{-# LANGUAGE TupleSections #-} -- | -- Module : Control.Auto.Effects -- Description : Accessing, executing, and manipulating underyling monadic -- effects. -- Copyright : (c) Justin Le 2015 -- License : MIT -- Maintainer : justin@jle.im -- Stability : unstable -- Portability : portable -- -- This module exports the preferred ways of interacting with the -- underlying 'Monad' of the 'Auto' type, including accessing, executing, -- and manipulating such effects. -- module Control.Auto.Effects ( -- * Running effects -- ** Continually arrM , effect -- ** From inputs , effects -- ** On 'Blip's , arrMB , effectB , execB -- ** One-time effects , cache , execOnce , cache_ , execOnce_ -- * Hoists , hoistA , generalizeA -- * Specific underlying monads -- $monads -- ** 'ReaderT' -- $reader , runReaderA , sealReader , sealReader_ , readerA -- ** 'WriterT' -- $writer , writerA , runWriterA -- ** 'StateT' -- $state , sealState , sealState_ , runStateA , stateA , accumA -- ** 'Traversable' , runTraversableA -- ** 'IO' , catchA ) where import Control.Applicative import Control.Auto.Blip import Control.Auto.Core import Control.Auto.Generate import Control.Category import Control.Exception import Control.Monad hiding (mapM, mapM_) import Control.Monad.Trans.Reader (ReaderT(ReaderT), runReaderT) import Control.Monad.Trans.State (StateT(StateT), runStateT) import Control.Monad.Trans.Writer (WriterT(WriterT), runWriterT) import Data.Foldable import Data.Monoid import Data.Serialize import Data.Traversable import Prelude hiding ((.), id, mapM, mapM_) -- | The very first output executes a monadic action and uses the result as -- the output, ignoring all input. From then on, it persistently outputs -- that first result. -- -- Like 'execOnce', except outputs the result of the action instead of -- ignoring it. -- -- Useful for loading resources in IO on the "first step", like -- a word list: -- -- @ -- dictionary :: Auto IO a [String] -- dictionary = cache (lines <$> readFile "wordlist.txt") -- @ -- cache :: (Serialize b, Monad m) => m b -- ^ monadic action to execute and use the result of -> Auto m a b cache m = snd <$> iteratorM (_cacheF m) (False, undefined) -- | The non-resumable/non-serializable version of 'cache'. Every time the -- 'Auto' is deserialized/reloaded, it re-executes the action to retrieve -- the result again. -- -- Useful in cases where you want to "re-load" an expensive resource on -- every startup, instead of saving it to in the save states. -- -- @ -- dictionary :: Auto IO a [String] -- dictionary = cache_ (lines <$> readFile "dictionary.txt") -- @ cache_ :: Monad m => m b -- ^ monadic action to execute and use the result of -> Auto m a b cache_ m = snd <$> iteratorM_ (_cacheF m) (False, undefined) _cacheF :: Monad m => m b -> (Bool, b) -> m (Bool, b) _cacheF m (False, _) = liftM (True,) m _cacheF _ (True , x) = return (True, x) {-# INLINE _cacheF #-} -- | Always outputs '()', but when asked for the first output, executes the -- given monadic action. -- -- Pretty much like 'cache', but always outputs '()'. -- execOnce :: Monad m => m b -- ^ monadic action to execute; result discared -> Auto m a () execOnce m = mkStateM (\_ -> _execOnceF m) False -- | The non-resumable/non-serializable version of 'execOnce'. Every time -- the 'Auto' is deserialized/reloaded, the action is re-executed again. execOnce_ :: Monad m => m b -- ^ monadic action to execute; result discared -> Auto m a () execOnce_ m = mkStateM_ (\_ -> _execOnceF m) False _execOnceF :: Monad m => m a -> Bool -> m ((), Bool) _execOnceF m = go where go False = liftM (const ((), True)) m go _ = return ((), True) -- | The input stream is a stream of monadic actions, and the output stream -- is the result of their executions, through executing them. effects :: Monad m => Auto m (m a) a effects = arrM id -- | Applies the given "monadic function" (function returning a monadic -- action) to every incoming item; the result is the result of executing -- the action returned. -- -- Note that this essentially lifts a "Kleisli arrow"; it's like 'arr', but -- for "monadic functions" instead of normal functions: -- -- @ -- arr :: (a -> b) -> Auto m a b -- arrM :: (a -> m b) -> Auto m a b -- @ -- -- prop> arrM f . arrM g == arrM (f <=< g) -- -- One neat trick you can do is that you can "tag on effects" to a normal -- 'Auto' by using '*>' from "Control.Applicative". For example: -- -- >>> let a = arrM print *> sumFrom 0 -- >>> ys <- streamAuto a [1..5] -- 1 -- IO output -- 2 -- 3 -- 4 -- 5 -- >>> ys -- [1,3,6,10,15] -- the result -- -- Here, @a@ behaves "just like" @'sumFrom' 0@...except, when you step it, -- it prints out to stdout as a side-effect. We just gave automatic -- stdout logging behavior! -- arrM :: (a -> m b) -- ^ monadic function -> Auto m a b arrM = mkFuncM {-# INLINE arrM #-} -- | Maps one blip stream to another; replaces every emitted value with the -- result of the monadic function, executing it to get the result. arrMB :: Monad m => (a -> m b) -> Auto m (Blip a) (Blip b) arrMB = perBlip . arrM {-# INLINE arrMB #-} -- | Maps one blip stream to another; replaces every emitted value with the -- result of a fixed monadic action, run every time an emitted value is -- received. effectB :: Monad m => m b -> Auto m (Blip a) (Blip b) effectB = perBlip . effect {-# INLINE effectB #-} -- | Outputs the identical blip stream that is received; however, every -- time it sees an emitted value, executes the given monadic action on the -- side. execB :: Monad m => m b -> Auto m (Blip a) (Blip a) execB mx = perBlip (arrM $ \x -> mx >> return x) {-# INLINE execB #-} -- $monads -- -- 'Auto's can be run in the context of an underlying monad; this means -- that, instead of just being a straight-up @[a] -> [b]@, pairing up each -- @a@ with a @b@, you can actually attach a "context" to the @b@-making -- process, in order to enrich your streaming logic with things like -- a global read-only environment, a global sink, or global mutable state. -- The main benefit is that these things all /compose/ like any other -- 'Auto'...they compose with '.', you can use 'Applicative', 'Arrow', -- etc., and they'll combine properly. -- -- For the most part, a good general philosophy is to only have a "small -- part" of your program over a monad. You might have a small region of -- your program that would benefit from having a global environment, a -- small region of your program that would benefit from having a sink, or -- a small program that would benefit from global mutable state. Exercise -- good style and write maintainable code by limiting the effectful parts -- to the bare minimum essential, then using 'runReaderA', 'sealReader', -- 'runWriterA', 'sealStateA', etc. to "close off" or seal the effects, and -- use the 'Auto' like a normal one without effects. -- -- In this section are combinators for working with specific underlying -- monads...and a little description on how each might be useful. Remember -- to use them wisely! Adding any underlying monad causes the complexity -- of reasoning with your code to go up (depending on which monad), so make -- sure that you get a real gain before using these! -- $reader -- 'Reader', or 'ReaderT' is probably one of the most useful underlying -- monads to work with. Basically, instead of @[a] -> [b]@, you have @[a] -- -> r -> [b]@. Generate @b@'s, but with an @r@ parameter you can always -- access. In practice, you can use 'Reader' to hide a lot of boilerplate -- threading, add an extra "side input" channel, or compose 'Auto's with -- a /static guarantee/ that all 'Auto's composed will use the /same/ @r@ -- environment. -- -- Using 'effect', you have access to the environment: -- -- @ -- 'effect' 'ask' :: 'MonadReader' r m => 'Auto' m a r -- @ -- -- Which is an 'Auto' where the only thing it does is continually output -- the environment @r@. You can throw this into any /proc/ block over -- 'Reader', and you have a way to bring your environment "into scope": -- -- @ -- env <- 'effect' 'ask' -< () -- @ -- -- -- For a use case example, you might have: -- -- @ -- foo :: Auto m (Int, Database) Bool -- bar :: Auto m (Bool, Database) Int -- baz :: Auto m (Bool, Database) String -- @ -- -- Where every 'Auto' use a @Database@ parameter to do their job...and it -- only makes sense when all of them are composed under the same -- @Database@. You can use normal proc notation: -- -- @ -- full :: Auto m (Int, Database) String -- full = proc (inp, db) -> do -- fo <- foo -< (inp, db) -- br <- bar -< (fo, db) -- bz <- baz -< (fo, db) -- id -< replicate br bz -- @ -- -- Or, you can put them all under 'Reader' and have the parameters pass -- implicitly: -- -- @ -- fullR :: Auto (ReaderT Database m) Int String -- fullR = proc inp -> do -- fo <- readerA foo -< inp -- br <- readerA bar -< fo -- bz <- readerA baz -< fo -- id -< replicate br bz -- @ -- -- You can recover the original behavior of @full@ by using 'runReaderA' to -- "unroll" the implicit argument: -- -- @ -- full' :: Auto m (Int, Database) String -- full' = runReaderA fullR -- @ -- -- You can also "seal" @fullR@ so that it always runs with the same -- @Database@ at every step using 'sealReader': -- -- @ -- fullSealed :: Database -> Auto m Int String -- fullSealed = sealReader fullR -- @ -- -- @fullSealed db@ will now assume that @foo@, @bar@, and @baz@ all get the -- same environment forever when they are stepped/streamed. -- | "Unrolls" the underlying 'ReaderT' of an 'Auto' into an 'Auto' that -- takes in the input "environment" every turn in addition to the normal -- input. -- -- So you can use any @'ReaderT' r m@ as if it were an @m@. Useful if you -- want to compose and create some isolated 'Auto's with access to an -- underlying environment, but not your entire program. -- -- Also just simply useful as a convenient way to use an 'Auto' over -- 'Reader' with 'stepAuto' and friends. -- -- When used with @'Reader' r@, it turns an @'Auto' ('Reader' r) a b@ into -- an @'Auto'' (a, r) b@. runReaderA :: Monad m => Auto (ReaderT r m) a b -- ^ 'Auto' run over global environment -> Auto m (a, r) b -- ^ 'Auto' receiving environments runReaderA a = mkAutoM (runReaderA <$> resumeAuto a) (saveAuto a) $ \(x, r) -> do (y, a') <- runReaderT (stepAuto a x) r return (y, runReaderA a') -- | Takes an 'Auto' that operates under the context of a read-only -- environment, an environment value, and turns it into a normal 'Auto' -- that always "sees" that value when it asks for one. -- -- >>> let a = effect ask :: Auto (Reader b) a b -- >>> let rdr = streamAuto' a [1..5] :: Reader b [b] -- >>> runReader rdr "hey" -- ["hey", "hey", "hey", "hey", "hey"] -- -- Useful if you wanted to use it inside/composed with an 'Auto' that does -- not have a global environment: -- -- @ -- bar :: Auto' Int String -- bar = proc x -> do -- hey <- sealReader (effect ask) "hey" -< () -- id -< hey ++ show x -- @ -- -- >>> streamAuto' bar [1..5] -- ["hey1", "hey2", "hey3", "hey4", "hey5"] -- -- Note that this version serializes the given @r@ environment, so that -- every time the 'Auto' is reloaded/resumed, it resumes with the -- originally given @r@ environment, ignoring whatever @r@ is given to it -- when trying to resume it. If this is not the behavior you want, use -- 'sealReader_'. -- -- 'Reader' is convenient because it allows you to "chain" and "compose" -- 'Auto's with a common environment, instead of explicitly passing in -- values every time. For a convenient way of generating 'Auto's under -- 'ReaderT', and also for some motivating examples, see 'readerA' and -- 'runReaderA'. -- sealReader :: (Monad m, Serialize r) => Auto (ReaderT r m) a b -- ^ 'Auto' run over 'Reader' -> r -- ^ the perpetual environment -> Auto m a b sealReader a r = mkAutoM (sealReader <$> resumeAuto a <*> get) (saveAuto a *> put r) $ \x -> do (y, a') <- runReaderT (stepAuto a x) r return (y, sealReader a' r) -- | The non-resuming/non-serializing version of 'sealReader'. Does not -- serialize/reload the @r@ environment, so that whenever you "resume" the -- 'Auto', it uses the new @r@ given when you are trying to resume, instead -- of loading the originally given one. sealReader_ :: Monad m => Auto (ReaderT r m) a b -- ^ 'Auto' run over 'Reader' -> r -- ^ the perpetual environment -> Auto m a b sealReader_ a r = mkAutoM (sealReader_ <$> resumeAuto a <*> pure r) (saveAuto a) $ \x -> do (y, a') <- runReaderT (stepAuto a x) r return (y, sealReader_ a' r) -- | Transforms an 'Auto' on two input streams ( a "normal input" stream -- @a@ and an "environment input stream" @r@) into an 'Auto' on one input -- stream @a@ with an underlying environment @r@ through a 'Reader' monad. -- -- Why is this useful? Well, if you have several 'Auto's that all take in -- a side @r@ stream, and you want to convey that every single one should -- get the /same/ @r@ at every step, you can instead have all of them pull -- from a common underlying global environment. -- -- Note: Function is the inverse of 'runReaderA': -- -- @ -- 'readerA' . 'runReaderA' == 'id' -- 'runReaderA' . 'readerA' == 'id' -- @ readerA :: Monad m => Auto m (a, r) b -- ^ 'Auto' receiving an environment. -> Auto (ReaderT r m) a b -- ^ 'Auto' run over an environment. readerA a = mkAutoM (readerA <$> resumeAuto a) (saveAuto a) $ \x -> ReaderT $ \r -> do (y, a') <- stepAuto a (x, r) return (y, readerA a') -- $writer -- 'WriterT' gives you a shared "sink" to dump data into. You can dump in -- data by using -- -- @ -- 'arrM' 'tell' :: 'MonadWriter' w m => 'Auto' m w () -- 'effect' . 'tell' :: 'MonadWriter' w m => w -> 'Auto' m a () -- @ -- -- @ -- foo :: Auto (Writer (Sum Int)) Int Int -- foo = effect (tell 1) *> effect (tell 1) *> sumFrom 0 -- @ -- -- >>> let fooWriter = streamAuto foo -- >>> runWriter $ fooWriter [1..10] -- ([1,3,6,10,15,21,28,36,45,55], Sum 20) -- -- @foo@ increments an underlying counter twice every time it is stepped; -- its "result" is just the cumulative sum of the inputs. -- -- If you have several 'Auto's that all output some "side-channel" value -- that is just all accumulated at the end, and you want to implicitly -- accumulate it all, you can just have them all dump into an underlying -- 'Writer' sink instead of aggregating them explicitly. -- -- For example: -- -- @ -- foo :: Auto m Int (Bool, [String]) -- bar :: Auto m Bool (Int, [String]) -- baz :: Auto m Bool (String, [String]) -- @ -- -- Each of these has a "logging output" that should be aggregated all at -- the end. -- -- One way you can do this is by using an explicit proc block: -- -- @ -- full :: Auto m Int (String, [String]) -- full = proc inp -> do -- x <- sumFrom 0 -< inp -- (fo, foW) <- foo -< inp + x -- (br, brW) <- bar -< fo -- (bz, bzW) <- baz -< fo -- id -< (replicate br bz, foW <> brW <> bzW) -- @ -- -- Or, you can handle the extra output implicitly using 'writerA': -- -- @ -- fullW :: Auto (WriterT [String] m) Int String -- fullW = proc inp -> do -- x <- sumFrom 0 -< inp -- fo <- writerA foo -< inp + x -- br <- writerA bar -< fo -- bz <- writerA baz -< fo -- id -< replicate br bz -- @ -- -- Note that @'sumFrom' 0@ still works the same and doesn't interfere, -- logging nothing. -- -- You can recover the original @full@ with 'runWriterA', which -- "unwraps" the underlying 'Writer': -- -- @ -- full' :: Auto m Int (String, [String]) -- full' = runWriterA fullW -- @ -- -- | "Unrolls" the underlying @'WriterT' w m@ 'Monad', so that an 'Auto' -- that takes in a stream of @a@ and outputs a stream of @b@ will now -- output a stream @(b, w)@, where @w@ is the "new log" of the underlying -- 'Writer' at every step. -- -- Examples: -- -- @ -- foo :: Auto (Writer (Sum Int)) Int Int -- foo = effect (tell 1) *> effect (tell 1) *> sumFrom 0 -- @ -- -- >>> let fooWriter = streamAuto foo -- >>> runWriter $ fooWriter [1..10] -- ([1,3,6,10,15,21,28,36,45,55], Sum 20) -- -- @foo@ increments an underlying counter twice every time it is stepped; -- its "result" is just the cumulative sum of the inputs. -- -- When we "stream" it, we get a @[Int] -> 'Writer' (Sum Int) -- [Int]@...which we can give an input list and 'runWriter' it, getting -- a list of outputs and a "final accumulator state" of 10, for stepping it -- ten times. -- -- However, if we use 'runWriterA' before streaming it, we get: -- -- >>> let fooW = runWriterA foo -- >>> streamAuto' fooW [1..10] -- [ (1 , Sum 2), (3 , Sum 2), (6 , Sum 2) -- , (10, Sum 2), (15, Sum 2), (21, Sum 2), -- ... -- -- Instead of accumulating it between steps, we get to "catch" the 'Writer' -- output at every individual step. -- -- We can write and compose our own 'Auto's under 'Writer', using the -- convenience of a shared accumulator, and then "use them" with other -- 'Auto's: -- -- @ -- bar :: Auto' Int Int -- bar = proc x -> do -- (y, w) <- runWriterA foo -< x -- blah <- blah -< w -- @ -- -- And now you have access to the underlying accumulator of @foo@ to -- access. There, @w@ represents the continually updating accumulator -- under @foo@, and will be different/growing at every "step". -- -- For a convenient way to /create/ an 'Auto' under 'WriterT', see -- 'writerA'. runWriterA :: (Monad m, Monoid w) => Auto (WriterT w m) a b -> Auto m a (b, w) runWriterA a = mkAutoM (runWriterA <$> resumeAuto a) (saveAuto a) $ \x -> do ((y, a'), w) <- runWriterT (stepAuto a x) return ((y, w), runWriterA a') -- | Transforms an 'Auto' on with two output streams (a "normal output -- stream" @b@, and a "logging output stream" @w@) into an 'Auto' with just -- one output stream @a@, funneling the logging stream @w@ into an -- underlying 'WriterT' monad. -- -- Note: Function is the inverse of 'runWriterA': -- -- @ -- 'writerA' . 'runWriterA' == 'id' -- 'runWriterA' . 'writerA' == 'id' -- @ writerA :: (Monad m, Monoid w) => Auto m a (b, w) -- ^ 'Auto' with a "normal" output -- stream @b@s and a "logging" -- stream @w@s -> Auto (WriterT w m) a b -- ^ 'Auto' under an underlying -- 'WriterT', logging @w@s writerA a = mkAutoM (writerA <$> resumeAuto a) (saveAuto a) $ \x -> WriterT $ do ((y, w), a') <- stepAuto a x return ((y, writerA a'), w) -- $state -- An underlying 'StateT' gives you access to a global, mutable state. -- -- At first this might be seem a little silly. We went through all this -- trouble to avoid the headache of global mutable state, and now we add ti -- back in? -- -- One nice usage is an underlying entropy generator (you can deal with -- this more explicitly with 'sealRandom' in -- "Control.Auto.Process.Random"), or maybe some underlying pool that every -- 'Auto' shares that would be a big headache to thread manually. -- -- The main benefit here is that, using tools like 'sealState' and -- 'runStateA', we can /isolate/ the portion of our program that takes -- advantage of shared mutable state, and /seal off/ or only give that part -- access to the state... and nobody else. -- -- Anyways, it should go without saying that you should think really long -- and really hard before adding in global state to your program. It is -- almost always better to use principles of local statefulness and -- denotative composition to achieve what you want. Relying on this -- construct might lead to very unmaintainable code, and definitely code -- that is much more difficult to reason with. I suggest trying to find -- another solution first in all cases! -- | Takes an 'Auto' that works with underlying global, mutable state, and -- "seals off the state" from the outside world. -- -- An 'Auto (StateT s m) a b' maps a stream of 'a' to a stream of 'b', but -- does so in the context of requiring an initial 's' to start, and -- outputting a modified 's'. -- -- Consider this example 'State' 'Auto': -- -- @ -- foo :: Auto (State s) Int Int -- foo = proc x -> do -- execB (modify (+1)) . emitOn odd -< x -- execB (modify (*2)) . emitOn even -< x -- st <- effect get -< () -- sumX <- sumFrom 0 -< x -- id -< sumX + st -- @ -- -- On every output, the "global" state is incremented if the input is odd -- and doubled if the input is even. The stream @st@ is always the value -- of the global state at that point. @sumX@ is the cumulative sum of the -- inputs. The final result is the sum of the value of the global state -- and the cumulative sum. -- -- In writing like this, you lose some of the denotative properties because -- you are working with a global state that updates at every output. You -- have some benefit of now being able to work with global state, if that's -- what you wanted I guess. -- -- To "run" it, you could use 'streamAuto' to get a @'State' Int Int@: -- -- >>> let st = streamAuto foo [1..10] :: State Int Int -- >>> runState st 5 -- ([ 7, 15, 19, 36, 42, 75, 83,136,156,277], 222) -- -- (The starting state is 5 and the ending state after all of that is 222) -- -- However, writing your entire program with global state is a bad bad -- idea! So, how can you get the "benefits" of having small parts like -- @foo@ be written using 'State', and being able to use it in a program -- with no global state? -- -- Using 'sealState'! Write the part of your program that would like -- shared global state with 'State'...and compose it with the rest as if it -- doesn't, locking it away! -- -- @ -- sealState :: Auto (State s) a b -> s -> Auto' a b -- sealState foo 5 :: Auto' Int Int -- @ -- -- @ -- bar :: Auto' Int (Int, String) -- bar = proc x -> do -- food <- sealState foo 5 -< x -- id -< (food, show x) -- @ -- -- >>> streamAuto' bar [1..10] -- [ (7, "1"), (15, "2"), (19, "3"), (36, "4"), (42, "5"), (75, "6") ... -- -- We say that @'sealState' f s0@ takes an input stream, and the output -- stream is the result of running the stream through @f@, first with an -- initial state of @s0@, and afterwards with each next updated state. -- -- For a convenient way of "creating" an 'Auto' under 'StateT' in the first -- place, see 'stateA'. -- sealState :: (Monad m, Serialize s) => Auto (StateT s m) a b -- ^ 'Auto' run over 'State' -> s -- ^ initial state -> Auto m a b sealState a s0 = mkAutoM (sealState <$> resumeAuto a <*> get) (saveAuto a *> put s0) $ \x -> do ((y, a'), s1) <- runStateT (stepAuto a x) s0 return (y, sealState a' s1) -- | The non-resuming/non-serializing version of 'sealState'. sealState_ :: Monad m => Auto (StateT s m) a b -- ^ 'Auto' run over 'State' -> s -- ^ initial state -> Auto m a b sealState_ a s0 = mkAutoM (sealState_ <$> resumeAuto a <*> pure s0) (saveAuto a) $ \x -> do ((y, a'), s1) <- runStateT (stepAuto a x) s0 return (y, sealState_ a' s1) -- | "Unrolls" the underlying 'StateT' of an 'Auto' into an 'Auto' that -- takes in an input state every turn (in addition to the normal input) and -- outputs, along with the original result, the modified state. -- -- So now you can use any @'StateT' s m@ as if it were an @m@. Useful if -- you want to compose and create some isolated 'Auto's with access to an -- underlying state, but not your entire program. -- -- Also just simply useful as a convenient way to use an 'Auto' over -- 'State' with 'stepAuto' and friends. -- -- When used with @'State' s@, it turns an @'Auto' ('State' s) a b@ into an -- @'Auto'' (a, s) (b, s)@. -- -- For a convenient way to "generate" an 'Auto' 'StateT', see 'stateA' -- runStateA :: Monad m => Auto (StateT s m) a b -- ^ 'Auto' run over a state transformer -> Auto m (a, s) (b, s) -- ^ 'Auto' whose inputs and outputs are a state transformer runStateA a = mkAutoM (runStateA <$> resumeAuto a) (saveAuto a) $ \(x, s) -> do ((y, a'), s') <- runStateT (stepAuto a x) s return ((y, s'), runStateA a') -- | Transforms an 'Auto' with two input streams and two output streams (a -- "normal" input @a@ output @b@ stream, and a "state transforming" -- side-stream taking in @s@ and outputting @s@), abstracts away the @s@ -- stream as a modifcation to an underyling 'StateT' monad. That is, your -- normal inputs and outputs are now your /only/ inputs and outputs, and -- your input @s@ comes from the underlying global mutable state, and the -- output @s@ goes to update the underlying global mutable state. -- -- For example, you might have a bunch of 'Auto's that interact with -- a global mutable state: -- -- @ -- foo :: Auto (StateT Double m) Int Bool -- bar :: Auto (StateT Double m) Bool Int -- baz :: Auto (StateT Double m) Bool String -- @ -- -- Where @foo@, @bar@, and @baz@ all interact with global mutable state. -- You'd use them like this: -- -- @ -- full :: Auto (StateT Double m) Int String -- full = proc inp -> do -- fo <- foo -< inp -- br <- bar -< fo -- bz <- baz -< fo -- id -< replicae br bz -- @ -- -- 'stateA' allows you generate a new @Auto@ under 'StateT': -- -- @ -- thing :: Auto m (Int, Double) (Bool, Double) -- stateA thing :: Auto (StateT Double m) Int Bool -- @ -- -- So now the two side-channels are interpreted as working with the global -- state: -- -- @ -- full :: Auto (StateT Double m) Int String -- full = proc inp -> do -- fo <- foo -< inp -- tg <- stateA thing -< inp -- br <- bar -< fo || tg -- bz <- baz -< fo && tg -- id -< replicae br bz -- @ -- -- You can then "seal it all up" in the end with an initial state, that -- keeps on re-running itself with the resulting state every time: -- -- @ -- full' :: Double -> Auto m Int String -- full' = sealState full -- @ -- -- Admittedly, this is a bit more esoteric and dangerous (programming with -- global state? what?) than its components 'readerA' and 'writerA'; -- I don't actually recommend you programming with global state unless it -- really is the best solution to your problem...it tends to encourage -- imperative code/loops, and "unreasonable" and manageable code. See -- documentation for 'sealStateA' for best practices. Basically every bad -- thing that comes with global mutable state. But, this is provided here -- for sake of completeness with 'readerA' and 'writerA'. -- -- Note: function is the inverse of 'runstateA'. -- -- @ -- 'stateA' . 'runStateA' == 'id' -- 'runStateA' . 'stateA' == 'id' -- @ stateA :: Monad m => Auto m (a, s) (b, s) -- ^ 'Auto' whose inputs and outputs are a -- state transformer -> Auto (StateT s m) a b -- ^ 'Auto' run over a state transformer stateA a = mkAutoM (stateA <$> resumeAuto a) (saveAuto a) $ \x -> StateT $ \s -> do ((y, s'), a') <- stepAuto a (x, s) return ((y, stateA a'), s') -- | Like 'stateA', but assumes that the output is the modified state. accumA :: Monad m => Auto m (a, s) s -- ^ 'Auto' taking inputs and states and -- returning updated states -> Auto (StateT s m) a s -- ^ 'Auto' over a state transformer accumA a = mkAutoM (accumA <$> resumeAuto a) (saveAuto a) $ \x -> StateT $ \s -> do (s', a') <- stepAuto a (x, s) return ((s', accumA a'), s') -- | "Unrolls" the underlying 'Monad' of an 'Auto' if it happens to be -- 'Traversable' ('[]', 'Maybe', etc.). -- -- It can turn, for example, an @'Auto' [] a b@ into an @'Auto'' a [b]@; it -- collects all of the results together. Or an @'Auto' 'Maybe' a b@ into -- an @'Auto'' a ('Maybe' b)@. -- -- This might be useful if you want to make some sort of "underlying -- inhibiting" 'Auto' where the entire computation might just end up being -- 'Nothing' in the end. With this, you can turn that -- possibly-catastrophically-failing 'Auto' (with an underlying 'Monad' of -- 'Maybe') into a normal 'Auto', and use it as a normal 'Auto' in -- composition with other 'Auto's...returning 'Just' if your computation -- succeeded. -- -- @ -- 'runTraversableA' :: 'Auto' 'Maybe' a b -> 'Interval'' a b -- @ -- -- @ -- foo :: Auto Maybe Int Int -- foo = arrM $ \x -> if even x then Just (x `div` 2) else Nothing -- -- bar :: Auto Maybe Int Int -- bar = arrM Just -- @ -- -- >>> streamAuto (foo &&& bar) [2,4,6] -- Just [(1, 2),(2, 4),(3, 6)] -- >>> streamAuto (foo &&& bar) [2,4,6,7] -- Nothing -- >>> streamAuto' ('runTraversableA' foo '<|?>' 'runTraversableA' bar) [2,4,6,7] -- [Just 1, Just 2, Just 3, Just 7] runTraversableA :: (Monad f, Traversable f) => Auto f a b -- ^ 'Auto' run over traversable structure -> Auto m a (f b) -- ^ 'Auto' returning traversable structure runTraversableA = go . return where go a = mkAuto (go <$> mapM resumeAuto a) (mapM_ saveAuto a) $ \x -> let o = a >>= (`stepAuto` x) y = liftM fst o a' = liftM snd o in (y, go a') -- | Wraps a "try" over an underlying 'IO' monad; if the Auto encounters a -- runtime exception while trying to "step" itself, it'll output a 'Left' -- with the 'Exception'. Otherwise, will output 'left'. -- -- Note that you have to explicitly specify the type of the exceptions you -- are catching; see "Control.Exception" documentation for more details. catchA :: Exception e => Auto IO a b -- ^ Auto over IO, expecting an -- exception of a secific type. -> Auto IO a (Either e b) catchA a = a_ where a_ = mkAutoM (catchA <$> resumeAuto a) (saveAuto a) $ \x -> do eya' <- try $ stepAuto a x case eya' of Right (y, a') -> return (Right y, catchA a') Left e -> return (Left e , a_) -- TODO: Possibly look into bringing in some more robust tools from -- monad-control and other industry established error handling routes? -- Also, can we modify an underlying monad with implicit catching behavior?