    {-# LANGUAGE MagicHash, UnboxedTuples #-}
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Control.Parallel.Strategies
    -- Copyright   :  (c) The University of Glasgow 2001-2010
    -- License     :  BSD-style (see the file libraries/base/LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- Parallel Evaluation Strategies, or Strategies for short, provide
    -- ways to express parallel computations.  Strategies have the following
    -- key features:
    --
    --  * Strategies express /deterministic parallelism/:
    --    the result of the program is unaffected by evaluating in parallel.
    --    The parallel tasks evaluated by a Strategy may have no side effects.
    --    For non-deterministic parallel programming, see "Control.Concurrent".
    --
    --  * Strategies let you separate the description of the parallelism from the
    --    logic of your program, enabling modular parallelism.  The basic idea
    --    is to build a lazy data structure representing the computation, and
    --    then write a Strategy that describes how to traverse the data structure
    --    and evaluate components of it sequentially or in parallel.
    --
    --  * Strategies are /compositional/: larger strategies can be built
    --    by gluing together smaller ones.
    --
    --  * 'Monad' and 'Applicative' instances are provided, for quickly building
    --    strategies that involve traversing structures in a regular way.
    --
    -- For API history and changes in this release, see "Control.Parallel.Strategies#history".

    -----------------------------------------------------------------------------

    module Control.Parallel.Strategies (
             -- * The strategy type
             Strategy

             -- * Application of strategies
           , using             -- :: a -> Strategy a -> a
           , withStrategy      -- :: Strategy a -> a -> a

             -- * Composition of strategies
           , dot               -- :: Strategy a -> Strategy a -> Strategy a

             -- * Basic strategies
           , r0                -- :: Strategy a
           , rseq
           , rdeepseq          -- :: NFData a => Strategy a
           , rpar              -- :: Strategy a
           , rparWith          -- :: Strategy a -> Strategy a

             -- * Injection of sequential strategies
           , evalSeq           -- :: Seq.Strategy a -> Strategy a
           , SeqStrategy

             -- * Strategies for traversable data types
           , evalTraversable   -- :: Traversable t => Strategy a -> Strategy (t a)
           , parTraversable

             -- * Strategies for lists
           , evalList          -- :: Strategy a -> Strategy [a]
           , parList
           , evalListN         -- :: Int -> Strategy a -> Strategy [a]
           , parListN
           , evalListNth       -- :: Int -> Strategy a -> Strategy [a]
           , parListNth
           , evalListSplitAt   -- :: Int -> Strategy [a] -> Strategy [a] -> Strategy [a]
           , parListSplitAt
           , parListChunk
           , parMap

             -- ** Strategies for lazy lists
           , evalBuffer        -- :: Int -> Strategy a -> Strategy [a]
           , parBuffer

             -- * Strategies for tuples

             -- | Evaluate the components of a tuple according to the
             -- given strategies.

           , evalTuple2        -- :: Strategy a -> ... -> Strategy (a,...)
           , evalTuple3
           , evalTuple4
           , evalTuple5
           , evalTuple6
           , evalTuple7
           , evalTuple8
           , evalTuple9

           -- | Evaluate the components of a tuple in parallel according to
           -- the given strategies.

           , parTuple2         -- :: Strategy a -> ... -> Strategy (a,...)
           , parTuple3
           , parTuple4
           , parTuple5
           , parTuple6
           , parTuple7
           , parTuple8
           , parTuple9

             -- * Strategic function application
           , ($|)              -- :: (a -> b) -> Strategy a -> a -> b
           , ($||)
           , (.|)              -- :: (b -> c) -> Strategy b -> (a -> b) -> a -> c
           , (.||)
           , (-|)              -- :: (a -> b) -> Strategy b -> (b -> c) -> a -> c
           , (-||)

             -- * For Strategy programmers
           , Eval              -- instances: Monad, Functor, Applicative
           , runEval           -- :: Eval a -> a
           ,

        -- * API History

        -- $history

        -- * Backwards compatibility

        -- | These functions and types are all deprecated, and will be
        -- removed in a future release.  In all cases they have been
        -- either renamed or replaced with equivalent functionality.

        Done, demanding, sparking, (>|), (>||),
        rwhnf, unEval,
        seqTraverse, parTraverse,
        seqList,
        seqPair, parPair,
        seqTriple, parTriple,

        -- * For API completeness

        -- | so users of 'rdeepseq' aren't required to import Control.DeepSeq:
        NFData
      ) where

    import Data.Traversable
    import Control.Applicative
    import Control.Parallel
    import Control.DeepSeq
    import Control.Monad

    import qualified Control.Seq

    import GHC.Exts

    infixr 9 `dot`     -- same as (.)
    infixl 0 `using`   -- lowest precedence and associate to the left

    -- -----------------------------------------------------------------------------
    -- Eval monad (isomorphic to Lift monad from MonadLib 3.6.1)

    -- | 'Eval' is a Monad that makes it easier to define parallel
    -- strategies.  It is a strict identity monad: that is, in
    --
    --  > m >>= f
    --
    -- @m@ is evaluated before the result is passed to @f@.
    --
    --  > instance Monad Eval where
    --  >   return  = Done
    --  >   m >>= k = case m of
    --  >               Done x -> k x
    --
    -- If you wanted to construct a 'Strategy' for a pair that sparked the
    -- first component in parallel and then evaluated the second
    -- component, you could write
    --
    -- > myStrat :: Strategy (a,b)
    -- > myStrat (a,b) = do { a' <- rpar a; b' <- rseq b; return (a',b') }
    --
    -- Alternatively, you could write this more compactly using the
    -- Applicative style as
    --
    -- > myStrat (a,b) = (,) <$> rpar a <*> rseq b

    -- More examples, using the Applicative instance:
    --
    -- > parList :: Strategy a -> Strategy [a]
    -- > parList strat = traverse (rpar `dot` strat))
    --
    -- > evalPair :: Strategy a -> Strategy b -> Strategy (a,b)
    -- > evalPair f g (a,b) = pure (,) <$> f a <*> g b
    --

    #if __GLASGOW_HASKELL__ >= 702

    newtype Eval a = Eval (State# RealWorld -> (# State# RealWorld, a #))
      -- GHC 7.2.1 added the seq# and spark# primitives, that we use in
      -- the Eval monad implementation in order to get the correct
      -- strictness behaviour.

    -- | Pull the result out of the monad.
    runEval :: Eval a -> a
    runEval (Eval x) = case x realWorld# of (# _, a #) -> a

    instance Monad Eval where
      return x = Eval $ \s -> (# s, x #)
      Eval x >>= k = Eval $ \s -> case x s of
                                    (# s', a #) -> case k a of
                                                          Eval f -> f s'
    #else

    data Eval a = Done a

    -- | Pull the result out of the monad.
    runEval :: Eval a -> a
    runEval (Done x) = x

    instance Monad Eval where
      return x = Done x
      Done x >>= k = lazy (k x)   -- Note: pattern 'Done x' makes '>>=' strict

    {-# RULES "lazy Done" forall x . lazy (Done x) = Done x #-}

    #endif

    instance Functor Eval where
      fmap = liftM

    instance Applicative Eval where
      (<*>) = ap
      pure  = return

    -- The Eval monad satisfies the monad laws.
    --
    -- (1) Left identity:
    --     return x >>= f ==> Done x >>= f ==> f x
    --
    -- (2) Right identity:
    --     (i)  m >>= return =*> Done u >>= return
    --                       ==> return u
    --                       ==> Done u <*= m
    --     (ii) m >>= return =*> undefined >>= return
    --                       ==> undefined <*= m
    --
    -- (3) Associativity:
    --     (i)  (m >>= f) >>= g =*> (Done u >>= f) >>= g
    --                          ==> f u >>= g <== (\x -> f x >>= g) u
    --                                        <== Done u >>= (\x -> f x >>= g)
    --                                        <*= m >>= (\x -> f x >>= g)
    --     (ii) (m >>= f) >>= g =*> (undefined >>= f) >>= g
    --                          ==> undefined >>= g
    --                          ==> undefined <== undefined >>= (\x -> f x >>= g)
    --                                        <*= m >>= (\x -> f x >>= g)

    -- -----------------------------------------------------------------------------
    -- Strategies

    -- | A 'Strategy' is a function that embodies a parallel evaluation strategy.
    -- The function traverses (parts of) its argument, evaluating subexpressions
    -- in parallel or in sequence.
    --
    -- A 'Strategy' may do an arbitrary amount of evaluation of its
    -- argument, but should not return a value different from the one it
    -- was passed.
    --
    -- Parallel computations may be discarded by the runtime system if the
    -- program no longer requires their result, which is why a 'Strategy'
    -- function returns a new value equivalent to the old value.  The
    -- intention is that the program applies the 'Strategy' to a
    -- structure, and then uses the returned value, discarding the old
    -- value.  This idiom is expressed by the 'using' function.
    --
    type Strategy a = a -> Eval a

    -- | Evaluate a value using the given 'Strategy'.
    --
    -- > x `using` s = runEval (s x)
    --
    using :: a -> Strategy a -> a
    x `using` strat = runEval (strat x)

    -- | evaluate a value using the given 'Strategy'.  This is simply
    -- 'using' with the arguments reversed.
    --
    withStrategy :: Strategy a -> a -> a
    withStrategy = flip using

    -- | Compose two strategies sequentially.
    -- This is the analogue to function composition on strategies.
    --
    -- > strat2 `dot` strat1 == strat2 . withStrategy strat1
    --
    dot :: Strategy a -> Strategy a -> Strategy a
    strat2 `dot` strat1 = strat2 . runEval . strat1

    -- Proof of strat2 `dot` strat1 == strat2 . withStrategy strat1
    --
    --    strat2 . withStrategy strat1
    -- == \x -> strat2 (withStrategy strat1 x)
    -- == \x -> strat2 (x `using` strat1)
    -- == \x -> strat2 (runEval (strat1 x))
    -- == \x -> (strat2 . runEval . strat1) x
    -- == strat2 `dot` strat1

    -- One might be tempted to think that 'dot' is equivalent to '(<=<)',
    -- the right-to-left Kleisli composition in the Eval monad, because
    -- '(<=<)' can take the type @Strategy a -> Strategy a -> Strategy a@
    -- and intuitively does what 'dot' does: First apply the strategy to the
    -- right then the one to the left. However, there is a subtle difference
    -- in strictness, witnessed by the following example:
    --
    -- > (r0 `dot` rseq) undefined == Done undefined
    -- > (r0 <=< rseq) undefined == undefined
    --

    -- | Inject a sequential strategy (ie. coerce a sequential strategy
    -- to a general strategy).
    --
    -- Thanks to 'evalSeq', the type @Control.Seq.Strategy a@ is a subtype
    -- of @'Strategy' a@.
    evalSeq :: SeqStrategy a -> Strategy a
    evalSeq strat x = strat x `pseq` return x

    -- | a name for @Control.Seq.Strategy@, for documetnation only.
    type SeqStrategy a = Control.Seq.Strategy a

    -- --------------------------------------------------------------------------
    -- Basic strategies (some imported from SeqStrategies)

    -- | 'r0' performs *no* evaluation.
    --
    -- > r0 == evalSeq Control.Seq.r0
    --
    r0 :: Strategy a
    r0 x = return x

    -- Proof of r0 == evalSeq Control.Seq.r0
    --
    --    evalSeq Control.Seq.r0
    -- == \x -> Control.Seq.r0 x `pseq` return x
    -- == \x -> Control.Seq.Done `pseq` return x
    -- == \x -> return x
    -- == r0

    -- | 'rseq' evaluates its argument to weak head normal form.
    --
    -- > rseq == evalSeq Control.Seq.rseq
    --
    rseq :: Strategy a
    #if __GLASGOW_HASKELL__ >= 702
    rseq x = Eval $ \s -> seq# x s
    #else
    rseq x = x `seq` return x
    #endif

    -- Proof of rseq == evalSeq Control.Seq.rseq
    --
    --    evalSeq Control.Seq.rseq
    -- == \x -> Control.Seq.rseq x `pseq` return x
    -- == \x -> (x `seq` Control.Seq.Done) `pseq` return x
    -- == \x -> x `pseq` return x
    -- == rseq

    -- | 'rdeepseq' fully evaluates its argument.
    --
    -- > rdeepseq == evalSeq Control.Seq.rdeepseq
    --
    rdeepseq :: NFData a => Strategy a
    rdeepseq x = do rseq (rnf x); return x

    -- Proof of rdeepseq == evalSeq Control.Seq.rdeepseq
    --
    --    evalSeq Control.Seq.rdeepseq
    -- == \x -> Control.Seq.rdeepseq x `pseq` return x
    -- == \x -> (x `deepseq` Control.Seq.Done) `pseq` return x
    -- == \x -> (rnf x `seq` Control.Seq.Done) `pseq` return x
    -- == \x -> rnf x `pseq` return x
    -- == rdeepseq

    -- | 'rpar' sparks its argument (for evaluation in parallel).
    rpar :: a -> Eval a
    #if __GLASGOW_HASKELL__ >= 702
    rpar  x = Eval $ \s -> spark# x s
    #else
    rpar  x = case (par# x) of { _ -> Done x }
    #endif
    {-# INLINE rpar  #-}

    -- | instead of saying @rpar `dot` strat@, you can say
    -- @rparWith strat@.  Compared to 'rpar', 'rparWith'
    --
    --  * does not exit the `Eval` monad
    --
    --  * does not have a built-in `rseq`, so for example `rparWith r0`
    --    behaves as you might expect (it is a strategy that creates a
    --    spark that does no evaluation).
    --
    --
    rparWith :: Strategy a -> Strategy a
    #if __GLASGOW_HASKELL__ >= 702
    rparWith s a = do l <- rpar r; return (case l of Lift x -> x)
      where r = case s a of
                  Eval f -> case f realWorld# of
                              (# _, a' #) -> Lift a'

    data Lift a = Lift a
    #else
    rparWith s a = do l <- rpar (s a); return (case l of Done x -> x)
    #endif

    -- --------------------------------------------------------------------------
    -- Strategy combinators for Traversable data types

    -- | Evaluate the elements of a traversable data structure
    -- according to the given strategy.
    evalTraversable :: Traversable t => Strategy a -> Strategy (t a)
    evalTraversable = traverse
    {-# INLINE evalTraversable #-}

    -- | Like 'evalTraversable' but evaluates all elements in parallel.
    parTraversable :: Traversable t => Strategy a -> Strategy (t a)
    parTraversable strat = evalTraversable (rparWith strat)
    {-# INLINE parTraversable #-}

    -- --------------------------------------------------------------------------
    -- Strategies for lists

    -- | Evaluate each element of a list according to the given strategy.
    --  Equivalent to 'evalTraversable' at the list type.
    evalList :: Strategy a -> Strategy [a]
    evalList = evalTraversable
    -- Alternative explicitly recursive definition:
    -- evalList strat []     = return []
    -- evalList strat (x:xs) = strat x >>= \x' ->
    --                         evalList strat xs >>= \xs' ->
    --                         return (x':xs')

    -- | Evaluate each element of a list in parallel according to given strategy.
    --  Equivalent to 'parTraversable' at the list type.
    parList :: Strategy a -> Strategy [a]
    parList = parTraversable
    -- Alternative definition via evalList:
    -- parList strat = evalList (rparWith strat)

    -- | @'evaListSplitAt' n stratPref stratSuff@ evaluates the prefix
    -- (of length @n@) of a list according to @stratPref@ and its the suffix
    -- according to @stratSuff@.
    evalListSplitAt :: Int -> Strategy [a] -> Strategy [a] -> Strategy [a]
    evalListSplitAt n stratPref stratSuff xs
      = let (ys,zs) = splitAt n xs in
        stratPref ys >>= \ys' ->
        stratSuff zs >>= \zs' ->
        return (ys' ++ zs')

    -- | Like 'evalListSplitAt' but evaluates both sublists in parallel.
    parListSplitAt :: Int -> Strategy [a] -> Strategy [a] -> Strategy [a]
    parListSplitAt n stratPref stratSuff = evalListSplitAt n (rparWith stratPref) (rparWith stratSuff)

    -- | Evaluate the first n elements of a list according to the given strategy.
    evalListN :: Int -> Strategy a -> Strategy [a]
    evalListN n strat = evalListSplitAt n (evalList strat) r0

    -- | Like 'evalListN' but evaluates the first n elements in parallel.
    parListN :: Int -> Strategy a -> Strategy [a]
    parListN n strat = evalListN n (rparWith strat)

    -- | Evaluate the nth element of a list (if there is such) according to
    -- the given strategy.
    -- The spine of the list up to the nth element is evaluated as a side effect.
    evalListNth :: Int -> Strategy a -> Strategy [a]
    evalListNth n strat = evalListSplitAt n r0 (evalListN 1 strat)

    -- | Like 'evalListN' but evaluates the nth element in parallel.
    parListNth :: Int -> Strategy a -> Strategy [a]
    parListNth n strat = evalListNth n (rparWith strat)

    -- | Divides a list into chunks, and applies the strategy
    -- @'evalList' strat@ to each chunk in parallel.
    --
    -- It is expected that this function will be replaced by a more
    -- generic clustering infrastructure in the future.
    --
    -- If the chunk size is 1 or less, 'parListChunk' is equivalent to
    -- 'parList'
    --
    parListChunk :: Int -> Strategy a -> Strategy [a]
    parListChunk n strat xs
      | n <= 1    = parList strat xs
      | otherwise = concat `fmap` parList (evalList strat) (chunk n xs)

    chunk :: Int -> [a] -> [[a]]
    chunk _ [] = []
    chunk n xs = as : chunk n bs where (as,bs) = splitAt n xs

    -- Non-compositional version of 'parList', evaluating list elements
    -- to weak head normal form.
    -- Not to be exported; used for optimisation.

    -- | DEPRECATED: use @'parList' 'rseq'@ instead
    parListWHNF :: Strategy [a]
    parListWHNF xs = go xs `pseq` return xs
      where -- go :: [a] -> [a]
               go []     = []
               go (y:ys) = y `par` go ys

    -- The non-compositional 'parListWHNF' might be more efficient than its
    -- more compositional counterpart; use RULES to do the specialisation.

    {-# RULES
     "parList/rseq" parList rseq = parListWHNF
     #-}

    -- --------------------------------------------------------------------------
    -- Convenience

    -- | A combination of 'parList' and 'map', encapsulating a common pattern:
    --
    -- > parMap strat f = withStrategy (parList strat) . map f
    --
    parMap :: Strategy b -> (a -> b) -> [a] -> [b]
    parMap strat f = (`using` parList strat) . map f

    -- --------------------------------------------------------------------------
    -- Strategies for lazy lists

    -- List-based non-compositional rolling buffer strategy, evaluating list
    -- elements to weak head normal form.
    -- Not to be exported; used in evalBuffer and for optimisation.
    evalBufferWHNF :: Int -> Strategy [a]
    evalBufferWHNF n0 xs0 = return (ret xs0 (start n0 xs0))
      where -- ret :: [a] -> [a] -> [a]
               ret (x:xs) (y:ys) = y `pseq` (x : ret xs ys)
               ret xs     _      = xs

            -- start :: Int -> [a] -> [a]
               start 0   ys     = ys
               start !_n []     = []
               start !n  (y:ys) = y `pseq` start (n-1) ys

    -- | 'evalBuffer' is a rolling buffer strategy combinator for (lazy) lists.
    --
    -- 'evalBuffer' is not as compositional as the type suggests. In fact,
    -- it evaluates list elements at least to weak head normal form,
    -- disregarding a strategy argument 'r0'.
    --
    -- > evalBuffer n r0 == evalBuffer n rseq
    --
    evalBuffer :: Int -> Strategy a -> Strategy [a]
    evalBuffer n strat =  evalBufferWHNF n . map (withStrategy strat)

    -- Like evalBufferWHNF but sparks the list elements when pushing them
    -- into the buffer.
    -- Not to be exported; used in parBuffer and for optimisation.
    parBufferWHNF :: Int -> Strategy [a]
    parBufferWHNF n0 xs0 = return (ret xs0 (start n0 xs0))
      where -- ret :: [a] -> [a] -> [a]
               ret (x:xs) (y:ys) = y `par` (x : ret xs ys)
               ret xs     _      = xs

            -- start :: Int -> [a] -> [a]
               start 0   ys     = ys
               start !_n []     = []
               start !n  (y:ys) = y `par` start (n-1) ys

    -- | Like 'evalBuffer' but evaluates the list elements in parallel when
    -- pushing them into the buffer.
    parBuffer :: Int -> Strategy a -> Strategy [a]
    parBuffer n strat = parBufferWHNF n . map (withStrategy strat)
    -- Alternative definition via evalBuffer (may compromise firing of RULES):
    -- parBuffer n strat = evalBuffer n (rparWith strat)

    -- Deforest the intermediate list in parBuffer/evalBuffer when it is
    -- unnecessary:

    {-# RULES
    "evalBuffer/rseq"  forall n . evalBuffer  n rseq = evalBufferWHNF n
    "parBuffer/rseq"   forall n . parBuffer   n rseq = parBufferWHNF  n
     #-}

    -- --------------------------------------------------------------------------
    -- Strategies for tuples

    evalTuple2 :: Strategy a -> Strategy b -> Strategy (a,b)
    evalTuple2 strat1 strat2 (x1,x2) =
      pure (,) <*> strat1 x1 <*> strat2 x2

    evalTuple3 :: Strategy a -> Strategy b -> Strategy c -> Strategy (a,b,c)
    evalTuple3 strat1 strat2 strat3 (x1,x2,x3) =
      pure (,,) <*> strat1 x1 <*> strat2 x2 <*> strat3 x3

    evalTuple4 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy (a,b,c,d)
    evalTuple4 strat1 strat2 strat3 strat4 (x1,x2,x3,x4) =
      pure (,,,) <*> strat1 x1 <*> strat2 x2 <*> strat3 x3 <*> strat4 x4

    evalTuple5 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy (a,b,c,d,e)
    evalTuple5 strat1 strat2 strat3 strat4 strat5 (x1,x2,x3,x4,x5) =
      pure (,,,,) <*> strat1 x1 <*> strat2 x2 <*> strat3 x3 <*> strat4 x4 <*> strat5 x5

    evalTuple6 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy f -> Strategy (a,b,c,d,e,f)
    evalTuple6 strat1 strat2 strat3 strat4 strat5 strat6 (x1,x2,x3,x4,x5,x6) =
      pure (,,,,,) <*> strat1 x1 <*> strat2 x2 <*> strat3 x3 <*> strat4 x4 <*> strat5 x5 <*> strat6 x6

    evalTuple7 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy f -> Strategy g -> Strategy (a,b,c,d,e,f,g)
    evalTuple7 strat1 strat2 strat3 strat4 strat5 strat6 strat7 (x1,x2,x3,x4,x5,x6,x7) =
      pure (,,,,,,) <*> strat1 x1 <*> strat2 x2 <*> strat3 x3 <*> strat4 x4 <*> strat5 x5 <*> strat6 x6 <*> strat7 x7

    evalTuple8 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy f -> Strategy g -> Strategy h -> Strategy (a,b,c,d,e,f,g,h)
    evalTuple8 strat1 strat2 strat3 strat4 strat5 strat6 strat7 strat8 (x1,x2,x3,x4,x5,x6,x7,x8) =
      pure (,,,,,,,) <*> strat1 x1 <*> strat2 x2 <*> strat3 x3 <*> strat4 x4 <*> strat5 x5 <*> strat6 x6 <*> strat7 x7 <*> strat8 x8

    evalTuple9 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy f -> Strategy g -> Strategy h -> Strategy i -> Strategy (a,b,c,d,e,f,g,h,i)
    evalTuple9 strat1 strat2 strat3 strat4 strat5 strat6 strat7 strat8 strat9 (x1,x2,x3,x4,x5,x6,x7,x8,x9) =
      pure (,,,,,,,,) <*> strat1 x1 <*> strat2 x2 <*> strat3 x3 <*> strat4 x4 <*> strat5 x5 <*> strat6 x6 <*> strat7 x7 <*> strat8 x8 <*> strat9 x9

    parTuple2 :: Strategy a -> Strategy b -> Strategy (a,b)
    parTuple2 strat1 strat2 =
      evalTuple2 (rparWith strat1) (rparWith strat2)

    parTuple3 :: Strategy a -> Strategy b -> Strategy c -> Strategy (a,b,c)
    parTuple3 strat1 strat2 strat3 =
      evalTuple3 (rparWith strat1) (rparWith strat2) (rparWith strat3)

    parTuple4 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy (a,b,c,d)
    parTuple4 strat1 strat2 strat3 strat4 =
      evalTuple4 (rparWith strat1) (rparWith strat2) (rparWith strat3) (rparWith strat4)

    parTuple5 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy (a,b,c,d,e)
    parTuple5 strat1 strat2 strat3 strat4 strat5 =
      evalTuple5 (rparWith strat1) (rparWith strat2) (rparWith strat3) (rparWith strat4) (rparWith strat5)

    parTuple6 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy f -> Strategy (a,b,c,d,e,f)
    parTuple6 strat1 strat2 strat3 strat4 strat5 strat6 =
      evalTuple6 (rparWith strat1) (rparWith strat2) (rparWith strat3) (rparWith strat4) (rparWith strat5) (rparWith strat6)

    parTuple7 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy f -> Strategy g -> Strategy (a,b,c,d,e,f,g)
    parTuple7 strat1 strat2 strat3 strat4 strat5 strat6 strat7 =
      evalTuple7 (rparWith strat1) (rparWith strat2) (rparWith strat3) (rparWith strat4) (rparWith strat5) (rparWith strat6) (rparWith strat7)

    parTuple8 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy f -> Strategy g -> Strategy h -> Strategy (a,b,c,d,e,f,g,h)
    parTuple8 strat1 strat2 strat3 strat4 strat5 strat6 strat7 strat8 =
      evalTuple8 (rparWith strat1) (rparWith strat2) (rparWith strat3) (rparWith strat4) (rparWith strat5) (rparWith strat6) (rparWith strat7) (rparWith strat8)

    parTuple9 :: Strategy a -> Strategy b -> Strategy c -> Strategy d -> Strategy e -> Strategy f -> Strategy g -> Strategy h -> Strategy i -> Strategy (a,b,c,d,e,f,g,h,i)
    parTuple9 strat1 strat2 strat3 strat4 strat5 strat6 strat7 strat8 strat9 =
      evalTuple9 (rparWith strat1) (rparWith strat2) (rparWith strat3) (rparWith strat4) (rparWith strat5) (rparWith strat6) (rparWith strat7) (rparWith strat8) (rparWith strat9)

    -- --------------------------------------------------------------------------
    -- Strategic function application

    {-
    These are very handy when writing pipeline parallelism asa sequence of
    @$@, @$|@ and @$||@'s. There is no need of naming intermediate values
    in this case. The separation of algorithm from strategy is achieved by
    allowing strategies only as second arguments to @$|@ and @$||@.
    -}

    -- | Sequential function application. The argument is evaluated using
    --   the given strategy before it is given to the function.
    ($|) :: (a -> b) -> Strategy a -> a -> b
    f $| s  = \ x -> let z = x `using` s in z `pseq` f z

    -- | Parallel function application. The argument is evaluated using
    -- the given strategy, in parallel with the function application.
    ($||) :: (a -> b) -> Strategy a -> a -> b
    f $|| s = \ x -> let z = x `using` s in z `par` f z

    -- | Sequential function composition. The result of
    -- the second function is evaluated using the given strategy,
    -- and then given to the first function.
    (.|) :: (b -> c) -> Strategy b -> (a -> b) -> (a -> c)
    (.|) f s g = \ x -> let z = g x `using` s in
                        z `pseq` f z

    -- | Parallel function composition. The result of the second
    -- function is evaluated using the given strategy,
    -- in parallel with the application of the first function.
    (.||) :: (b -> c) -> Strategy b -> (a -> b) -> (a -> c)
    (.||) f s g = \ x -> let z = g x `using` s in
                        z `par` f z

    -- | Sequential inverse function composition,
    -- for those who read their programs from left to right.
    -- The result of the first function is evaluated using the
    -- given strategy, and then given to the second function.
    (-|) :: (a -> b) -> Strategy b -> (b -> c) -> (a -> c)
    (-|) f s g = \ x -> let z = f x `using` s in
                        z `pseq` g z

    -- | Parallel inverse function composition,
    -- for those who read their programs from left to right.
    -- The result of the first function is evaluated using the
    -- given strategy, in parallel with the application of the
    -- second function.
    (-||) :: (a -> b) -> Strategy b -> (b -> c) -> (a -> c)
    (-||) f s g = \ x -> let z = f x `using` s in
                        z `par` g z

    -- -----------------------------------------------------------------------------
    -- Old/deprecated stuff

    {-# DEPRECATED Done "The Strategy type is now a -> Eval a, not a -> Done" #-}
    -- | DEPRECCATED: replaced by the 'Eval' monad
    type Done = ()

    {-# DEPRECATED demanding "Use pseq or $| instead" #-}
    -- | DEPRECATED: Use 'pseq' or '$|' instead
    demanding :: a -> Done -> a
    demanding = flip pseq

    {-# DEPRECATED sparking "Use par or $|| instead" #-}
    -- | DEPRECATED: Use 'par' or '$||' instead
    sparking :: a -> Done -> a
    sparking  = flip par

    {-# DEPRECATED (>|) "Use pseq or $| instead" #-}
    -- | DEPRECATED: Use 'pseq' or '$|' instead
    (>|) :: Done -> Done -> Done
    (>|) = Prelude.seq

    {-# DEPRECATED (>||) "Use par or $|| instead" #-}
    -- | DEPRECATED: Use 'par' or '$||' instead
    (>||) :: Done -> Done -> Done
    (>||) = par

    {-# DEPRECATED rwhnf "renamed to rseq" #-}
    -- | DEPRECATED: renamed to 'rseq'
    rwhnf :: Strategy a
    rwhnf = rseq

    {-# DEPRECATED seqTraverse "renamed to evalTraversable" #-}
    -- | DEPRECATED: renamed to 'evalTraversable'
    seqTraverse :: Traversable t => Strategy a -> Strategy (t a)
    seqTraverse = evalTraversable

    {-# DEPRECATED parTraverse "renamed to parTraversable" #-}
    -- | DEPRECATED: renamed to 'parTraversable'
    parTraverse :: Traversable t => Strategy a -> Strategy (t a)
    parTraverse = parTraversable

    {-# DEPRECATED parListWHNF "use (parList rseq) instead" #-}

    {-# DEPRECATED seqList "renamed to evalList" #-}
    -- | DEPRECATED: renamed to 'evalList'
    seqList :: Strategy a -> Strategy [a]
    seqList = evalList

    {-# DEPRECATED seqPair "renamed to evalTuple2" #-}
    -- | DEPRECATED: renamed to 'evalTuple2'
    seqPair :: Strategy a -> Strategy b -> Strategy (a,b)
    seqPair = evalTuple2

    {-# DEPRECATED parPair "renamed to parTuple2" #-}
    -- | DEPRECATED: renamed to 'parTuple2'
    parPair :: Strategy a -> Strategy b -> Strategy (a,b)
    parPair = parTuple2

    {-# DEPRECATED seqTriple "renamed to evalTuple3" #-}
    -- | DEPRECATED: renamed to 'evalTuple3'
    seqTriple :: Strategy a -> Strategy b -> Strategy c -> Strategy (a,b,c)
    seqTriple = evalTuple3

    {-# DEPRECATED parTriple "renamed to parTuple3" #-}
    -- | DEPRECATED: renamed to 'parTuple3'
    parTriple :: Strategy a -> Strategy b -> Strategy c -> Strategy (a,b,c)
    parTriple = parTuple3

    {-# DEPRECATED unEval "renamed to runEval" #-}
    -- | DEPRECATED: renamed to 'runEval'
    unEval :: Eval a -> a
    unEval = runEval

    {- $history #history#

    The strategies library has a long history.  What follows is a
    summary of how the current design evolved, and is mostly of
    interest to those who are familiar with an older version, or need
    to adapt old code to use the newer API.

    Version 1.x

      The original Strategies design is described in /Algorithm + Strategy = Parallelism/ <http://www.macs.hw.ac.uk/~dsg/gph/papers/html/Strategies/strategies.html>
      and the code was written by
         Phil Trinder, Hans-Wolfgang Loidl, Kevin Hammond et al.

    Version 2.x

    Later, during work on the shared-memory implementation of
    parallelism in GHC, we discovered that the original formulation of
    Strategies had some problems, in particular it lead to space leaks
    and difficulties expressing speculative parallelism.  Details are in
    the paper /Runtime Support for Multicore Haskell/ <http://www.haskell.org/~simonmar/papers/multicore-ghc.pdf>.

    This module has been rewritten in version 2. The main change is to
    the 'Strategy a' type synonym, which was previously @a -> Done@ and
    is now @a -> Eval a@.  This change helps to fix the space leak described
    in \"Runtime Support for Multicore Haskell\".  The problem is that
    the runtime will currently retain the memory referenced by all
    sparks, until they are evaluated.  Hence, we must arrange to
    evaluate all the sparks eventually, just in case they aren't
    evaluated in parallel, so that they don't cause a space leak.  This
    is why we must return a \"new\" value after applying a 'Strategy',
    so that the application can evaluate each spark created by the
    'Strategy'.

    The simple rule is this: you /must/ use the result of applying
    a 'Strategy' if the strategy creates parallel sparks, and you
    should probably discard the the original value.  If you don't
    do this, currently it may result in a space leak.  In the
    future (GHC 6.14), it will probably result in lost parallelism
    instead, as we plan to change GHC so that unreferenced sparks
    are discarded rather than retained (we can't make this change
    until most code is switched over to this new version of
    Strategies, because code using the old verison of Strategies
    would be broken by the change in policy).

    The other changes in version 2.x are:

      * Strategies can now be defined using a convenient Monad/Applicative
        type, 'Eval'.  e.g. @parList s = traverse (Par . (``using`` s))@

      * 'parList' has been generalised to 'parTraverse', which works on
        any 'Traversable' type, and similarly 'seqList' has been generalised
        to 'seqTraverse'

      * 'parList' and 'parBuffer' have versions specialised to 'rwhnf',
        and there are transformation rules that automatically translate
        e.g. @parList rwnhf@ into a call to the optimised version.

      * 'NFData' has been moved to @Control.DeepSeq@ in the @deepseq@
        package.  Note that since the 'Strategy' type changed, 'rnf'
        is no longer a 'Strategy': use 'rdeepseq' instead.

    Version 2.1 moved NFData into a separate package, @deepseq@.

    Version 2.2 changed the type of Strategy to @a -> Eval a@, and
    re-introduced the @r0@ strategy which was missing in version 2.1.

    Version 2.3 simplified the @Eval@ type, so that @Eval@ is now just
    the strict identity monad.  This change and various other
    improvements and refactorings are thanks to Patrick Maier who
    noticed that @Eval@ didn't satisfy the monad laws, and that a
    simpler version would fix that problem.

    (version 2.3 was not released on Hackage).

    Version 3 introduced a major overhaul of the API, to match what is
    presented in the paper

      /Seq no More: Better Strategies for Parallel Haskell/
      <http://www.haskell.org/~simonmar/papers/strategies.pdf>

    The major differenes in the API are:

     * The addition of Sequential strategies ("Control.Seq") as
       a composable means for specifying sequential evaluation.

     * Changes to the naming scheme: 'rwhnf' renamed to 'rseq',
       'seqList' renamed to 'evalList', 'seqPair' renamed to
       'evalTuple2',

    The naming scheme is now as follows:

      * Basic polymorphic strategies (of type @'Strategy' a@) are called @r...@.
        Examples: 'r0', 'rseq', 'rpar', 'rdeepseq'.

      * A strategy combinator for a particular type constructor
        or constructor class @T@ is called @evalT...@, @parT...@ or @seqT...@.

      * The @seqT...@ combinators (residing in module
         "Control.Seq") yield sequential strategies.
         Thus, @seqT...@ combinators cannot spark, nor can the sequential
         strategies to which they may be applied.
         Examples: 'seqTuple2', 'seqListN', 'seqFoldable'.

      * The @evalT...@ combinators do not spark themselves, yet they may
         be applied to strategies that do spark. (They may also be applied
         to non-sparking strategies; however, in that case the corresponding
         @seqT...@ combinator might be a better choice.)
         Examples: 'evalTuple2', 'evalListN', 'evalTraversable'.

      * The @parT...@ combinators, which are derived from their @evalT...@
         counterparts, do spark. They may be applied to all strategies,
         whether sparking or not.
         Examples: 'parTuple2', 'parListN', 'parTraversable'.

      * An exception to the type driven naming scheme are 'evalBuffer' and
         'parBuffer', which are not named after their type constructor (lists)
         but after their function (rolling buffer of fixed size).
    -}