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+{-# LANGUAGE FlexibleInstances, GADTs #-}
+module Utilities where
+
+import Test.QuickCheck
+
+import qualified Data.Vector as DV
+import qualified Data.Vector.Generic as DVG
+import qualified Data.Vector.Primitive as DVP
+import qualified Data.Vector.Storable as DVS
+import qualified Data.Vector.Unboxed as DVU
+import qualified Data.Vector.Fusion.Bundle as S
+
+import Control.Monad (foldM, foldM_, zipWithM, zipWithM_)
+import Control.Monad.Trans.Writer
+import Data.Function (on)
+import Data.Functor.Identity
+import Data.List ( sortBy )
+import Data.Monoid
+import Data.Maybe (catMaybes)
+
+instance Show a => Show (S.Bundle v a) where
+    show s = "Data.Vector.Fusion.Bundle.fromList " ++ show (S.toList s)
+
+
+instance Arbitrary a => Arbitrary (DV.Vector a) where
+    arbitrary = fmap DV.fromList arbitrary
+
+instance CoArbitrary a => CoArbitrary (DV.Vector a) where
+    coarbitrary = coarbitrary . DV.toList
+
+instance (Arbitrary a, DVP.Prim a) => Arbitrary (DVP.Vector a) where
+    arbitrary = fmap DVP.fromList arbitrary
+
+instance (CoArbitrary a, DVP.Prim a) => CoArbitrary (DVP.Vector a) where
+    coarbitrary = coarbitrary . DVP.toList
+
+instance (Arbitrary a, DVS.Storable a) => Arbitrary (DVS.Vector a) where
+    arbitrary = fmap DVS.fromList arbitrary
+
+instance (CoArbitrary a, DVS.Storable a) => CoArbitrary (DVS.Vector a) where
+    coarbitrary = coarbitrary . DVS.toList
+
+instance (Arbitrary a, DVU.Unbox a) => Arbitrary (DVU.Vector a) where
+    arbitrary = fmap DVU.fromList arbitrary
+
+instance (CoArbitrary a, DVU.Unbox a) => CoArbitrary (DVU.Vector a) where
+    coarbitrary = coarbitrary . DVU.toList
+
+instance Arbitrary a => Arbitrary (S.Bundle v a) where
+    arbitrary = fmap S.fromList arbitrary
+
+instance CoArbitrary a => CoArbitrary (S.Bundle v a) where
+    coarbitrary = coarbitrary . S.toList
+
+instance (Arbitrary a, Arbitrary b) => Arbitrary (Writer a b) where
+    arbitrary = do b <- arbitrary
+                   a <- arbitrary
+                   return $ writer (b,a)
+
+instance CoArbitrary a => CoArbitrary (Writer a ()) where
+    coarbitrary = coarbitrary . runWriter
+
+class (Testable (EqTest a), Conclusion (EqTest a)) => TestData a where
+  type Model a
+  model :: a -> Model a
+  unmodel :: Model a -> a
+
+  type EqTest a
+  equal :: a -> a -> EqTest a
+
+instance Eq a => TestData (S.Bundle v a) where
+  type Model (S.Bundle v a) = [a]
+  model = S.toList
+  unmodel = S.fromList
+
+  type EqTest (S.Bundle v a) = Property
+  equal x y = property (x == y)
+
+instance Eq a => TestData (DV.Vector a) where
+  type Model (DV.Vector a) = [a]
+  model = DV.toList
+  unmodel = DV.fromList
+
+  type EqTest (DV.Vector a) = Property
+  equal x y = property (x == y)
+
+instance (Eq a, DVP.Prim a) => TestData (DVP.Vector a) where
+  type Model (DVP.Vector a) = [a]
+  model = DVP.toList
+  unmodel = DVP.fromList
+
+  type EqTest (DVP.Vector a) = Property
+  equal x y = property (x == y)
+
+instance (Eq a, DVS.Storable a) => TestData (DVS.Vector a) where
+  type Model (DVS.Vector a) = [a]
+  model = DVS.toList
+  unmodel = DVS.fromList
+
+  type EqTest (DVS.Vector a) = Property
+  equal x y = property (x == y)
+
+instance (Eq a, DVU.Unbox a) => TestData (DVU.Vector a) where
+  type Model (DVU.Vector a) = [a]
+  model = DVU.toList
+  unmodel = DVU.fromList
+
+  type EqTest (DVU.Vector a) = Property
+  equal x y = property (x == y)
+
+#define id_TestData(ty) \
+instance TestData ty where { \
+  type Model ty = ty;        \
+  model = id;                \
+  unmodel = id;              \
+                             \
+  type EqTest ty = Property; \
+  equal x y = property (x == y) }
+
+id_TestData(())
+id_TestData(Bool)
+id_TestData(Int)
+id_TestData(Float)
+id_TestData(Double)
+id_TestData(Ordering)
+
+-- Functorish models
+-- All of these need UndecidableInstances although they are actually well founded. Oh well.
+instance (Eq a, TestData a) => TestData (Maybe a) where
+  type Model (Maybe a) = Maybe (Model a)
+  model = fmap model
+  unmodel = fmap unmodel
+
+  type EqTest (Maybe a) = Property
+  equal x y = property (x == y)
+
+instance (Eq a, TestData a) => TestData [a] where
+  type Model [a] = [Model a]
+  model = fmap model
+  unmodel = fmap unmodel
+
+  type EqTest [a] = Property
+  equal x y = property (x == y)
+
+instance (Eq a, TestData a) => TestData (Identity a) where
+  type Model (Identity a) = Identity (Model a)
+  model = fmap model
+  unmodel = fmap unmodel
+
+  type EqTest (Identity a) = Property
+  equal = (property .) . on (==) runIdentity
+
+instance (Eq a, TestData a, Eq b, TestData b, Monoid a) => TestData (Writer a b) where
+  type Model (Writer a b) = Writer (Model a) (Model b)
+  model = mapWriter model
+  unmodel = mapWriter unmodel
+
+  type EqTest (Writer a b) = Property
+  equal = (property .) . on (==) runWriter
+
+instance (Eq a, Eq b, TestData a, TestData b) => TestData (a,b) where
+  type Model (a,b) = (Model a, Model b)
+  model (a,b) = (model a, model b)
+  unmodel (a,b) = (unmodel a, unmodel b)
+
+  type EqTest (a,b) = Property
+  equal x y = property (x == y)
+
+instance (Eq a, Eq b, Eq c, TestData a, TestData b, TestData c) => TestData (a,b,c) where
+  type Model (a,b,c) = (Model a, Model b, Model c)
+  model (a,b,c) = (model a, model b, model c)
+  unmodel (a,b,c) = (unmodel a, unmodel b, unmodel c)
+
+  type EqTest (a,b,c) = Property
+  equal x y = property (x == y)
+
+instance (Arbitrary a, Show a, TestData a, TestData b) => TestData (a -> b) where
+  type Model (a -> b) = Model a -> Model b
+  model f = model . f . unmodel
+  unmodel f = unmodel . f . model
+
+  type EqTest (a -> b) = a -> EqTest b
+  equal f g x = equal (f x) (g x)
+
+newtype P a = P { unP :: EqTest a }
+
+instance TestData a => Testable (P a) where
+  property (P a) = property a
+
+infix 4 `eq`
+eq :: TestData a => a -> Model a -> P a
+eq x y = P (equal x (unmodel y))
+
+class Conclusion p where
+  type Predicate p
+
+  predicate :: Predicate p -> p -> p
+
+instance Conclusion Property where
+  type Predicate Property = Bool
+
+  predicate = (==>)
+
+instance Conclusion p => Conclusion (a -> p) where
+  type Predicate (a -> p) = a -> Predicate p
+
+  predicate f p = \x -> predicate (f x) (p x)
+
+infixr 0 ===>
+(===>) :: TestData a => Predicate (EqTest a) -> P a -> P a
+p ===> P a = P (predicate p a)
+
+notNull2 _ xs = not $ DVG.null xs
+notNullS2 _ s = not $ S.null s
+
+-- Generators
+index_value_pairs :: Arbitrary a => Int -> Gen [(Int,a)]
+index_value_pairs 0 = return []
+index_value_pairs m = sized $ \n ->
+  do
+    len <- choose (0,n)
+    is <- sequence [choose (0,m-1) | i <- [1..len]]
+    xs <- vector len
+    return $ zip is xs
+
+indices :: Int -> Gen [Int]
+indices 0 = return []
+indices m = sized $ \n ->
+  do
+    len <- choose (0,n)
+    sequence [choose (0,m-1) | i <- [1..len]]
+
+
+-- Additional list functions
+singleton x = [x]
+snoc xs x = xs ++ [x]
+generate n f = [f i | i <- [0 .. n-1]]
+slice i n xs = take n (drop i xs)
+backpermute xs is = map (xs!!) is
+prescanl f z = init . scanl f z
+postscanl f z = tail . scanl f z
+prescanr f z = tail . scanr f z
+postscanr f z = init . scanr f z
+
+accum :: (a -> b -> a) -> [a] -> [(Int,b)] -> [a]
+accum f xs ps = go xs ps' 0
+  where
+    ps' = sortBy (\p q -> compare (fst p) (fst q)) ps
+
+    go (x:xs) ((i,y) : ps) j
+      | i == j     = go (f x y : xs) ps j
+    go (x:xs) ps j = x : go xs ps (j+1)
+    go [] _ _      = []
+
+(//) :: [a] -> [(Int, a)] -> [a]
+xs // ps = go xs ps' 0
+  where
+    ps' = sortBy (\p q -> compare (fst p) (fst q)) ps
+
+    go (x:xs) ((i,y) : ps) j
+      | i == j     = go (y:xs) ps j
+    go (x:xs) ps j = x : go xs ps (j+1)
+    go [] _ _      = []
+
+
+withIndexFirst m f = m (uncurry f) . zip [0..]
+
+imap :: (Int -> a -> a) -> [a] -> [a]
+imap = withIndexFirst map
+
+imapM :: Monad m => (Int -> a -> m a) -> [a] -> m [a]
+imapM = withIndexFirst mapM
+
+imapM_ :: Monad m => (Int -> a -> m b) -> [a] -> m ()
+imapM_ = withIndexFirst mapM_
+
+izipWith :: (Int -> a -> a -> a) -> [a] -> [a] -> [a]
+izipWith = withIndexFirst zipWith
+
+izipWithM :: Monad m => (Int -> a -> a -> m a) -> [a] -> [a] -> m [a]
+izipWithM = withIndexFirst zipWithM
+
+izipWithM_ :: Monad m => (Int -> a -> a -> m b) -> [a] -> [a] -> m ()
+izipWithM_ = withIndexFirst zipWithM_
+
+izipWith3 :: (Int -> a -> a -> a -> a) -> [a] -> [a] -> [a] -> [a]
+izipWith3 = withIndexFirst zipWith3
+
+ifilter :: (Int -> a -> Bool) -> [a] -> [a]
+ifilter f = map snd . withIndexFirst filter f
+
+mapMaybe :: (a -> Maybe b) -> [a] -> [b]
+mapMaybe f = catMaybes . map f
+
+imapMaybe :: (Int -> a -> Maybe b) -> [a] -> [b]
+imapMaybe f = catMaybes . withIndexFirst map f
+
+indexedLeftFold fld f z = fld (uncurry . f) z . zip [0..]
+
+ifoldl :: (a -> Int -> a -> a) -> a -> [a] -> a
+ifoldl = indexedLeftFold foldl
+
+iscanl :: (Int -> a -> b -> a) -> a -> [b] -> [a]
+iscanl f z = scanl (\a (i, b) -> f i a b) z . zip [0..]
+
+iscanr :: (Int -> a -> b -> b) -> b -> [a] -> [b]
+iscanr f z = scanr (uncurry f) z . zip [0..]
+
+ifoldr :: (Int -> a -> b -> b) -> b -> [a] -> b
+ifoldr f z = foldr (uncurry f) z . zip [0..]
+
+ifoldM :: Monad m => (a -> Int -> a -> m a) -> a -> [a] -> m a
+ifoldM = indexedLeftFold foldM
+
+ifoldM_ :: Monad m => (b -> Int -> a -> m b) -> b -> [a] -> m ()
+ifoldM_ = indexedLeftFold foldM_
+
+minIndex :: Ord a => [a] -> Int
+minIndex = fst . foldr1 imin . zip [0..]
+  where
+    imin (i,x) (j,y) | x <= y    = (i,x)
+                     | otherwise = (j,y)
+
+maxIndex :: Ord a => [a] -> Int
+maxIndex = fst . foldr1 imax . zip [0..]
+  where
+    imax (i,x) (j,y) | x >= y    = (i,x)
+                     | otherwise = (j,y)
+
+iterateNM :: Monad m => Int -> (a -> m a) -> a -> m [a]
+iterateNM n f x
+    | n <= 0    = return []
+    | n == 1    = return [x]
+    | otherwise =  do x' <- f x
+                      xs <- iterateNM (n-1) f x'
+                      return (x : xs)
+
+unfoldrM :: Monad m => (b -> m (Maybe (a,b))) -> b -> m [a]
+unfoldrM step b0 = do
+    r <- step b0
+    case r of
+      Nothing    -> return []
+      Just (a,b) -> do as <- unfoldrM step b
+                       return (a : as)
+
+
+limitUnfolds f (theirs, ours)
+    | ours >= 0
+    , Just (out, theirs') <- f theirs = Just (out, (theirs', ours - 1))
+    | otherwise                       = Nothing