -> [Dict a]

Eq (Dict a)

Methods

(==) :: Dict a -> Dict a -> Bool

(/=) :: Dict a -> Dict a -> Bool

(Typeable Constraint p, p) => Data (Dict p)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dict p -> c (Dict p)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dict p)

toConstr :: Dict p -> Constr

dataTypeOf :: Dict p -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Dict p))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dict p))

gmapT :: (forall b. Data b => b -> b) -> Dict p -> Dict p

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dict p -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dict p -> r

gmapQ :: (forall d. Data d => d -> u) -> Dict p -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Dict p -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dict p -> m (Dict p)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dict p -> m (Dict p)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dict p -> m (Dict p)

Ord (Dict a)

Methods

compare :: Dict a -> Dict a -> Ordering

(<) :: Dict a -> Dict a -> Bool

(<=) :: Dict a -> Dict a -> Bool

(>) :: Dict a -> Dict a -> Bool

(>=) :: Dict a -> Dict a -> Bool

max :: Dict a -> Dict a -> Dict a

min :: Dict a -> Dict a -> Dict a

a => Read (Dict a)

Methods

readsPrec :: Int -> ReadS (Dict a)

readList :: ReadS [Dict a]

readPrec :: ReadPrec (Dict a)

readListPrec :: ReadPrec [Dict a]

Show (Dict a)

Methods

showsPrec :: Int -> Dict a -> ShowS

show :: Dict a -> String

showList :: [Dict a] -> ShowS

Semigroup (Dict a)

Methods

(<>) :: Dict a -> Dict a -> Dict a

sconcat :: NonEmpty (Dict a) -> Dict a

stimes :: Integral b => b -> Dict a -> Dict a

a => Monoid (Dict a)

Methods

mempty :: Dict a

mappend :: Dict a -> Dict a -> Dict a

mconcat :: [Dict a] -> Dict a

NFData (Dict c)

Methods

rnf :: Dict c -> ()

data Proxy k (t :: k) :: forall k. k -> *

A concrete, poly-kinded proxy type

Constructors

Proxy

Instances

Generic1 k (Proxy k)

Associated Types

type Rep1 (Proxy k) (f :: Proxy k -> *) :: k -> *

Methods

from1 :: f a -> Rep1 (Proxy k) f a

to1 :: Rep1 (Proxy k) f a -> f a

Monad (Proxy *)

Since: 4.7.0.0

Methods

(>>=) :: Proxy * a -> (a -> Proxy * b) -> Proxy * b

(>>) :: Proxy * a -> Proxy * b -> Proxy * b

return :: a -> Proxy * a

fail :: String -> Proxy * a

Functor (Proxy *)

Since: 4.7.0.0

Methods

fmap :: (a -> b) -> Proxy * a -> Proxy * b

(<$) :: a -> Proxy * b -> Proxy * a

Applicative (Proxy *)

Since: 4.7.0.0

Methods

pure :: a -> Proxy * a

(<*>) :: Proxy * (a -> b) -> Proxy * a -> Proxy * b

liftA2 :: (a -> b -> c) -> Proxy * a -> Proxy * b -> Proxy * c

(*>) :: Proxy * a -> Proxy * b -> Proxy * b

(<*) :: Proxy * a -> Proxy * b -> Proxy * a

Foldable (Proxy *)

Since: 4.7.0.0

Methods

fold :: Monoid m => Proxy * m -> m

foldMap :: Monoid m => (a -> m) -> Proxy * a -> m

foldr :: (a -> b -> b) -> b -> Proxy * a -> b

foldr' :: (a -> b -> b) -> b -> Proxy * a -> b

foldl :: (b -> a -> b) -> b -> Proxy * a -> b

foldl' :: (b -> a -> b) -> b -> Proxy * a -> b

foldr1 :: (a -> a -> a) -> Proxy * a -> a

foldl1 :: (a -> a -> a) -> Proxy * a -> a

toList :: Proxy * a -> [a]

null :: Proxy * a -> Bool

length :: Proxy * a -> Int

elem :: Eq a => a -> Proxy * a -> Bool

maximum :: Ord a => Proxy * a -> a

minimum :: Ord a => Proxy * a -> a

sum :: Num a => Proxy * a -> a

product :: Num a => Proxy * a -> a

Traversable (Proxy *)

Since: 4.7.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Proxy * a -> f (Proxy * b)

sequenceA :: Applicative f => Proxy * (f a) -> f (Proxy * a)

mapM :: Monad m => (a -> m b) -> Proxy * a -> m (Proxy * b)

sequence :: Monad m => Proxy * (m a) -> m (Proxy * a)

Eq1 (Proxy *)

Since: 4.9.0.0

Methods

liftEq :: (a -> b -> Bool) -> Proxy * a -> Proxy * b -> Bool

Ord1 (Proxy *)

Since: 4.9.0.0

Methods

liftCompare :: (a -> b -> Ordering) -> Proxy * a -> Proxy * b -> Ordering

Read1 (Proxy *)

Since: 4.9.0.0

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Proxy * a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Proxy * a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Proxy * a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Proxy * a]

Show1 (Proxy *)

Since: 4.9.0.0

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Proxy * a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Proxy * a] -> ShowS

Alternative (Proxy *)

Since: 4.9.0.0

Methods

empty :: Proxy * a

(<|>) :: Proxy * a -> Proxy * a -> Proxy * a

some :: Proxy * a -> Proxy * [a]

many :: Proxy * a -> Proxy * [a]

MonadPlus (Proxy *)

Since: 4.9.0.0

Methods

mzero :: Proxy * a

mplus :: Proxy * a -> Proxy * a -> Proxy * a

Bounded (Proxy k t)

Methods

minBound :: Proxy k t

maxBound :: Proxy k t

Enum (Proxy k s)

Since: 4.7.0.0

Methods

succ :: Proxy k s -> Proxy k s

pred :: Proxy k s -> Proxy k s

toEnum :: Int -> Proxy k s

fromEnum :: Proxy k s -> Int

enumFrom :: Proxy k s -> [Proxy k s]

enumFromThen :: Proxy k s -> Proxy k s -> [Proxy k s]

enumFromTo :: Proxy k s -> Proxy k s -> [Proxy k s]

enumFromThenTo :: Proxy k s -> Proxy k s -> Proxy k s -> [Proxy k s]

Eq (Proxy k s)

Since: 4.7.0.0

Methods

(==) :: Proxy k s -> Proxy k s -> Bool

(/=) :: Proxy k s -> Proxy k s -> Bool

Ord (Proxy k s)

Since: 4.7.0.0

Methods

compare :: Proxy k s -> Proxy k s -> Ordering

(<) :: Proxy k s -> Proxy k s -> Bool

(<=) :: Proxy k s -> Proxy k s -> Bool

(>) :: Proxy k s -> Proxy k s -> Bool

(>=) :: Proxy k s -> Proxy k s -> Bool

max :: Proxy k s -> Proxy k s -> Proxy k s

min :: Proxy k s -> Proxy k s -> Proxy k s

Read (Proxy k s)

Since: 4.7.0.0

Methods

readsPrec :: Int -> ReadS (Proxy k s)

readList :: ReadS [Proxy k s]

readPrec :: ReadPrec (Proxy k s)

readListPrec :: ReadPrec [Proxy k s]

Show (Proxy k s)

Since: 4.7.0.0

Methods

showsPrec :: Int -> Proxy k s -> ShowS

show :: Proxy k s -> String

showList :: [Proxy k s] -> ShowS

Ix (Proxy k s)

Since: 4.7.0.0

Methods

range :: (Proxy k s, Proxy k s) -> [Proxy k s]

index :: (Proxy k s, Proxy k s) -> Proxy k s -> Int

unsafeIndex :: (Proxy k s, Proxy k s) -> Proxy k s -> Int

inRange :: (Proxy k s, Proxy k s) -> Proxy k s -> Bool

rangeSize :: (Proxy k s, Proxy k s) -> Int

unsafeRangeSize :: (Proxy k s, Proxy k s) -> Int

Generic (Proxy k t)

Associated Types

type Rep (Proxy k t) :: * -> *

Methods

from :: Proxy k t -> Rep (Proxy k t) x

to :: Rep (Proxy k t) x -> Proxy k t

Semigroup (Proxy k s)

Since: 4.9.0.0

Methods

(<>) :: Proxy k s -> Proxy k s -> Proxy k s

sconcat :: NonEmpty (Proxy k s) -> Proxy k s

stimes :: Integral b => b -> Proxy k s -> Proxy k s

Monoid (Proxy k s)

Since: 4.7.0.0

Methods

mempty :: Proxy k s

mappend :: Proxy k s -> Proxy k s -> Proxy k s

mconcat :: [Proxy k s] -> Proxy k s

type Rep1 k (Proxy k)

type Rep1 k (Proxy k) = D1 k (MetaData "Proxy" "Data.Proxy" "base" False) (C1 k (MetaCons "Proxy" PrefixI False) (U1 k))

type Rep (Proxy k t)

type Rep (Proxy k t) = D1 * (MetaData "Proxy" "Data.Proxy" "base" False) (C1 * (MetaCons "Proxy" PrefixI False) (U1 *))

class Arbitrary a

Random generation and shrinking of values.

QuickCheck provides Arbitrary instances for most types in base, except those which incur extra dependencies. For a wider range of Arbitrary instances see the quickcheck-instances package.

Minimal complete definition

arbitrary

Instances

Arbitrary Bool

Methods

arbitrary :: Gen Bool

shrink :: Bool -> [Bool]

Arbitrary Char

Methods

arbitrary :: Gen Char

shrink :: Char -> [Char]

Arbitrary Double

Methods

arbitrary :: Gen Double

shrink :: Double -> [Double]

Arbitrary Float

Methods

arbitrary :: Gen Float

shrink :: Float -> [Float]

Arbitrary Int

Methods

arbitrary :: Gen Int

shrink :: Int -> [Int]

Arbitrary Int8

Methods

arbitrary :: Gen Int8

shrink :: Int8 -> [Int8]

Arbitrary Int16

Methods

arbitrary :: Gen Int16

shrink :: Int16 -> [Int16]

Arbitrary Int32

Methods

arbitrary :: Gen Int32

shrink :: Int32 -> [Int32]

Arbitrary Int64

Methods

arbitrary :: Gen Int64

shrink :: Int64 -> [Int64]

Arbitrary Integer

Methods

arbitrary :: Gen Integer

shrink :: Integer -> [Integer]

Arbitrary Ordering

Methods

arbitrary :: Gen Ordering

shrink :: Ordering -> [Ordering]

Arbitrary Word

Methods

arbitrary :: Gen Word

shrink :: Word -> [Word]

Arbitrary Word8

Methods

arbitrary :: Gen Word8

shrink :: Word8 -> [Word8]

Arbitrary Word16

Methods

arbitrary :: Gen Word16

shrink :: Word16 -> [Word16]

Arbitrary Word32

Methods

arbitrary :: Gen Word32

shrink :: Word32 -> [Word32]

Arbitrary Word64

Methods

arbitrary :: Gen Word64

shrink :: Word64 -> [Word64]

Arbitrary ()

Methods

arbitrary :: Gen ()

shrink :: () -> [()]

Arbitrary Version

Generates Version with non-empty non-negative versionBranch, and empty versionTags

Methods

arbitrary :: Gen Version

shrink :: Version -> [Version]

Arbitrary QCGen

Methods

arbitrary :: Gen QCGen

shrink :: QCGen -> [QCGen]

Arbitrary ExitCode

Methods

arbitrary :: Gen ExitCode

shrink :: ExitCode -> [ExitCode]

Arbitrary All

Methods

arbitrary :: Gen All

shrink :: All -> [All]

Arbitrary Any

Methods

arbitrary :: Gen Any

shrink :: Any -> [Any]

Arbitrary CChar

Methods

arbitrary :: Gen CChar

shrink :: CChar -> [CChar]

Arbitrary CSChar

Methods

arbitrary :: Gen CSChar

shrink :: CSChar -> [CSChar]

Arbitrary CUChar

Methods

arbitrary :: Gen CUChar

shrink :: CUChar -> [CUChar]

Arbitrary CShort

Methods

arbitrary :: Gen CShort

shrink :: CShort -> [CShort]

Arbitrary CUShort

Methods

arbitrary :: Gen CUShort

shrink :: CUShort -> [CUShort]

Arbitrary CInt

Methods

arbitrary :: Gen CInt

shrink :: CInt -> [CInt]

Arbitrary CUInt

Methods

arbitrary :: Gen CUInt

shrink :: CUInt -> [CUInt]

Arbitrary CLong

Methods

arbitrary :: Gen CLong

shrink :: CLong -> [CLong]

Arbitrary CULong

Methods

arbitrary :: Gen CULong

shrink :: CULong -> [CULong]

Arbitrary CLLong

Methods

arbitrary :: Gen CLLong

shrink :: CLLong -> [CLLong]

Arbitrary CULLong

Methods

arbitrary :: Gen CULLong

shrink :: CULLong -> [CULLong]

Arbitrary CFloat

Methods

arbitrary :: Gen CFloat

shrink :: CFloat -> [CFloat]

Arbitrary CDouble

Methods

arbitrary :: Gen CDouble

shrink :: CDouble -> [CDouble]

Arbitrary CPtrdiff

Methods

arbitrary :: Gen CPtrdiff

shrink :: CPtrdiff -> [CPtrdiff]

Arbitrary CSize

Methods

arbitrary :: Gen CSize

shrink :: CSize -> [CSize]

Arbitrary CWchar

Methods

arbitrary :: Gen CWchar

shrink :: CWchar -> [CWchar]

Arbitrary CSigAtomic

Methods

arbitrary :: Gen CSigAtomic

shrink :: CSigAtomic -> [CSigAtomic]

Arbitrary CClock

Methods

arbitrary :: Gen CClock

shrink :: CClock -> [CClock]

Arbitrary CTime

Methods

arbitrary :: Gen CTime

shrink :: CTime -> [CTime]

Arbitrary CUSeconds

Methods

arbitrary :: Gen CUSeconds

shrink :: CUSeconds -> [CUSeconds]

Arbitrary CSUSeconds

Methods

arbitrary :: Gen CSUSeconds

shrink :: CSUSeconds -> [CSUSeconds]

Arbitrary CIntPtr

Methods

arbitrary :: Gen CIntPtr

shrink :: CIntPtr -> [CIntPtr]

Arbitrary CUIntPtr

Methods

arbitrary :: Gen CUIntPtr

shrink :: CUIntPtr -> [CUIntPtr]

Arbitrary CIntMax

Methods

arbitrary :: Gen CIntMax

shrink :: CIntMax -> [CIntMax]

Arbitrary CUIntMax

Methods

arbitrary :: Gen CUIntMax

shrink :: CUIntMax -> [CUIntMax]

Arbitrary IntSet

Methods

arbitrary :: Gen IntSet

shrink :: IntSet -> [IntSet]

Arbitrary a => Arbitrary [a]

Methods

arbitrary :: Gen [a]

shrink :: [a] -> [[a]]

Arbitrary a => Arbitrary (Maybe a)

Methods

arbitrary :: Gen (Maybe a)

shrink :: Maybe a -> [Maybe a]

Integral a => Arbitrary (Ratio a)

Methods

arbitrary :: Gen (Ratio a)

shrink :: Ratio a -> [Ratio a]

(Ord a, Num a, Real a, Enum a) => Arbitrary (Bounds a)

Methods

arbitrary :: Gen (Bounds a)

shrink :: Bounds a -> [Bounds a]

(RealFloat a, Arbitrary a) => Arbitrary (Complex a)

Methods

arbitrary :: Gen (Complex a)

shrink :: Complex a -> [Complex a]

HasResolution a => Arbitrary (Fixed a)

Methods

arbitrary :: Gen (Fixed a)

shrink :: Fixed a -> [Fixed a]

Arbitrary a => Arbitrary (ZipList a)

Methods

arbitrary :: Gen (ZipList a)

shrink :: ZipList a -> [ZipList a]

Arbitrary a => Arbitrary (Identity a)

Methods

arbitrary :: Gen (Identity a)

shrink :: Identity a -> [Identity a]

Arbitrary a => Arbitrary (Dual a)

Methods

arbitrary :: Gen (Dual a)

shrink :: Dual a -> [Dual a]

(Arbitrary a, CoArbitrary a) => Arbitrary (Endo a)

Methods

arbitrary :: Gen (Endo a)

shrink :: Endo a -> [Endo a]

Arbitrary a => Arbitrary (Sum a)

Methods

arbitrary :: Gen (Sum a)

shrink :: Sum a -> [Sum a]

Arbitrary a => Arbitrary (Product a)

Methods

arbitrary :: Gen (Product a)

shrink :: Product a -> [Product a]

Arbitrary a => Arbitrary (First a)

Methods

arbitrary :: Gen (First a)

shrink :: First a -> [First a]

Arbitrary a => Arbitrary (Last a)

Methods

arbitrary :: Gen (Last a)

shrink :: Last a -> [Last a]

Arbitrary a => Arbitrary (IntMap a)

Methods

arbitrary :: Gen (IntMap a)

shrink :: IntMap a -> [IntMap a]

Arbitrary a => Arbitrary (Seq a)

Methods

arbitrary :: Gen (Seq a)

shrink :: Seq a -> [Seq a]

(Ord a, Arbitrary a) => Arbitrary (Set a)

Methods

arbitrary :: Gen (Set a)

shrink :: Set a -> [Set a]

(CoArbitrary a, Arbitrary b) => Arbitrary (a -> b)

Methods

arbitrary :: Gen (a -> b)

shrink :: (a -> b) -> [a -> b]

(Arbitrary a, Arbitrary b) => Arbitrary (Either a b)

Methods

arbitrary :: Gen (Either a b)

shrink :: Either a b -> [Either a b]

(Arbitrary a, Arbitrary b) => Arbitrary (a, b)

Methods

arbitrary :: Gen (a, b)

shrink :: (a, b) -> [(a, b)]

Arbitrary (m a) => Arbitrary (WrappedMonad m a)

Methods

arbitrary :: Gen (WrappedMonad m a)

shrink :: WrappedMonad m a -> [WrappedMonad m a]

(Ord k, Arbitrary k, Arbitrary v) => Arbitrary (Map k v)

Methods

arbitrary :: Gen (Map k v)

shrink :: Map k v -> [Map k v]

(Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (a, b, c)

Methods

arbitrary :: Gen (a, b, c)

shrink :: (a, b, c) -> [(a, b, c)]

Arbitrary (a b c) => Arbitrary (WrappedArrow a b c)

Methods

arbitrary :: Gen (WrappedArrow a b c)

shrink :: WrappedArrow a b c -> [WrappedArrow a b c]

Arbitrary a => Arbitrary (Const k a b)

Methods

arbitrary :: Gen (Const k a b)

shrink :: Const k a b -> [Const k a b]

Arbitrary (f a) => Arbitrary (Alt k f a)

Methods

arbitrary :: Gen (Alt k f a)

shrink :: Alt k f a -> [Alt k f a]

Arbitrary a => Arbitrary (Constant k a b)

Methods

arbitrary :: Gen (Constant k a b)

shrink :: Constant k a b -> [Constant k a b]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d) => Arbitrary (a, b, c, d)

Methods

arbitrary :: Gen (a, b, c, d)

shrink :: (a, b, c, d) -> [(a, b, c, d)]

(Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (Product * f g a)

Methods

arbitrary :: Gen (Product * f g a)

shrink :: Product * f g a -> [Product * f g a]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e) => Arbitrary (a, b, c, d, e)

Methods

arbitrary :: Gen (a, b, c, d, e)

shrink :: (a, b, c, d, e) -> [(a, b, c, d, e)]

(Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (Compose * * f g a)

Methods

arbitrary :: Gen (Compose * * f g a)

shrink :: Compose * * f g a -> [Compose * * f g a]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f) => Arbitrary (a, b, c, d, e, f)

Methods

arbitrary :: Gen (a, b, c, d, e, f)

shrink :: (a, b, c, d, e, f) -> [(a, b, c, d, e, f)]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g) => Arbitrary (a, b, c, d, e, f, g)

Methods

arbitrary :: Gen (a, b, c, d, e, f, g)

shrink :: (a, b, c, d, e, f, g) -> [(a, b, c, d, e, f, g)]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h) => Arbitrary (a, b, c, d, e, f, g, h)

Methods

arbitrary :: Gen (a, b, c, d, e, f, g, h)

shrink :: (a, b, c, d, e, f, g, h) -> [(a, b, c, d, e, f, g, h)]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h, Arbitrary i) => Arbitrary (a, b, c, d, e, f, g, h, i)

Methods

arbitrary :: Gen (a, b, c, d, e, f, g, h, i)

shrink :: (a, b, c, d, e, f, g, h, i) -> [(a, b, c, d, e, f, g, h, i)]

(Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e, Arbitrary f, Arbitrary g, Arbitrary h, Arbitrary i, Arbitrary j) => Arbitrary (a, b, c, d, e, f, g, h, i, j)

Methods

arbitrary :: Gen (a, b, c, d, e, f, g, h, i, j)

shrink :: (a, b, c, d, e, f, g, h, i, j) -> [(a, b, c, d, e, f, g, h, i, j)]