-- | Type classes for random generation of values. {-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleContexts #-} #ifndef NO_GENERICS {-# LANGUAGE DefaultSignatures, FlexibleContexts, TypeOperators #-} {-# LANGUAGE FlexibleInstances, KindSignatures, ScopedTypeVariables #-} {-# LANGUAGE MultiParamTypeClasses #-} #if __GLASGOW_HASKELL__ >= 710 #define OVERLAPPING_ {-# OVERLAPPING #-} #else {-# LANGUAGE OverlappingInstances #-} #define OVERLAPPING_ #endif #endif #ifndef NO_POLYKINDS {-# LANGUAGE PolyKinds #-} #endif #ifndef NO_SAFE_HASKELL {-# LANGUAGE Trustworthy #-} #endif #ifndef NO_NEWTYPE_DERIVING {-# LANGUAGE GeneralizedNewtypeDeriving #-} #endif module Test.QuickCheck.Arbitrary ( -- * Arbitrary and CoArbitrary classes Arbitrary(..) , CoArbitrary(..) -- ** Unary and Binary classes , Arbitrary1(..) , arbitrary1 , shrink1 , Arbitrary2(..) , arbitrary2 , shrink2 -- ** Helper functions for implementing arbitrary , arbitrarySizedIntegral -- :: Integral a => Gen a , arbitrarySizedNatural -- :: Integral a => Gen a , arbitraryBoundedIntegral -- :: (Bounded a, Integral a) => Gen a , arbitrarySizedBoundedIntegral -- :: (Bounded a, Integral a) => Gen a , arbitrarySizedFractional -- :: Fractional a => Gen a , arbitraryBoundedRandom -- :: (Bounded a, Random a) => Gen a , arbitraryBoundedEnum -- :: (Bounded a, Enum a) => Gen a -- ** Generators for various kinds of character , arbitraryUnicodeChar -- :: Gen Char , arbitraryASCIIChar -- :: Gen Char , arbitraryPrintableChar -- :: Gen Char -- ** Helper functions for implementing shrink #ifndef NO_GENERICS , genericShrink -- :: (Generic a, Arbitrary a, RecursivelyShrink (Rep a), GSubterms (Rep a) a) => a -> [a] , subterms -- :: (Generic a, Arbitrary a, GSubterms (Rep a) a) => a -> [a] , recursivelyShrink -- :: (Generic a, RecursivelyShrink (Rep a)) => a -> [a] , genericCoarbitrary -- :: (Generic a, GCoArbitrary (Rep a)) => a -> Gen b -> Gen b #endif , shrinkNothing -- :: a -> [a] , shrinkList -- :: (a -> [a]) -> [a] -> [[a]] , shrinkMap -- :: Arbitrary a -> (a -> b) -> (b -> a) -> b -> [b] , shrinkMapBy -- :: (a -> b) -> (b -> a) -> (a -> [a]) -> b -> [b] , shrinkIntegral -- :: Integral a => a -> [a] , shrinkRealFrac -- :: RealFrac a => a -> [a] -- ** Helper functions for implementing coarbitrary , coarbitraryIntegral -- :: Integral a => a -> Gen b -> Gen b , coarbitraryReal -- :: Real a => a -> Gen b -> Gen b , coarbitraryShow -- :: Show a => a -> Gen b -> Gen b , coarbitraryEnum -- :: Enum a => a -> Gen b -> Gen b , (><) -- ** Generators which use arbitrary , vector -- :: Arbitrary a => Int -> Gen [a] , orderedList -- :: (Ord a, Arbitrary a) => Gen [a] , infiniteList -- :: Arbitrary a => Gen [a] ) where -------------------------------------------------------------------------- -- imports import Control.Applicative import Data.Foldable(toList) import System.Random(Random) import Test.QuickCheck.Gen import Test.QuickCheck.Random import Test.QuickCheck.Gen.Unsafe {- import Data.Generics ( (:*:)(..) , (:+:)(..) , Unit(..) ) -} import Data.Char ( ord , isLower , isUpper , toLower , isDigit , isSpace , isPrint , generalCategory , GeneralCategory(..) ) #ifndef NO_FIXED import Data.Fixed ( Fixed , HasResolution ) #endif import Data.Ratio ( Ratio , (%) , numerator , denominator ) import Data.Complex ( Complex((:+)) ) import Data.List ( sort , nub ) import Data.Version (Version (..)) import Control.Monad ( liftM , liftM2 , liftM3 , liftM4 , liftM5 ) import Data.Int(Int8, Int16, Int32, Int64) import Data.Word(Word, Word8, Word16, Word32, Word64) import System.Exit (ExitCode(..)) import Foreign.C.Types #ifndef NO_GENERICS import GHC.Generics #endif import qualified Data.Set as Set import qualified Data.Map as Map import qualified Data.IntSet as IntSet import qualified Data.IntMap as IntMap import qualified Data.Sequence as Sequence import qualified Data.Monoid as Monoid #ifndef NO_TRANSFORMERS import Data.Functor.Identity import Data.Functor.Constant import Data.Functor.Compose import Data.Functor.Product #endif -------------------------------------------------------------------------- -- ** class Arbitrary -- | 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 -- <http://hackage.haskell.org/package/quickcheck-instances quickcheck-instances> -- package. class Arbitrary a where -- | A generator for values of the given type. -- -- It is worth spending time thinking about what sort of test data -- you want - good generators are often the difference between -- finding bugs and not finding them. You can use 'sample', -- 'label' and 'classify' to check the quality of your test data. -- -- There is no generic @arbitrary@ implementation included because we don't -- know how to make a high-quality one. If you want one, consider using the -- <http://hackage.haskell.org/package/testing-feat testing-feat> package. -- -- The <http://www.cse.chalmers.se/~rjmh/QuickCheck/manual.html QuickCheck manual> -- goes into detail on how to write good generators. Make sure to look at it, -- especially if your type is recursive! arbitrary :: Gen a -- | Produces a (possibly) empty list of all the possible -- immediate shrinks of the given value. -- -- The default implementation returns the empty list, so will not try to -- shrink the value. If your data type has no special invariants, you can -- enable shrinking by defining @shrink = 'genericShrink'@, but by customising -- the behaviour of @shrink@ you can often get simpler counterexamples. -- -- Most implementations of 'shrink' should try at least three things: -- -- 1. Shrink a term to any of its immediate subterms. -- You can use 'subterms' to do this. -- -- 2. Recursively apply 'shrink' to all immediate subterms. -- You can use 'recursivelyShrink' to do this. -- -- 3. Type-specific shrinkings such as replacing a constructor by a -- simpler constructor. -- -- For example, suppose we have the following implementation of binary trees: -- -- > data Tree a = Nil | Branch a (Tree a) (Tree a) -- -- We can then define 'shrink' as follows: -- -- > shrink Nil = [] -- > shrink (Branch x l r) = -- > -- shrink Branch to Nil -- > [Nil] ++ -- > -- shrink to subterms -- > [l, r] ++ -- > -- recursively shrink subterms -- > [Branch x' l' r' | (x', l', r') <- shrink (x, l, r)] -- -- There are a couple of subtleties here: -- -- * QuickCheck tries the shrinking candidates in the order they -- appear in the list, so we put more aggressive shrinking steps -- (such as replacing the whole tree by @Nil@) before smaller -- ones (such as recursively shrinking the subtrees). -- -- * It is tempting to write the last line as -- @[Branch x' l' r' | x' <- shrink x, l' <- shrink l, r' <- shrink r]@ -- but this is the /wrong thing/! It will force QuickCheck to shrink -- @x@, @l@ and @r@ in tandem, and shrinking will stop once /one/ of -- the three is fully shrunk. -- -- There is a fair bit of boilerplate in the code above. -- We can avoid it with the help of some generic functions. -- The function 'genericShrink' tries shrinking a term to all of its -- subterms and, failing that, recursively shrinks the subterms. -- Using it, we can define 'shrink' as: -- -- > shrink x = shrinkToNil x ++ genericShrink x -- > where -- > shrinkToNil Nil = [] -- > shrinkToNil (Branch _ l r) = [Nil] -- -- 'genericShrink' is a combination of 'subterms', which shrinks -- a term to any of its subterms, and 'recursivelyShrink', which shrinks -- all subterms of a term. These may be useful if you need a bit more -- control over shrinking than 'genericShrink' gives you. -- -- A final gotcha: we cannot define 'shrink' as simply @'shrink' x = Nil:'genericShrink' x@ -- as this shrinks @Nil@ to @Nil@, and shrinking will go into an -- infinite loop. -- -- If all this leaves you bewildered, you might try @'shrink' = 'genericShrink'@ to begin with, -- after deriving @Generic@ for your type. However, if your data type has any -- special invariants, you will need to check that 'genericShrink' can't break those invariants. shrink :: a -> [a] shrink _ = [] -- | Lifting of the 'Arbitrary' class to unary type constructors. class Arbitrary1 f where liftArbitrary :: Gen a -> Gen (f a) liftShrink :: (a -> [a]) -> f a -> [f a] liftShrink _ _ = [] arbitrary1 :: (Arbitrary1 f, Arbitrary a) => Gen (f a) arbitrary1 = liftArbitrary arbitrary shrink1 :: (Arbitrary1 f, Arbitrary a) => f a -> [f a] shrink1 = liftShrink shrink -- | Lifting of the 'Arbitrary' class to binary type constructors. class Arbitrary2 f where liftArbitrary2 :: Gen a -> Gen b -> Gen (f a b) liftShrink2 :: (a -> [a]) -> (b -> [b]) -> f a b -> [f a b] liftShrink2 _ _ _ = [] arbitrary2 :: (Arbitrary2 f, Arbitrary a, Arbitrary b) => Gen (f a b) arbitrary2 = liftArbitrary2 arbitrary arbitrary shrink2 :: (Arbitrary2 f, Arbitrary a, Arbitrary b) => f a b -> [f a b] shrink2 = liftShrink2 shrink shrink #ifndef NO_GENERICS -- | Shrink a term to any of its immediate subterms, -- and also recursively shrink all subterms. genericShrink :: (Generic a, RecursivelyShrink (Rep a), GSubterms (Rep a) a) => a -> [a] genericShrink x = subterms x ++ recursivelyShrink x -- | Recursively shrink all immediate subterms. recursivelyShrink :: (Generic a, RecursivelyShrink (Rep a)) => a -> [a] recursivelyShrink = map to . grecursivelyShrink . from class RecursivelyShrink f where grecursivelyShrink :: f a -> [f a] instance (RecursivelyShrink f, RecursivelyShrink g) => RecursivelyShrink (f :*: g) where grecursivelyShrink (x :*: y) = [x' :*: y | x' <- grecursivelyShrink x] ++ [x :*: y' | y' <- grecursivelyShrink y] instance (RecursivelyShrink f, RecursivelyShrink g) => RecursivelyShrink (f :+: g) where grecursivelyShrink (L1 x) = map L1 (grecursivelyShrink x) grecursivelyShrink (R1 x) = map R1 (grecursivelyShrink x) instance RecursivelyShrink f => RecursivelyShrink (M1 i c f) where grecursivelyShrink (M1 x) = map M1 (grecursivelyShrink x) instance Arbitrary a => RecursivelyShrink (K1 i a) where grecursivelyShrink (K1 x) = map K1 (shrink x) instance RecursivelyShrink U1 where grecursivelyShrink U1 = [] instance RecursivelyShrink V1 where -- The empty type can't be shrunk to anything. grecursivelyShrink _ = [] -- | All immediate subterms of a term. subterms :: (Generic a, GSubterms (Rep a) a) => a -> [a] subterms = gSubterms . from class GSubterms f a where -- | Provides the immediate subterms of a term that are of the same type -- as the term itself. -- -- Requires a constructor to be stripped off; this means it skips through -- @M1@ wrappers and returns @[]@ on everything that's not `(:*:)` or `(:+:)`. -- -- Once a `(:*:)` or `(:+:)` constructor has been reached, this function -- delegates to `gSubtermsIncl` to return the immediately next constructor -- available. gSubterms :: f a -> [a] instance GSubterms V1 a where -- The empty type can't be shrunk to anything. gSubterms _ = [] instance GSubterms U1 a where gSubterms U1 = [] instance (GSubtermsIncl f a, GSubtermsIncl g a) => GSubterms (f :*: g) a where gSubterms (l :*: r) = gSubtermsIncl l ++ gSubtermsIncl r instance (GSubtermsIncl f a, GSubtermsIncl g a) => GSubterms (f :+: g) a where gSubterms (L1 x) = gSubtermsIncl x gSubterms (R1 x) = gSubtermsIncl x instance GSubterms f a => GSubterms (M1 i c f) a where gSubterms (M1 x) = gSubterms x instance GSubterms (K1 i a) b where gSubterms (K1 _) = [] class GSubtermsIncl f a where -- | Provides the immediate subterms of a term that are of the same type -- as the term itself. -- -- In contrast to `gSubterms`, this returns the immediate next constructor -- available. gSubtermsIncl :: f a -> [a] instance GSubtermsIncl V1 a where -- The empty type can't be shrunk to anything. gSubtermsIncl _ = [] instance GSubtermsIncl U1 a where gSubtermsIncl U1 = [] instance (GSubtermsIncl f a, GSubtermsIncl g a) => GSubtermsIncl (f :*: g) a where gSubtermsIncl (l :*: r) = gSubtermsIncl l ++ gSubtermsIncl r instance (GSubtermsIncl f a, GSubtermsIncl g a) => GSubtermsIncl (f :+: g) a where gSubtermsIncl (L1 x) = gSubtermsIncl x gSubtermsIncl (R1 x) = gSubtermsIncl x instance GSubtermsIncl f a => GSubtermsIncl (M1 i c f) a where gSubtermsIncl (M1 x) = gSubtermsIncl x -- This is the important case: We've found a term of the same type. instance OVERLAPPING_ GSubtermsIncl (K1 i a) a where gSubtermsIncl (K1 x) = [x] instance OVERLAPPING_ GSubtermsIncl (K1 i a) b where gSubtermsIncl (K1 _) = [] #endif -- instances instance (CoArbitrary a) => Arbitrary1 ((->) a) where liftArbitrary arbB = promote (`coarbitrary` arbB) instance (CoArbitrary a, Arbitrary b) => Arbitrary (a -> b) where arbitrary = arbitrary1 instance Arbitrary () where arbitrary = return () instance Arbitrary Bool where arbitrary = choose (False,True) shrink True = [False] shrink False = [] instance Arbitrary Ordering where arbitrary = elements [LT, EQ, GT] shrink GT = [EQ, LT] shrink LT = [EQ] shrink EQ = [] instance Arbitrary1 Maybe where liftArbitrary arb = frequency [(1, return Nothing), (3, liftM Just arb)] liftShrink shr (Just x) = Nothing : [ Just x' | x' <- shr x ] liftShrink _ Nothing = [] instance Arbitrary a => Arbitrary (Maybe a) where arbitrary = arbitrary1 shrink = shrink1 instance Arbitrary2 Either where liftArbitrary2 arbA arbB = oneof [liftM Left arbA, liftM Right arbB] liftShrink2 shrA _ (Left x) = [ Left x' | x' <- shrA x ] liftShrink2 _ shrB (Right y) = [ Right y' | y' <- shrB y ] instance Arbitrary a => Arbitrary1 (Either a) where liftArbitrary = liftArbitrary2 arbitrary liftShrink = liftShrink2 shrink instance (Arbitrary a, Arbitrary b) => Arbitrary (Either a b) where arbitrary = arbitrary2 shrink = shrink2 instance Arbitrary1 [] where liftArbitrary = listOf liftShrink = shrinkList instance Arbitrary a => Arbitrary [a] where arbitrary = arbitrary1 shrink = shrink1 -- | Shrink a list of values given a shrinking function for individual values. shrinkList :: (a -> [a]) -> [a] -> [[a]] shrinkList shr xs = concat [ removes k n xs | k <- takeWhile (>0) (iterate (`div`2) n) ] ++ shrinkOne xs where n = length xs shrinkOne [] = [] shrinkOne (x:xs) = [ x':xs | x' <- shr x ] ++ [ x:xs' | xs' <- shrinkOne xs ] removes k n xs | k > n = [] | null xs2 = [[]] | otherwise = xs2 : map (xs1 ++) (removes k (n-k) xs2) where xs1 = take k xs xs2 = drop k xs {- -- "standard" definition for lists: shrink [] = [] shrink (x:xs) = [ xs ] ++ [ x:xs' | xs' <- shrink xs ] ++ [ x':xs | x' <- shrink x ] -} instance Integral a => Arbitrary (Ratio a) where arbitrary = arbitrarySizedFractional shrink = shrinkRealFrac instance (RealFloat a, Arbitrary a) => Arbitrary (Complex a) where arbitrary = liftM2 (:+) arbitrary arbitrary shrink (x :+ y) = [ x' :+ y | x' <- shrink x ] ++ [ x :+ y' | y' <- shrink y ] #ifndef NO_FIXED instance HasResolution a => Arbitrary (Fixed a) where arbitrary = arbitrarySizedFractional shrink = shrinkRealFrac #endif instance Arbitrary2 (,) where liftArbitrary2 = liftM2 (,) liftShrink2 shrA shrB (x, y) = [ (x', y) | x' <- shrA x ] ++ [ (x, y') | y' <- shrB y ] instance (Arbitrary a) => Arbitrary1 ((,) a) where liftArbitrary = liftArbitrary2 arbitrary liftShrink = liftShrink2 shrink instance (Arbitrary a, Arbitrary b) => Arbitrary (a,b) where arbitrary = arbitrary2 shrink = shrink2 instance (Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (a,b,c) where arbitrary = liftM3 (,,) arbitrary arbitrary arbitrary shrink (x, y, z) = [ (x', y', z') | (x', (y', z')) <- shrink (x, (y, z)) ] instance (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d) => Arbitrary (a,b,c,d) where arbitrary = liftM4 (,,,) arbitrary arbitrary arbitrary arbitrary shrink (w, x, y, z) = [ (w', x', y', z') | (w', (x', (y', z'))) <- shrink (w, (x, (y, z))) ] instance (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e) => Arbitrary (a,b,c,d,e) where arbitrary = liftM5 (,,,,) arbitrary arbitrary arbitrary arbitrary arbitrary shrink (v, w, x, y, z) = [ (v', w', x', y', z') | (v', (w', (x', (y', z')))) <- shrink (v, (w, (x, (y, z)))) ] instance ( Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e , Arbitrary f ) => Arbitrary (a,b,c,d,e,f) where arbitrary = return (,,,,,) <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary shrink (u, v, w, x, y, z) = [ (u', v', w', x', y', z') | (u', (v', (w', (x', (y', z'))))) <- shrink (u, (v, (w, (x, (y, z))))) ] instance ( Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e , Arbitrary f, Arbitrary g ) => Arbitrary (a,b,c,d,e,f,g) where arbitrary = return (,,,,,,) <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary shrink (t, u, v, w, x, y, z) = [ (t', u', v', w', x', y', z') | (t', (u', (v', (w', (x', (y', z')))))) <- shrink (t, (u, (v, (w, (x, (y, z)))))) ] instance ( 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) where arbitrary = return (,,,,,,,) <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary shrink (s, t, u, v, w, x, y, z) = [ (s', t', u', v', w', x', y', z') | (s', (t', (u', (v', (w', (x', (y', z'))))))) <- shrink (s, (t, (u, (v, (w, (x, (y, z))))))) ] instance ( 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) where arbitrary = return (,,,,,,,,) <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary shrink (r, s, t, u, v, w, x, y, z) = [ (r', s', t', u', v', w', x', y', z') | (r', (s', (t', (u', (v', (w', (x', (y', z')))))))) <- shrink (r, (s, (t, (u, (v, (w, (x, (y, z)))))))) ] instance ( 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) where arbitrary = return (,,,,,,,,,) <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary shrink (q, r, s, t, u, v, w, x, y, z) = [ (q', r', s', t', u', v', w', x', y', z') | (q', (r', (s', (t', (u', (v', (w', (x', (y', z'))))))))) <- shrink (q, (r, (s, (t, (u, (v, (w, (x, (y, z))))))))) ] -- typical instance for primitive (numerical) types instance Arbitrary Integer where arbitrary = arbitrarySizedIntegral shrink = shrinkIntegral instance Arbitrary Int where arbitrary = arbitrarySizedIntegral shrink = shrinkIntegral instance Arbitrary Int8 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Int16 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Int32 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Int64 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Word where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Word8 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Word16 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Word32 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Word64 where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary Char where arbitrary = frequency [(3, arbitraryASCIIChar), (1, arbitraryUnicodeChar)] shrink c = filter (<. c) $ nub $ ['a','b','c'] ++ [ toLower c | isUpper c ] ++ ['A','B','C'] ++ ['1','2','3'] ++ [' ','\n'] where a <. b = stamp a < stamp b stamp a = ( (not (isLower a) , not (isUpper a) , not (isDigit a)) , (not (a==' ') , not (isSpace a) , a) ) instance Arbitrary Float where arbitrary = arbitrarySizedFractional shrink = shrinkRealFrac instance Arbitrary Double where arbitrary = arbitrarySizedFractional shrink = shrinkRealFrac instance Arbitrary CChar where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CSChar where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CUChar where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CShort where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CUShort where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CInt where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CUInt where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CLong where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CULong where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CPtrdiff where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CSize where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CWchar where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CSigAtomic where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CLLong where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CULLong where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CIntPtr where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CUIntPtr where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CIntMax where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral instance Arbitrary CUIntMax where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral #ifndef NO_NEWTYPE_DERIVING -- The following four types have no Bounded instance, -- so we fake it by discovering the bounds at runtime. instance Arbitrary CClock where arbitrary = fmap unBounds arbitrary shrink = shrinkMap unBounds Bounds instance Arbitrary CTime where arbitrary = fmap unBounds arbitrary shrink = shrinkMap unBounds Bounds #ifndef NO_FOREIGN_C_USECONDS instance Arbitrary CUSeconds where arbitrary = fmap unBounds arbitrary shrink = shrinkMap unBounds Bounds instance Arbitrary CSUSeconds where arbitrary = fmap unBounds arbitrary shrink = shrinkMap unBounds Bounds #endif newtype Bounds a = Bounds { unBounds :: a } deriving (Eq, Ord, Num, Enum, Real, Show) instance (Ord a, Num a) => Bounded (Bounds a) where -- assume max has all 1s in binary expansion maxBound = maximum (nubIterate (\x -> 2*x+1) 1) -- assume min has a leading 1 and rest 0s in binary expansion (or is 0) minBound = minimum (0:nubIterate (*2) 1) instance (Num a, Real a, Enum a) => Integral (Bounds a) where toInteger = fromIntegral . fromEnum x `quotRem` y = let (z, w) = toInteger x `quotRem` toInteger y in (fromInteger z, fromInteger w) instance (Ord a, Num a, Real a, Enum a) => Arbitrary (Bounds a) where arbitrary = arbitrarySizedBoundedIntegral shrink = shrinkIntegral -- Like iterate, but stop when you reach an existing value. nubIterate :: Eq a => (a -> a) -> a -> [a] nubIterate f x = iter [] x where iter xs x | x `elem` xs = [] | otherwise = x:iter (x:xs) (f x) #endif instance Arbitrary CFloat where arbitrary = arbitrarySizedFractional shrink = shrinkRealFrac instance Arbitrary CDouble where arbitrary = arbitrarySizedFractional shrink = shrinkRealFrac -- Arbitrary instances for container types instance (Ord a, Arbitrary a) => Arbitrary (Set.Set a) where arbitrary = fmap Set.fromList arbitrary shrink = map Set.fromList . shrink . Set.toList instance (Ord k, Arbitrary k) => Arbitrary1 (Map.Map k) where liftArbitrary = fmap Map.fromList . liftArbitrary . liftArbitrary liftShrink shr = map Map.fromList . liftShrink (liftShrink shr) . Map.toList instance (Ord k, Arbitrary k, Arbitrary v) => Arbitrary (Map.Map k v) where arbitrary = arbitrary1 shrink = shrink1 instance Arbitrary IntSet.IntSet where arbitrary = fmap IntSet.fromList arbitrary shrink = map IntSet.fromList . shrink . IntSet.toList instance Arbitrary1 IntMap.IntMap where liftArbitrary = fmap IntMap.fromList . liftArbitrary . liftArbitrary liftShrink shr = map IntMap.fromList . liftShrink (liftShrink shr) . IntMap.toList instance Arbitrary a => Arbitrary (IntMap.IntMap a) where arbitrary = arbitrary1 shrink = shrink1 instance Arbitrary1 Sequence.Seq where liftArbitrary = fmap Sequence.fromList . liftArbitrary liftShrink shr = map Sequence.fromList . liftShrink shr . toList instance Arbitrary a => Arbitrary (Sequence.Seq a) where arbitrary = arbitrary1 shrink = shrink1 -- Arbitrary instance for Ziplist instance Arbitrary1 ZipList where liftArbitrary = fmap ZipList . liftArbitrary liftShrink shr = map ZipList . liftShrink shr . getZipList instance Arbitrary a => Arbitrary (ZipList a) where arbitrary = arbitrary1 shrink = shrink1 #ifndef NO_TRANSFORMERS -- Arbitrary instance for transformers' Functors instance Arbitrary1 Identity where liftArbitrary = fmap Identity liftShrink shr = map Identity . shr . runIdentity instance Arbitrary a => Arbitrary (Identity a) where arbitrary = arbitrary1 shrink = shrink1 instance Arbitrary2 Constant where liftArbitrary2 arbA _ = fmap Constant arbA liftShrink2 shrA _ = fmap Constant . shrA . getConstant instance Arbitrary a => Arbitrary1 (Constant a) where liftArbitrary = liftArbitrary2 arbitrary liftShrink = liftShrink2 shrink -- Have to be defined explicitly, as Constant is kind polymorphic instance Arbitrary a => Arbitrary (Constant a b) where arbitrary = fmap Constant arbitrary shrink = map Constant . shrink . getConstant instance (Arbitrary1 f, Arbitrary1 g) => Arbitrary1 (Product f g) where liftArbitrary arb = liftM2 Pair (liftArbitrary arb) (liftArbitrary arb) liftShrink shr (Pair f g) = [ Pair f' g | f' <- liftShrink shr f ] ++ [ Pair f g' | g' <- liftShrink shr g ] instance (Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (Product f g a) where arbitrary = arbitrary1 shrink = shrink1 instance (Arbitrary1 f, Arbitrary1 g) => Arbitrary1 (Compose f g) where liftArbitrary = fmap Compose . liftArbitrary . liftArbitrary liftShrink shr = map Compose . liftShrink (liftShrink shr) . getCompose instance (Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (Compose f g a) where arbitrary = arbitrary1 shrink = shrink1 #endif -- Arbitrary instance for Const instance Arbitrary2 Const where liftArbitrary2 arbA _ = fmap Const arbA liftShrink2 shrA _ = fmap Const . shrA . getConst instance Arbitrary a => Arbitrary1 (Const a) where liftArbitrary = liftArbitrary2 arbitrary liftShrink = liftShrink2 shrink -- Have to be defined explicitly, as Const is kind polymorphic instance Arbitrary a => Arbitrary (Const a b) where arbitrary = fmap Const arbitrary shrink = map Const . shrink . getConst instance Arbitrary (m a) => Arbitrary (WrappedMonad m a) where arbitrary = WrapMonad <$> arbitrary shrink (WrapMonad a) = map WrapMonad (shrink a) instance Arbitrary (a b c) => Arbitrary (WrappedArrow a b c) where arbitrary = WrapArrow <$> arbitrary shrink (WrapArrow a) = map WrapArrow (shrink a) -- Arbitrary instances for Monoid instance Arbitrary a => Arbitrary (Monoid.Dual a) where arbitrary = fmap Monoid.Dual arbitrary shrink = map Monoid.Dual . shrink . Monoid.getDual instance (Arbitrary a, CoArbitrary a) => Arbitrary (Monoid.Endo a) where arbitrary = fmap Monoid.Endo arbitrary shrink = map Monoid.Endo . shrink . Monoid.appEndo instance Arbitrary Monoid.All where arbitrary = fmap Monoid.All arbitrary shrink = map Monoid.All . shrink . Monoid.getAll instance Arbitrary Monoid.Any where arbitrary = fmap Monoid.Any arbitrary shrink = map Monoid.Any . shrink . Monoid.getAny instance Arbitrary a => Arbitrary (Monoid.Sum a) where arbitrary = fmap Monoid.Sum arbitrary shrink = map Monoid.Sum . shrink . Monoid.getSum instance Arbitrary a => Arbitrary (Monoid.Product a) where arbitrary = fmap Monoid.Product arbitrary shrink = map Monoid.Product . shrink . Monoid.getProduct #if defined(MIN_VERSION_base) #if MIN_VERSION_base(3,0,0) instance Arbitrary a => Arbitrary (Monoid.First a) where arbitrary = fmap Monoid.First arbitrary shrink = map Monoid.First . shrink . Monoid.getFirst instance Arbitrary a => Arbitrary (Monoid.Last a) where arbitrary = fmap Monoid.Last arbitrary shrink = map Monoid.Last . shrink . Monoid.getLast #endif #if MIN_VERSION_base(4,8,0) instance Arbitrary (f a) => Arbitrary (Monoid.Alt f a) where arbitrary = fmap Monoid.Alt arbitrary shrink = map Monoid.Alt . shrink . Monoid.getAlt #endif #endif -- | Generates 'Version' with non-empty non-negative @versionBranch@, and empty @versionTags@ instance Arbitrary Version where arbitrary = sized $ \n -> do k <- choose (0, log2 n) xs <- vectorOf (k+1) arbitrarySizedNatural return (Version xs []) where log2 :: Int -> Int log2 n | n <= 1 = 0 | otherwise = 1 + log2 (n `div` 2) shrink (Version xs _) = [ Version xs' [] | xs' <- shrink xs , length xs' > 0 , all (>=0) xs' ] instance Arbitrary QCGen where arbitrary = MkGen (\g _ -> g) instance Arbitrary ExitCode where arbitrary = frequency [(1, return ExitSuccess), (3, liftM ExitFailure arbitrary)] shrink (ExitFailure x) = ExitSuccess : [ ExitFailure x' | x' <- shrink x ] shrink _ = [] -- ** Helper functions for implementing arbitrary -- | Generates an integral number. The number can be positive or negative -- and its maximum absolute value depends on the size parameter. arbitrarySizedIntegral :: Integral a => Gen a arbitrarySizedIntegral = sized $ \n -> inBounds fromInteger (choose (-toInteger n, toInteger n)) -- | Generates a natural number. The number's maximum value depends on -- the size parameter. arbitrarySizedNatural :: Integral a => Gen a arbitrarySizedNatural = sized $ \n -> inBounds fromInteger (choose (0, toInteger n)) inBounds :: Integral a => (Integer -> a) -> Gen Integer -> Gen a inBounds fi g = fmap fi (g `suchThat` (\x -> toInteger (fi x) == x)) -- | Generates a fractional number. The number can be positive or negative -- and its maximum absolute value depends on the size parameter. arbitrarySizedFractional :: Fractional a => Gen a arbitrarySizedFractional = sized $ \n -> let n' = toInteger n in do a <- choose ((-n') * precision, n' * precision) b <- choose (1, precision) return (fromRational (a % b)) where precision = 9999999999999 :: Integer -- Useful for getting at minBound and maxBound without having to -- fiddle around with asTypeOf. withBounds :: Bounded a => (a -> a -> Gen a) -> Gen a withBounds k = k minBound maxBound -- | Generates an integral number. The number is chosen uniformly from -- the entire range of the type. You may want to use -- 'arbitrarySizedBoundedIntegral' instead. arbitraryBoundedIntegral :: (Bounded a, Integral a) => Gen a arbitraryBoundedIntegral = withBounds $ \mn mx -> do n <- choose (toInteger mn, toInteger mx) return (fromInteger n) -- | Generates an element of a bounded type. The element is -- chosen from the entire range of the type. arbitraryBoundedRandom :: (Bounded a, Random a) => Gen a arbitraryBoundedRandom = choose (minBound,maxBound) -- | Generates an element of a bounded enumeration. arbitraryBoundedEnum :: (Bounded a, Enum a) => Gen a arbitraryBoundedEnum = withBounds $ \mn mx -> do n <- choose (fromEnum mn, fromEnum mx) return (toEnum n) -- | Generates an integral number from a bounded domain. The number is -- chosen from the entire range of the type, but small numbers are -- generated more often than big numbers. Inspired by demands from -- Phil Wadler. arbitrarySizedBoundedIntegral :: (Bounded a, Integral a) => Gen a arbitrarySizedBoundedIntegral = withBounds $ \mn mx -> sized $ \s -> do let bits n | n == 0 = 0 | otherwise = 1 + bits (n `quot` 2) k = 2^(s*(bits mn `max` bits mx `max` 40) `div` 80) n <- choose (toInteger mn `max` (-k), toInteger mx `min` k) return (fromInteger n) -- ** Generators for various kinds of character -- | Generates any Unicode character (but not a surrogate) arbitraryUnicodeChar :: Gen Char arbitraryUnicodeChar = arbitraryBoundedEnum `suchThat` (not . isSurrogate) where isSurrogate c = generalCategory c == Surrogate -- | Generates a random ASCII character (0-127). arbitraryASCIIChar :: Gen Char arbitraryASCIIChar = choose ('\0', '\127') -- | Generates a printable Unicode character. arbitraryPrintableChar :: Gen Char arbitraryPrintableChar = arbitrary `suchThat` isPrint -- ** Helper functions for implementing shrink -- | Returns no shrinking alternatives. shrinkNothing :: a -> [a] shrinkNothing _ = [] -- | Map a shrink function to another domain. This is handy if your data type -- has special invariants, but is /almost/ isomorphic to some other type. -- -- @ -- shrinkOrderedList :: (Ord a, Arbitrary a) => [a] -> [[a]] -- shrinkOrderedList = shrinkMap sort id -- -- shrinkSet :: (Ord a, Arbitrary a) => Set a -> Set [a] -- shrinkSet = shrinkMap fromList toList -- @ shrinkMap :: Arbitrary a => (a -> b) -> (b -> a) -> b -> [b] shrinkMap f g = shrinkMapBy f g shrink -- | Non-overloaded version of `shrinkMap`. shrinkMapBy :: (a -> b) -> (b -> a) -> (a -> [a]) -> b -> [b] shrinkMapBy f g shr = map f . shr . g -- | Shrink an integral number. shrinkIntegral :: Integral a => a -> [a] shrinkIntegral x = nub $ [ -x | x < 0, -x > x ] ++ [ x' | x' <- takeWhile (<< x) (0:[ x - i | i <- tail (iterate (`quot` 2) x) ]) ] where -- a << b is "morally" abs a < abs b, but taking care of overflow. a << b = case (a >= 0, b >= 0) of (True, True) -> a < b (False, False) -> a > b (True, False) -> a + b < 0 (False, True) -> a + b > 0 -- | Shrink a fraction. shrinkRealFrac :: RealFrac a => a -> [a] shrinkRealFrac x = nub $ [ -x | x < 0 ] ++ map fromInteger (shrinkIntegral (truncate x)) -------------------------------------------------------------------------- -- ** CoArbitrary #ifndef NO_GENERICS -- | Used for random generation of functions. -- -- If you are using a recent GHC, there is a default definition of -- 'coarbitrary' using 'genericCoarbitrary', so if your type has a -- 'Generic' instance it's enough to say -- -- > instance CoArbitrary MyType -- -- You should only use 'genericCoarbitrary' for data types where -- equality is structural, i.e. if you can't have two different -- representations of the same value. An example where it's not -- safe is sets implemented using binary search trees: the same -- set can be represented as several different trees. -- Here you would have to explicitly define -- @coarbitrary s = coarbitrary (toList s)@. #else -- | Used for random generation of functions. #endif class CoArbitrary a where -- | Used to generate a function of type @a -> b@. -- The first argument is a value, the second a generator. -- You should use 'variant' to perturb the random generator; -- the goal is that different values for the first argument will -- lead to different calls to 'variant'. An example will help: -- -- @ -- instance CoArbitrary a => CoArbitrary [a] where -- coarbitrary [] = 'variant' 0 -- coarbitrary (x:xs) = 'variant' 1 . coarbitrary (x,xs) -- @ coarbitrary :: a -> Gen b -> Gen b #ifndef NO_GENERICS default coarbitrary :: (Generic a, GCoArbitrary (Rep a)) => a -> Gen b -> Gen b coarbitrary = genericCoarbitrary -- | Generic CoArbitrary implementation. genericCoarbitrary :: (Generic a, GCoArbitrary (Rep a)) => a -> Gen b -> Gen b genericCoarbitrary = gCoarbitrary . from class GCoArbitrary f where gCoarbitrary :: f a -> Gen b -> Gen b instance GCoArbitrary U1 where gCoarbitrary U1 = id instance (GCoArbitrary f, GCoArbitrary g) => GCoArbitrary (f :*: g) where -- Like the instance for tuples. gCoarbitrary (l :*: r) = gCoarbitrary l . gCoarbitrary r instance (GCoArbitrary f, GCoArbitrary g) => GCoArbitrary (f :+: g) where -- Like the instance for Either. gCoarbitrary (L1 x) = variant 0 . gCoarbitrary x gCoarbitrary (R1 x) = variant 1 . gCoarbitrary x instance GCoArbitrary f => GCoArbitrary (M1 i c f) where gCoarbitrary (M1 x) = gCoarbitrary x instance CoArbitrary a => GCoArbitrary (K1 i a) where gCoarbitrary (K1 x) = coarbitrary x #endif {-# DEPRECATED (><) "Use ordinary function composition instead" #-} -- | Combine two generator perturbing functions, for example the -- results of calls to 'variant' or 'coarbitrary'. (><) :: (Gen a -> Gen a) -> (Gen a -> Gen a) -> (Gen a -> Gen a) (><) = (.) instance (Arbitrary a, CoArbitrary b) => CoArbitrary (a -> b) where coarbitrary f gen = do xs <- arbitrary coarbitrary (map f xs) gen instance CoArbitrary () where coarbitrary _ = id instance CoArbitrary Bool where coarbitrary False = variant 0 coarbitrary True = variant 1 instance CoArbitrary Ordering where coarbitrary GT = variant 0 coarbitrary EQ = variant 1 coarbitrary LT = variant 2 instance CoArbitrary a => CoArbitrary (Maybe a) where coarbitrary Nothing = variant 0 coarbitrary (Just x) = variant 1 . coarbitrary x instance (CoArbitrary a, CoArbitrary b) => CoArbitrary (Either a b) where coarbitrary (Left x) = variant 0 . coarbitrary x coarbitrary (Right y) = variant 1 . coarbitrary y instance CoArbitrary a => CoArbitrary [a] where coarbitrary [] = variant 0 coarbitrary (x:xs) = variant 1 . coarbitrary (x,xs) instance (Integral a, CoArbitrary a) => CoArbitrary (Ratio a) where coarbitrary r = coarbitrary (numerator r,denominator r) #ifndef NO_FIXED instance HasResolution a => CoArbitrary (Fixed a) where coarbitrary = coarbitraryReal #endif instance (RealFloat a, CoArbitrary a) => CoArbitrary (Complex a) where coarbitrary (x :+ y) = coarbitrary x . coarbitrary y instance (CoArbitrary a, CoArbitrary b) => CoArbitrary (a,b) where coarbitrary (x,y) = coarbitrary x . coarbitrary y instance (CoArbitrary a, CoArbitrary b, CoArbitrary c) => CoArbitrary (a,b,c) where coarbitrary (x,y,z) = coarbitrary x . coarbitrary y . coarbitrary z instance (CoArbitrary a, CoArbitrary b, CoArbitrary c, CoArbitrary d) => CoArbitrary (a,b,c,d) where coarbitrary (x,y,z,v) = coarbitrary x . coarbitrary y . coarbitrary z . coarbitrary v instance (CoArbitrary a, CoArbitrary b, CoArbitrary c, CoArbitrary d, CoArbitrary e) => CoArbitrary (a,b,c,d,e) where coarbitrary (x,y,z,v,w) = coarbitrary x . coarbitrary y . coarbitrary z . coarbitrary v . coarbitrary w -- typical instance for primitive (numerical) types instance CoArbitrary Integer where coarbitrary = coarbitraryIntegral instance CoArbitrary Int where coarbitrary = coarbitraryIntegral instance CoArbitrary Int8 where coarbitrary = coarbitraryIntegral instance CoArbitrary Int16 where coarbitrary = coarbitraryIntegral instance CoArbitrary Int32 where coarbitrary = coarbitraryIntegral instance CoArbitrary Int64 where coarbitrary = coarbitraryIntegral instance CoArbitrary Word where coarbitrary = coarbitraryIntegral instance CoArbitrary Word8 where coarbitrary = coarbitraryIntegral instance CoArbitrary Word16 where coarbitrary = coarbitraryIntegral instance CoArbitrary Word32 where coarbitrary = coarbitraryIntegral instance CoArbitrary Word64 where coarbitrary = coarbitraryIntegral instance CoArbitrary Char where coarbitrary = coarbitrary . ord instance CoArbitrary Float where coarbitrary = coarbitraryReal instance CoArbitrary Double where coarbitrary = coarbitraryReal -- Coarbitrary instances for container types instance CoArbitrary a => CoArbitrary (Set.Set a) where coarbitrary = coarbitrary. Set.toList instance (CoArbitrary k, CoArbitrary v) => CoArbitrary (Map.Map k v) where coarbitrary = coarbitrary . Map.toList instance CoArbitrary IntSet.IntSet where coarbitrary = coarbitrary . IntSet.toList instance CoArbitrary a => CoArbitrary (IntMap.IntMap a) where coarbitrary = coarbitrary . IntMap.toList instance CoArbitrary a => CoArbitrary (Sequence.Seq a) where coarbitrary = coarbitrary . toList -- CoArbitrary instance for Ziplist instance CoArbitrary a => CoArbitrary (ZipList a) where coarbitrary = coarbitrary . getZipList #ifndef NO_TRANSFORMERS -- CoArbitrary instance for transformers' Functors instance CoArbitrary a => CoArbitrary (Identity a) where coarbitrary = coarbitrary . runIdentity instance CoArbitrary a => CoArbitrary (Constant a b) where coarbitrary = coarbitrary . getConstant #endif -- CoArbitrary instance for Const instance CoArbitrary a => CoArbitrary (Const a b) where coarbitrary = coarbitrary . getConst -- CoArbitrary instances for Monoid instance CoArbitrary a => CoArbitrary (Monoid.Dual a) where coarbitrary = coarbitrary . Monoid.getDual instance (Arbitrary a, CoArbitrary a) => CoArbitrary (Monoid.Endo a) where coarbitrary = coarbitrary . Monoid.appEndo instance CoArbitrary Monoid.All where coarbitrary = coarbitrary . Monoid.getAll instance CoArbitrary Monoid.Any where coarbitrary = coarbitrary . Monoid.getAny instance CoArbitrary a => CoArbitrary (Monoid.Sum a) where coarbitrary = coarbitrary . Monoid.getSum instance CoArbitrary a => CoArbitrary (Monoid.Product a) where coarbitrary = coarbitrary . Monoid.getProduct #if defined(MIN_VERSION_base) #if MIN_VERSION_base(3,0,0) instance CoArbitrary a => CoArbitrary (Monoid.First a) where coarbitrary = coarbitrary . Monoid.getFirst instance CoArbitrary a => CoArbitrary (Monoid.Last a) where coarbitrary = coarbitrary . Monoid.getLast #endif #if MIN_VERSION_base(4,8,0) instance CoArbitrary (f a) => CoArbitrary (Monoid.Alt f a) where coarbitrary = coarbitrary . Monoid.getAlt #endif #endif instance CoArbitrary Version where coarbitrary (Version a b) = coarbitrary (a, b) -- ** Helpers for implementing coarbitrary -- | A 'coarbitrary' implementation for integral numbers. coarbitraryIntegral :: Integral a => a -> Gen b -> Gen b coarbitraryIntegral = variant -- | A 'coarbitrary' implementation for real numbers. coarbitraryReal :: Real a => a -> Gen b -> Gen b coarbitraryReal x = coarbitrary (toRational x) -- | 'coarbitrary' helper for lazy people :-). coarbitraryShow :: Show a => a -> Gen b -> Gen b coarbitraryShow x = coarbitrary (show x) -- | A 'coarbitrary' implementation for enums. coarbitraryEnum :: Enum a => a -> Gen b -> Gen b coarbitraryEnum = variant . fromEnum -------------------------------------------------------------------------- -- ** arbitrary generators -- these are here and not in Gen because of the Arbitrary class constraint -- | Generates a list of a given length. vector :: Arbitrary a => Int -> Gen [a] vector k = vectorOf k arbitrary -- | Generates an ordered list. orderedList :: (Ord a, Arbitrary a) => Gen [a] orderedList = sort `fmap` arbitrary -- | Generates an infinite list. infiniteList :: Arbitrary a => Gen [a] infiniteList = infiniteListOf arbitrary -------------------------------------------------------------------------- -- the end.