-- | -- Module : Simulation.Aivika.Stream -- Copyright : Copyright (c) 2009-2017, David Sorokin <david.sorokin@gmail.com> -- License : BSD3 -- Maintainer : David Sorokin <david.sorokin@gmail.com> -- Stability : experimental -- Tested with: GHC 8.0.1 -- -- The infinite stream of data in time. -- module Simulation.Aivika.Stream (-- * Stream Type Stream(..), -- * Merging and Splitting Stream emptyStream, mergeStreams, mergeQueuedStreams, mergePriorityStreams, concatStreams, concatQueuedStreams, concatPriorityStreams, splitStream, splitStreamQueueing, splitStreamPrioritising, splitStreamFiltering, splitStreamFilteringQueueing, -- * Specifying Identifier streamUsingId, -- * Prefetching and Delaying Stream prefetchStream, delayStream, -- * Stream Arriving arrivalStream, -- * Memoizing, Zipping and Uzipping Stream memoStream, zipStreamSeq, zipStreamParallel, zip3StreamSeq, zip3StreamParallel, unzipStream, streamSeq, streamParallel, -- * Consuming and Sinking Stream consumeStream, sinkStream, -- * Useful Combinators repeatProcess, mapStream, mapStreamM, accumStream, apStream, apStreamM, filterStream, filterStreamM, takeStream, takeStreamWhile, takeStreamWhileM, dropStream, dropStreamWhile, dropStreamWhileM, singletonStream, joinStream, -- * Failover failoverStream, -- * Integrating with Signals signalStream, streamSignal, queuedSignalStream, -- * Utilities leftStream, rightStream, replaceLeftStream, replaceRightStream, partitionEitherStream, -- * Assemblying Streams cloneStream, firstArrivalStream, lastArrivalStream, assembleAccumStream, -- * Debugging traceStream) where import Data.IORef import Data.Maybe import Data.Monoid hiding ((<>)) import Data.Semigroup (Semigroup(..)) import Data.List.NonEmpty (NonEmpty((:|))) import Control.Applicative import Control.Monad import Control.Monad.Trans import Simulation.Aivika.Simulation import Simulation.Aivika.Dynamics import Simulation.Aivika.Event import Simulation.Aivika.Composite import Simulation.Aivika.Cont import Simulation.Aivika.Process import Simulation.Aivika.Signal import Simulation.Aivika.Resource.Base import Simulation.Aivika.QueueStrategy import qualified Simulation.Aivika.Queue.Infinite.Base as IQ import Simulation.Aivika.Internal.Arrival -- | Represents an infinite stream of data in time, -- some kind of the cons cell. newtype Stream a = Cons { runStream :: Process (a, Stream a) -- ^ Run the stream. } instance Functor Stream where fmap = mapStream instance Applicative Stream where pure a = let y = Cons (return (a, y)) in y (<*>) = apStream instance Alternative Stream where empty = emptyStream (<|>) = mergeStreams instance Semigroup (Stream a) where (<>) = mergeStreams sconcat (h :| t) = concatStreams (h : t) instance Monoid (Stream a) where mempty = emptyStream mappend = (<>) mconcat = concatStreams -- | Create a stream that will use the specified process identifier. -- It can be useful to refer to the underlying 'Process' computation which -- can be passivated, interrupted, canceled and so on. See also the -- 'processUsingId' function for more details. streamUsingId :: ProcessId -> Stream a -> Stream a streamUsingId pid (Cons s) = Cons $ processUsingId pid s -- | Memoize the stream so that it would always return the same data -- within the simulation run. memoStream :: Stream a -> Simulation (Stream a) memoStream (Cons s) = do p <- memoProcess $ do ~(x, xs) <- s xs' <- liftSimulation $ memoStream xs return (x, xs') return (Cons p) -- | Zip two streams trying to get data sequentially. zipStreamSeq :: Stream a -> Stream b -> Stream (a, b) zipStreamSeq (Cons sa) (Cons sb) = Cons y where y = do ~(x, xs) <- sa ~(y, ys) <- sb return ((x, y), zipStreamSeq xs ys) -- | Zip two streams trying to get data as soon as possible, -- launching the sub-processes in parallel. zipStreamParallel :: Stream a -> Stream b -> Stream (a, b) zipStreamParallel (Cons sa) (Cons sb) = Cons y where y = do ~((x, xs), (y, ys)) <- zipProcessParallel sa sb return ((x, y), zipStreamParallel xs ys) -- | Zip three streams trying to get data sequentially. zip3StreamSeq :: Stream a -> Stream b -> Stream c -> Stream (a, b, c) zip3StreamSeq (Cons sa) (Cons sb) (Cons sc) = Cons y where y = do ~(x, xs) <- sa ~(y, ys) <- sb ~(z, zs) <- sc return ((x, y, z), zip3StreamSeq xs ys zs) -- | Zip three streams trying to get data as soon as possible, -- launching the sub-processes in parallel. zip3StreamParallel :: Stream a -> Stream b -> Stream c -> Stream (a, b, c) zip3StreamParallel (Cons sa) (Cons sb) (Cons sc) = Cons y where y = do ~((x, xs), (y, ys), (z, zs)) <- zip3ProcessParallel sa sb sc return ((x, y, z), zip3StreamParallel xs ys zs) -- | Unzip the stream. unzipStream :: Stream (a, b) -> Simulation (Stream a, Stream b) unzipStream s = do s' <- memoStream s let sa = mapStream fst s' sb = mapStream snd s' return (sa, sb) -- | To form each new portion of data for the output stream, -- read data sequentially from the input streams. -- -- This is a generalization of 'zipStreamSeq'. streamSeq :: [Stream a] -> Stream [a] streamSeq xs = Cons y where y = do ps <- forM xs runStream return (map fst ps, streamSeq $ map snd ps) -- | To form each new portion of data for the output stream, -- read data from the input streams in parallel. -- -- This is a generalization of 'zipStreamParallel'. streamParallel :: [Stream a] -> Stream [a] streamParallel xs = Cons y where y = do ps <- processParallel $ map runStream xs return (map fst ps, streamParallel $ map snd ps) -- | Return a stream of values generated by the specified process. repeatProcess :: Process a -> Stream a repeatProcess p = Cons y where y = do a <- p return (a, repeatProcess p) -- | Map the stream according the specified function. mapStream :: (a -> b) -> Stream a -> Stream b mapStream f (Cons s) = Cons y where y = do (a, xs) <- s return (f a, mapStream f xs) -- | Compose the stream. mapStreamM :: (a -> Process b) -> Stream a -> Stream b mapStreamM f (Cons s) = Cons y where y = do (a, xs) <- s b <- f a return (b, mapStreamM f xs) -- | Accumulator that outputs a value determined by the supplied function. accumStream :: (acc -> a -> Process (acc, b)) -> acc -> Stream a -> Stream b accumStream f acc xs = Cons $ loop xs acc where loop (Cons s) acc = do (a, xs) <- s (acc', b) <- f acc a return (b, Cons $ loop xs acc') -- | Sequential application. apStream :: Stream (a -> b) -> Stream a -> Stream b apStream (Cons sf) (Cons sa) = Cons y where y = do (f, sf') <- sf (a, sa') <- sa return (f a, apStream sf' sa') -- | Sequential application. apStreamM :: Stream (a -> Process b) -> Stream a -> Stream b apStreamM (Cons sf) (Cons sa) = Cons y where y = do (f, sf') <- sf (a, sa') <- sa x <- f a return (x, apStreamM sf' sa') -- | Filter only those data values that satisfy to the specified predicate. filterStream :: (a -> Bool) -> Stream a -> Stream a filterStream p (Cons s) = Cons y where y = do (a, xs) <- s if p a then return (a, filterStream p xs) else let Cons z = filterStream p xs in z -- | Filter only those data values that satisfy to the specified predicate. filterStreamM :: (a -> Process Bool) -> Stream a -> Stream a filterStreamM p (Cons s) = Cons y where y = do (a, xs) <- s b <- p a if b then return (a, filterStreamM p xs) else let Cons z = filterStreamM p xs in z -- | The stream of 'Left' values. leftStream :: Stream (Either a b) -> Stream a leftStream (Cons s) = Cons y where y = do (a, xs) <- s case a of Left a -> return (a, leftStream xs) Right _ -> let Cons z = leftStream xs in z -- | The stream of 'Right' values. rightStream :: Stream (Either a b) -> Stream b rightStream (Cons s) = Cons y where y = do (a, xs) <- s case a of Left _ -> let Cons z = rightStream xs in z Right a -> return (a, rightStream xs) -- | Replace the 'Left' values. replaceLeftStream :: Stream (Either a b) -> Stream c -> Stream (Either c b) replaceLeftStream (Cons sab) (ys0 @ ~(Cons sc)) = Cons z where z = do (a, xs) <- sab case a of Left _ -> do (b, ys) <- sc return (Left b, replaceLeftStream xs ys) Right a -> return (Right a, replaceLeftStream xs ys0) -- | Replace the 'Right' values. replaceRightStream :: Stream (Either a b) -> Stream c -> Stream (Either a c) replaceRightStream (Cons sab) (ys0 @ ~(Cons sc)) = Cons z where z = do (a, xs) <- sab case a of Right _ -> do (b, ys) <- sc return (Right b, replaceRightStream xs ys) Left a -> return (Left a, replaceRightStream xs ys0) -- | Partition the stream of 'Either' values into two streams. partitionEitherStream :: Stream (Either a b) -> Simulation (Stream a, Stream b) partitionEitherStream s = do s' <- memoStream s return (leftStream s', rightStream s') -- | Split the input stream into the specified number of output streams -- after applying the 'FCFS' strategy for enqueuing the output requests. splitStream :: Int -> Stream a -> Simulation [Stream a] splitStream = splitStreamQueueing FCFS -- | Split the input stream into the specified number of output streams. -- -- If you don't know what the strategy to apply, then you probably -- need the 'FCFS' strategy, or function 'splitStream' that -- does namely this. splitStreamQueueing :: EnqueueStrategy s => s -- ^ the strategy applied for enqueuing the output requests -> Int -- ^ the number of output streams -> Stream a -- ^ the input stream -> Simulation [Stream a] -- ^ the splitted output streams splitStreamQueueing s n x = do ref <- liftIO $ newIORef x res <- newResource s 1 let reader = usingResource res $ do p <- liftIO $ readIORef ref (a, xs) <- runStream p liftIO $ writeIORef ref xs return a return $ map (\i -> repeatProcess reader) [1..n] -- | Split the input stream into a list of output streams -- using the specified priorities. splitStreamPrioritising :: PriorityQueueStrategy s p => s -- ^ the strategy applied for enqueuing the output requests -> [Stream p] -- ^ the streams of priorities -> Stream a -- ^ the input stream -> Simulation [Stream a] -- ^ the splitted output streams splitStreamPrioritising s ps x = do ref <- liftIO $ newIORef x res <- newResource s 1 let stream (Cons p) = Cons z where z = do (p', ps) <- p a <- usingResourceWithPriority res p' $ do p <- liftIO $ readIORef ref (a, xs) <- runStream p liftIO $ writeIORef ref xs return a return (a, stream ps) return $ map stream ps -- | Split the input stream into the specified number of output streams -- after filtering and applying the 'FCFS' strategy for enqueuing the output requests. splitStreamFiltering :: [a -> Event Bool] -> Stream a -> Simulation [Stream a] splitStreamFiltering = splitStreamFilteringQueueing FCFS -- | Split the input stream into the specified number of output streams after filtering. -- -- If you don't know what the strategy to apply, then you probably -- need the 'FCFS' strategy, or function 'splitStreamFiltering' that -- does namely this. splitStreamFilteringQueueing :: EnqueueStrategy s => s -- ^ the strategy applied for enqueuing the output requests -> [a -> Event Bool] -- ^ the filters for output streams -> Stream a -- ^ the input stream -> Simulation [Stream a] -- ^ the splitted output streams splitStreamFilteringQueueing s preds x = do ref <- liftIO $ newIORef x res <- newResource s 1 let reader pred = do a <- usingResource res $ do p <- liftIO $ readIORef ref (a, xs) <- runStream p liftEvent $ do f <- pred a if f then do liftIO $ writeIORef ref xs return $ Just a else do liftIO $ writeIORef ref $ Cons (return (a, xs)) return Nothing case a of Just a -> return a Nothing -> reader pred return $ map (repeatProcess . reader) preds -- | Concatenate the input streams applying the 'FCFS' strategy and -- producing one output stream. concatStreams :: [Stream a] -> Stream a concatStreams = concatQueuedStreams FCFS -- | Concatenate the input streams producing one output stream. -- -- If you don't know what the strategy to apply, then you probably -- need the 'FCFS' strategy, or function 'concatStreams' that -- does namely this. concatQueuedStreams :: EnqueueStrategy s => s -- ^ the strategy applied for enqueuing the input data -> [Stream a] -- ^ the input stream -> Stream a -- ^ the combined output stream concatQueuedStreams s streams = Cons z where z = do reading <- liftSimulation $ newResourceWithMaxCount FCFS 0 (Just 1) writing <- liftSimulation $ newResourceWithMaxCount s 1 (Just 1) conting <- liftSimulation $ newResourceWithMaxCount FCFS 0 (Just 1) ref <- liftIO $ newIORef Nothing let writer p = do (a, xs) <- runStream p requestResource writing liftIO $ writeIORef ref (Just a) releaseResource reading requestResource conting writer xs reader = do requestResource reading Just a <- liftIO $ readIORef ref liftIO $ writeIORef ref Nothing releaseResource writing return a forM_ streams $ spawnProcess . writer a <- reader let xs = repeatProcess (releaseResource conting >> reader) return (a, xs) -- | Concatenate the input priority streams producing one output stream. concatPriorityStreams :: PriorityQueueStrategy s p => s -- ^ the strategy applied for enqueuing the input data -> [Stream (p, a)] -- ^ the input stream -> Stream a -- ^ the combined output stream concatPriorityStreams s streams = Cons z where z = do reading <- liftSimulation $ newResourceWithMaxCount FCFS 0 (Just 1) writing <- liftSimulation $ newResourceWithMaxCount s 1 (Just 1) conting <- liftSimulation $ newResourceWithMaxCount FCFS 0 (Just 1) ref <- liftIO $ newIORef Nothing let writer p = do ((priority, a), xs) <- runStream p requestResourceWithPriority writing priority liftIO $ writeIORef ref (Just a) releaseResource reading requestResource conting writer xs reader = do requestResource reading Just a <- liftIO $ readIORef ref liftIO $ writeIORef ref Nothing releaseResource writing return a forM_ streams $ spawnProcess . writer a <- reader let xs = repeatProcess (releaseResource conting >> reader) return (a, xs) -- | Merge two streams applying the 'FCFS' strategy for enqueuing the input data. mergeStreams :: Stream a -> Stream a -> Stream a mergeStreams = mergeQueuedStreams FCFS -- | Merge two streams. -- -- If you don't know what the strategy to apply, then you probably -- need the 'FCFS' strategy, or function 'mergeStreams' that -- does namely this. mergeQueuedStreams :: EnqueueStrategy s => s -- ^ the strategy applied for enqueuing the input data -> Stream a -- ^ the fist input stream -> Stream a -- ^ the second input stream -> Stream a -- ^ the output combined stream mergeQueuedStreams s x y = concatQueuedStreams s [x, y] -- | Merge two priority streams. mergePriorityStreams :: PriorityQueueStrategy s p => s -- ^ the strategy applied for enqueuing the input data -> Stream (p, a) -- ^ the fist input stream -> Stream (p, a) -- ^ the second input stream -> Stream a -- ^ the output combined stream mergePriorityStreams s x y = concatPriorityStreams s [x, y] -- | An empty stream that never returns data. emptyStream :: Stream a emptyStream = Cons neverProcess -- | Consume the stream. It returns a process that infinitely reads data -- from the stream and then redirects them to the provided function. -- It is useful for modeling the process of enqueueing data in the queue -- from the input stream. consumeStream :: (a -> Process ()) -> Stream a -> Process () consumeStream f = p where p (Cons s) = do (a, xs) <- s f a p xs -- | Sink the stream. It returns a process that infinitely reads data -- from the stream. The resulting computation can be a moving force -- to simulate the whole system of the interconnected streams and -- processors. sinkStream :: Stream a -> Process () sinkStream = p where p (Cons s) = do (a, xs) <- s p xs -- | Prefetch the input stream requesting for one more data item in advance -- while the last received item is not yet fully processed in the chain of -- streams, usually by the processors. -- -- You can think of this as the prefetched stream could place its latest -- data item in some temporary space for later use, which is very useful -- for modeling a sequence of separate and independent work places. prefetchStream :: Stream a -> Stream a prefetchStream s = Cons z where z = do reading <- liftSimulation $ newResourceWithMaxCount FCFS 0 (Just 1) writing <- liftSimulation $ newResourceWithMaxCount FCFS 1 (Just 1) ref <- liftIO $ newIORef Nothing let writer p = do (a, xs) <- runStream p requestResource writing liftIO $ writeIORef ref (Just a) releaseResource reading writer xs reader = do requestResource reading Just a <- liftIO $ readIORef ref liftIO $ writeIORef ref Nothing releaseResource writing return a spawnProcess $ writer s runStream $ repeatProcess reader -- | Like 'signalStream' but allows specifying an arbitrary queue instead of the unbounded queue. queuedSignalStream :: (a -> Event ()) -- ^ enqueue -> Process a -- ^ dequeue -> Signal a -- ^ the input signal -> Composite (Stream a) -- ^ the output stream queuedSignalStream enqueue dequeue s = do h <- liftEvent $ handleSignal s enqueue disposableComposite h return $ repeatProcess dequeue -- | Return a stream of values triggered by the specified signal. -- -- Since the time at which the values of the stream are requested for may differ from -- the time at which the signal is triggered, it can be useful to apply the 'arrivalSignal' -- function to add the information about the time points at which the signal was -- actually received. -- -- The point is that the 'Stream' is requested outside, while the 'Signal' is triggered -- inside. They are different by nature. The former is passive, while the latter is active. -- -- The resulting stream may be a root of space leak as it uses an internal unbounded queue to store -- the values received from the signal. The oldest value is dequeued each time we request -- the stream and it is returned within the computation. Consider using 'queuedSignalStream' that -- allows specifying the bounded queue in case of need. signalStream :: Signal a -> Composite (Stream a) signalStream s = do q <- liftSimulation IQ.newFCFSQueue queuedSignalStream (IQ.enqueue q) (IQ.dequeue q) s -- | Return a computation of the disposable signal that triggers values from the specified stream, -- each time the next value of the stream is received within the underlying 'Process' -- computation. streamSignal :: Stream a -> Composite (Signal a) streamSignal z = do s <- liftSimulation newSignalSource pid <- liftSimulation newProcessId liftEvent $ runProcessUsingId pid $ consumeStream (liftEvent . triggerSignal s) z disposableComposite $ DisposableEvent $ cancelProcessWithId pid return $ publishSignal s -- | Transform a stream so that the resulting stream returns a sequence of arrivals -- saving the information about the time points at which the original stream items -- were received by demand. arrivalStream :: Stream a -> Stream (Arrival a) arrivalStream s = Cons $ loop s Nothing where loop s t0 = do (a, xs) <- runStream s t <- liftDynamics time let b = Arrival { arrivalValue = a, arrivalTime = t, arrivalDelay = case t0 of Nothing -> Nothing Just t0 -> Just (t - t0) } return (b, Cons $ loop xs (Just t)) -- | Delay the stream by one step using the specified initial value. delayStream :: a -> Stream a -> Stream a delayStream a0 s = Cons $ return (a0, s) -- | Return a stream consisting of exactly one element and inifinite tail. singletonStream :: a -> Stream a singletonStream a = Cons $ return (a, emptyStream) -- | Removes one level of the computation, projecting its bound stream into the outer level. joinStream :: Process (Stream a) -> Stream a joinStream m = Cons $ m >>= runStream -- | Takes the next stream from the list after the current stream fails because of cancelling the underlying process. failoverStream :: [Stream a] -> Stream a failoverStream ps = Cons z where z = do reading <- liftSimulation $ newResourceWithMaxCount FCFS 0 (Just 1) writing <- liftSimulation $ newResourceWithMaxCount FCFS 0 (Just 1) ref <- liftIO $ newIORef Nothing pid <- processId let writer p = do requestResource writing pid' <- processId (a, xs) <- finallyProcess (runStream p) $ liftEvent $ do cancelled' <- processCancelled pid' when cancelled' $ releaseResourceWithinEvent writing liftIO $ writeIORef ref (Just a) releaseResource reading writer xs reader = do releaseResource writing requestResource reading Just a <- liftIO $ readIORef ref liftIO $ writeIORef ref Nothing return a loop [] = return () loop (p: ps) = do pid' <- processId h' <- liftEvent $ handleSignal (processCancelling pid) $ \() -> cancelProcessWithId pid' finallyProcess (writer p) $ liftEvent $ do disposeEvent h' cancelled <- processCancelled pid unless cancelled $ do cancelled' <- processCancelled pid' unless cancelled' $ error "Expected the sub-process to be cancelled: failoverStream" runProcess $ loop ps liftEvent $ runProcess $ loop ps runStream $ repeatProcess reader -- | Return the prefix of the stream of the specified length. takeStream :: Int -> Stream a -> Stream a takeStream n s | n <= 0 = emptyStream | otherwise = Cons $ do (a, xs) <- runStream s return (a, takeStream (n - 1) xs) -- | Return the longest prefix of the stream of elements that satisfy the predicate. takeStreamWhile :: (a -> Bool) -> Stream a -> Stream a takeStreamWhile p s = Cons $ do (a, xs) <- runStream s if p a then return (a, takeStreamWhile p xs) else neverProcess -- | Return the longest prefix of the stream of elements that satisfy the computation. takeStreamWhileM :: (a -> Process Bool) -> Stream a -> Stream a takeStreamWhileM p s = Cons $ do (a, xs) <- runStream s f <- p a if f then return (a, takeStreamWhileM p xs) else neverProcess -- | Return the suffix of the stream after the specified first elements. dropStream :: Int -> Stream a -> Stream a dropStream n s | n <= 0 = s | otherwise = Cons $ do (a, xs) <- runStream s runStream $ dropStream (n - 1) xs -- | Return the suffix of the stream of elements remaining after 'takeStreamWhile'. dropStreamWhile :: (a -> Bool) -> Stream a -> Stream a dropStreamWhile p s = Cons $ do (a, xs) <- runStream s if p a then runStream $ dropStreamWhile p xs else return (a, xs) -- | Return the suffix of the stream of elements remaining after 'takeStreamWhileM'. dropStreamWhileM :: (a -> Process Bool) -> Stream a -> Stream a dropStreamWhileM p s = Cons $ do (a, xs) <- runStream s f <- p a if f then runStream $ dropStreamWhileM p xs else return (a, xs) -- | Create the specified number of equivalent clones of the input stream. cloneStream :: Int -> Stream a -> Simulation [Stream a] cloneStream n s = do qs <- forM [1..n] $ \i -> IQ.newFCFSQueue rs <- newFCFSResource 1 ref <- liftIO $ newIORef s let reader m q = do a <- liftEvent $ IQ.tryDequeue q case a of Just a -> return a Nothing -> usingResource rs $ do a <- liftEvent $ IQ.tryDequeue q case a of Just a -> return a Nothing -> do s <- liftIO $ readIORef ref (a, xs) <- runStream s liftIO $ writeIORef ref xs forM_ (zip [1..] qs) $ \(i, q) -> unless (i == m) $ liftEvent $ IQ.enqueue q a return a forM (zip [1..] qs) $ \(i, q) -> return $ repeatProcess $ reader i q -- | Return a stream of first arrivals after assembling the specified number of elements. firstArrivalStream :: Int -> Stream a -> Stream a firstArrivalStream n s = assembleAccumStream f (1, Nothing) s where f (i, a0) a = let a0' = Just $ fromMaybe a a0 in if i `mod` n == 0 then return ((1, Nothing), a0') else return ((i + 1, a0'), Nothing) -- | Return a stream of last arrivals after assembling the specified number of elements. lastArrivalStream :: Int -> Stream a -> Stream a lastArrivalStream n s = assembleAccumStream f 1 s where f i a = if i `mod` n == 0 then return (1, Just a) else return (i + 1, Nothing) -- | Assemble an accumulated stream using the supplied function. assembleAccumStream :: (acc -> a -> Process (acc, Maybe b)) -> acc -> Stream a -> Stream b assembleAccumStream f acc s = mapStream fromJust $ filterStream isJust $ accumStream f acc s -- | Show the debug messages with the current simulation time. traceStream :: Maybe String -- ^ the request message -> Maybe String -- ^ the response message -> Stream a -- ^ a stream -> Stream a traceStream request response s = Cons $ loop s where loop s = do (a, xs) <- case request of Nothing -> runStream s Just message -> traceProcess message $ runStream s case response of Nothing -> return (a, Cons $ loop xs) Just message -> traceProcess message $ return (a, Cons $ loop xs)