MIT licensed by Justin Le
Maintained by [email protected]
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$ cabal install auto

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-- Let's implement a PID feedback controller over a black box system.

import Control.Auto
import Prelude hiding ((.), id)

-- We represent a system as `System`, an `Auto` that takes stream of `Double`s
-- as input and transforms it into a stream of `Double`s as output.  The `m`
-- means that a `System IO` might do IO in the process of creating its ouputs,
-- for instance.
type System m = Auto m Double Double

-- A PID controller adjusts the input to the black box system until the
-- response matches the target.  It does this by adjusting the input based on
-- the current error, the cumulative sum, and the consecutive differences.
-- See
-- Here, we just lay out the "concepts"/time-varying values in our system as a
-- recursive/cyclic graph of dependencies.  It's a feedback system, after all.
pid :: MonadFix m => (Double, Double, Double) -> System m -> System m
pid (kp, ki, kd) blackbox = proc target -> do       -- proc syntax; see tutorial
    rec --  err :: Double
        --  the difference of the response from the target
        let err        = target - response

        -- cumulativeSum :: Double
        -- the cumulative sum of the errs
        cumulativeSum <- sumFrom 0 -< err

        -- changes :: Maybe Double
        -- the consecutive differences of the errors, with 'Nothing' at first.
        changes       <- deltas    -< err

        --  adjustment :: Double
        --  the adjustment term, from the PID algorithm
        let adjustment = kp * err
                       + ki * cumulativeSum
                       + kd * fromMaybe 0 changes

        -- the control input is the cumulative sum of the adjustments
        control  <- sumFromD 0 -< adjustment

        -- the response of the system, feeding the control into the blackbox
        response <- blackbox   -< control

    -- the output of this all is the value of the response
    id -< response

What is it?

Auto is a Haskell DSL and platform providing an API with declarative, compositional, denotative semantics for discrete-step, locally stateful, interactive programs, games, and automations, with implicitly derived serialization.

It is suited for any domain where your program’s input or output is a stream of values, input events, or output views. At the high-level, it allows you to describe your interactive program or simulation as a value stream transformer, by composition and transformation of other stream transformers. So, things like:

  1. Chat bots
  2. Turn-based games
  3. GUIs
  4. Numerical simulations
  5. Process controllers
  6. Text-based interfaces
  7. (Value) stream transformers, filters, mergers, processors

It’s been called “FRP for discrete time contexts”.

Intrigued? Excited? Start at the tutorial!

It’s a part of this package directory and also on github at the above link. The current development documentation server is found at

From there, you can check out my All About Auto series on my blog, where I break sample projects and show to approach projects in real life. You can also find examples and demonstrations in the auto-examples repo on github.

Buzzwords explained!

  • Haskell DSL/library: It’s a Haskell library that provides a domain-specific language for composing and declaring your programs/games.

    Why Haskell? Well, Haskell is one of the only languages that has a type system expressive enough to allow type-safe compositions without getting in your way. Every composition and component is checked at compile-time to make sure they even make sense, so you can work with an assurance that everything fits together in the end — and also in the correct way. The type system can also guide you in your development as well. All this without the productivity overhead of explicit type annotations. In all honesty, it cuts the headache of large projects down — and what you need to keep in your head as you develop and maintain — by at least 90%.

  • Platform: Not only gives the minimal tools for creating your programs, but also provides a platform to run and develop and integrate them, as well as many library/API functions for common processes.

  • Declarative: It’s not imperative. That is, unlike in other languages, you don’t program your program by saying “this happens, then this happens…and then in case A, this happens; in case B, something else happens”. Instead of specifying your program/game by a series of state-changing steps and procedures (a “game loop”), you instead declare “how things are”. You declare fixed or evolving relationships between entities and processes and interactions. And this declaration process is high-level and pure.

  • Denotative: Instead of your program being built of pieces that change things and execute things sequentially, your entire program is composed of meaningful semantic building blocks that “denote” constant relationships and concepts. The composition of such building blocks also denote new concepts. Your building blocks are well-defined ideas.

  • Compositional: You build your eventually complex program/game out of small, simple components. These simple components compose with each other; and compositions of components compose as well with other components. Every “layer” of composition is seamless. It’s the scalable program architecture principle in practice: If you combine an A with an A, you don’t get a B; you get another A, which can combine with any other A.

    Like unix pipes, where you can build up complex programs by simply piping together simple, basic ones.

  • Discrete-step: This library is meant for things that step discretely; there is no meaningful concept of “continuous time”. Good examples include turn-based games, chat bots, and cellular automata; bad examples include real-time games and day trading simulations.

  • Locally stateful: Every component encapsulates its own local (and “hidden”) state. There is no global or impicitly shared state. This is in contrast to those “giant state monad” libraries/abstractions where you carry around the entire game/program state in some giant data type, and have your game loop simply be an update of that state.

    If you have a component representing a player, and a component representing an enemy — the two components do not have to ever worry about the state of the other, or the structure of their shared state.

    Also, you never have to worry about something reading or modifying a part of the shared/global state it wasn’t meant to read or modify! (Something you cannot guaruntee in the naive implementatation of the “giant state monad” technique).

  • Interactive: The behavior and structure of your program can respond and vary dynamically with outside interaction. I’m not sure how else to elaborate on the word “interactive”, actually!

  • Interactive programs, games and automations: Programs, games, and automations/simulations. If you’re making anything discrete-time that encapsulates some sort of internal state, especially if it’s interactive, this is for you!! :D

  • Implicitly derived serialization: All components and their compositions by construction are automatically “freezable” and serializable, and re-loaded and resumed with all internal state restored. As it has been called by ertes, it’s “save states for free”.


The official support and discussion channel is #haskell-auto on freenode. You can also usually find me (the maintainer and developer) as jle` on #haskell-game or #haskell. There’s also a gitter channel if IRC is not your cup of tea. Also, contributions to documentation and tests are welcome! :D

Why Auto?

Auto is distinct from a “state transformer” (state monad, or explicit state passing) in that it gives you the ability to implicitly compose and isolate state transformers and state.

That is, imagine you have two different state monads with different states, and you can compose them together into one giant loop, and:

  1. You don’t have to make a new “composite type”; you can add a new component dealing with its own state without changing the total state type.

  2. You can’t write anything cross-talking. You can’t write anything that can interfere with the internal state of any components; each one is isolated.

So — Auto is useful over a state monad/state transformer approach in cases where you like to build your problem out of multiple individual components, and compose them all together at once.

Examples include a multiple-module stateful chat bot, where every module of the chat bot consists of its own internal state.

If you used a state monad approach, every time you added a new module with its own state, you’d have to “add it into” your total state type.

This simply does not scale.

Imagine a large architecture, where every composition adds more and more complexity.

Now, imagine you can just throw in another module with its own state without any other component even “caring”. Or be able to limit access implicitly, without explicit “limiting through lifting” with zoom from lens, etc. (Without that, you basically have “global state” — the very thing that we went to Functional Programming/Haskell to avoid in the first place! And the thing that languages have been trying to prevent in the last twenty years of language development. Why go “backwards”?)

In addition to all of these practical reasons, State imposes a large imperative shift in your design.

State forces you to begin modeling your problem as “this happens, then this happens, then this happens”. When you choose to use a State monad or State passing approach, you immediately begin to frame your entire program from an imperative approach.

Auto lets you structure your program denotatively and declaratively. It gives you that awesome style that functional programming promised in the first place.

Instead of saying “do this then that”, you say “this is how things…just are. This is the structure of my program, and this is the nature of the relationship between each component”.

If you’re already using Haskell…I shouldn’t have to explain to you the benefits of a high-level declarative style over an imperative one :)

Why not Auto?

That being said, there are cases where Auto is either the wrong tool or not very helpful.

  • Cases involving inherently continuous time. Auto is meant for situations where time progresses in discrete ticks — integers, not reals. You can “fake” it by faking continuous time with discrete sampling…but FRP is a much, much more powerful and safe abstraction/system for handling this than Auto is. See the later section on FRP.

  • Cases where you really don’t have interactions/compositions between different stateful components. If all your program is just one foldr or scanl or iterate, and you don’t have multiple interacting parts of your state, Auto really can’t offer much. If, however, you have multiple folds or states that you want run together and compose, then this might be useful!

  • Intense IO stuff and resource handling. Auto is not pipes or conduit. All IO is done “outside” of the Auto components; Auto can be useful for file processing and stream modification, but only if you separately handle the IO portions. Auto works very well with pipes or conduit; those libraries are used to “connect” Auto to the outside word, and provide a safe interface. In other words, Auto handles “value streams”, while pipes/conduit handle “effect streams”

Relation to FRP

Auto borrows a lot of concepts from Functional Reactive Programming — especially arrowized, locally stateful libraries like netwire. At best, Auto can be said to bring a lot of API ideas and borrows certain aspects of the semantic model of FRP and incorporates them as a part of a broader semantic model more suitable for discrete-time discrete-stel contexts. But, users of such libraries would likely be able to quickly pick up Auto, and the reverse is (hopefully) true too.

Note that this library is not meant to be any sort of meaningful substitution for implementing situations which involve concepts of continuous (“real number-valued”, as opposed to “integer valued”) time (like real-time games); you can “fake” it using Auto, but in those situations, FRP provides a much superior semantics and set of concepts for working in such contexts. That is, you can “fake” it, but you then lose almost all of the benefits of FRP in the first place.

A chatbot

import qualified Data.Map as M
import Data.Map (Map)
import Control.Auto
import Prelude hiding ((.), id)

-- Let's build a big chat bot by combining small chat bots.
-- A "ChatBot" is going to be an `Auto` taking in a stream of tuples of
-- incoming nick, message, and timestamps; the result is a "blip stream" that
-- emits with messages whenever it wants to respond.

type Message   = String
type Nick      = String
type ChatBot m = Auto m (Nick, Message, UTCTime) (Blip [Message])

-- Keeps track of last time a nick has spoken, and allows queries
seenBot :: Monad m => ChatBot m
seenBot = proc (nick, msg, time) -> do          -- proc syntax; see tutorial
    -- seens :: Map Nick UTCTime
    -- Map containing last time each nick has spoken
    seens <- accum addToMap M.empty -< (nick, time)

    -- query :: Blip Nick
    -- blip stream emits whenever someone queries for a last time seen;
    -- emits with the nick queried for
    query <- emitJusts getRequest -< words msg

        -- a function to get a response from a nick query
    let respond :: Nick -> [Message]
        respond qry = case M.lookup qry seens of
                        Just t  -> [qry ++ " last seen at " ++ show t ++ "."]
                        Nothing -> ["No record of " ++ qry ++ "."]

    -- output is, whenever the `query` stream emits, map `respond` to it.
    id -< respond <$> query
    addToMap :: Map Nick UTCTime -> (Nick, UTCTime) -> Map Nick UTCTime
    addToMap mp (nick, time) = M.insert nick time mp
    getRequest ("@seen":request:_) = Just request
    getRequest _                   = Nothing

-- Users can increase and decrease imaginary internet points for other users
karmaBot :: Monad m => ChatBot m
karmaBot = proc (_, msg, _) -> do
    -- karmaBlip :: Blip (Nick, Int)
    -- blip stream emits when someone modifies karma, with nick and increment
    karmaBlip <- emitJusts getComm -< msg

    -- karmas :: Map Nick Int
    -- keeps track of the total karma for each user by updating with karmaBlip
    karmas    <- scanB updateMap M.empty -< karmaBlip

    -- function to look up a nick, if one is asked for
    let lookupKarma :: Nick -> [Message]
        lookupKarma nick = let karm = M.findWithDefault 0 nick karmas
                           in  [nick ++ " has a karma of " ++ show karm ++ "."]

    -- output is, whenever `karmaBlip` stream emits, look up the result
    id -< lookupKarma . fst <$> karmaBlip
    getComm :: String -> Maybe (Nick, Int)
    getComm msg = case words msg of
                    "@addKarma":nick:_ -> Just (nick, 1 )
                    "@subKarma":nick:_ -> Just (nick, -1)
                    "@karma":nick:_    -> Just (nick, 0)
                    _                  -> Nothing
    updateMap :: Map Nick Int -> (Nick, Int) -> Map Nick Int
    updateMap mp (nick, change) = M.insertWith (+) nick change mp

-- Echos inputs prefaced with "@echo"...unless flood limit has been reached
echoBot :: Monad m => ChatBot m
echoBot = proc (nick, msg, time) -> do
    -- echoBlip :: Blip [Message]
    -- blip stream emits when someone wants an echo, with the message
    echoBlip   <- emitJusts getEcho  -< msg

    -- newDayBlip :: Blip UTCTime
    -- blip stream emits whenever the day changes
    newDayBlip <- onChange           -< utctDay time

    -- echoCounts :: Map Nick Int
    -- `countEchos` counts the number of times each user asks for an echo, and
    -- `resetOn` makes it "reset" itself whenever `newDayBlip` emits.
    echoCounts <- resetOn countEchos -< (nick <$ echoBlip, newDayBlip)

        -- has this user flooded today...?
    let hasFlooded = M.lookup nick echoCounts > Just floodLimit
        -- output :: Blip [Message]
        -- blip stream emits whenever someone asks for an echo, limiting flood
        output | hasFlooded = ["No flooding!"] <$ echoBlip
               | otherwise  = echoBlip

    -- output is the `output` blip stream
    id -< output
    floodLimit = 5
    getEcho msg = case words msg of
                    "@echo":xs -> Just [unwords xs]
                    _          -> Nothing
    countEchos :: Auto m (Blip Nick) (Map Nick Int)
    countEchos = scanB countingFunction M.empty
    countingFunction :: Map Nick Int -> Nick -> Map Nick Int
    countingFunction mp nick = M.insertWith (+) nick 1 mp

-- Our final chat bot is the `mconcat` of all the small forks the
-- input between all three, and mconcats the outputs.
chatBot :: Monad m => ChatBot m
chatBot = mconcat [seenBot, karmaBot, echoBot]

-- Here, our chatbot will automatically serialize itself to "data.dat"
-- whenever it is run.
chatBotSerialized :: ChatBot IO
chatBotSerialized = serializing' "data.dat" chatBot

Open questions

  • “Safecopy problem”; serialization schemes are implicitly derived, but if your program changes, it is unlikely that the new serialization scheme will be able to resume something from the old one. Right now the solution is to only serialize small aspects of your program that you can manage and manipulate directly when changing your program. A better solution might exist.

  • In principle very little of your program should be over IO as a monad…but sometimes, it becomes quite convenient for abstraction purposes. Handling IO errors in a robust way isn’t quite my strong point, and so while almost all auto idioms avoid IO and runtime, for some applications it might be unavoidable. auto is not and will never be about streaming IO effects…but knowing what parts of IO fit into the semantic model of value stream transformers would yield a lot of insight. Also, most of the Auto “runners” (the functions that translate an Auto into IO that executes it) might be able to benefit from a more rigorous look too.

  • Tests; tests aren’t really done yet, sorry! Working on those :)


  • Compatibility support for MonadRandom-0.5.

  • Control.Auto.Blip: New blip stream splitter onEitherB, which splits an incoming blip stream into two output streams based on whether the emitted items resolve to Left or Right when applied to the splitting function.

  • Control.Auto.Blip: New blip stream splitter onEitherB, which splits an incoming blip stream into two output streams based on whether the emitted items resolve to Left or Right when applied to the splitting function.

  • Control.Auto.Process.Random: Removed self-defeating Seralize constraint on the seed parameter of sealRandom_.
  • Control.Auto.Serialize: Fixed compiler warning on GHC 7.10 for redundant Applicative import.

  • Using the base-orphans library for a more sane compatibility layer than the previous method.
  • Many documentation fixes including haddock reconfigurations on specific modules.

DEPRECATED: Please use!

  • Added support for building with GHC 7.6.x.

  • Removed all upper bounds on dependencies except for base.
  • Control.Auto.Blip: Companions to emitJusts and onJusts added, for Either: emitEithers and onEithers. Emit every item inputted, but fork them into one of two output blit streams based on Right or Left properties. Only preserves blip semantics/makes sense if any given input’s Right or Leftness is expected to be independent from the last received one.
  • Control.Auto.Blip: New “blip stream collapsers”, asMaybes and substituteB. asMaybes turns a blip stream into a stream of Maybes, Just when something was emitted, and Nothing when not. substituteB takes a regular stream and a blip stream, and outputs the values of the regular stream whenever the blip stream doesn’t emit and the emitted value when it does — basically a more powerful version of fromBlips, where the “default” value now comes from a stream instead of being always the same.
  • Control.Auto.Blip: New blip stream creator, collectN, which emits every n steps with the last n items received.
  • Control.Auto.Blip: New blip stream modifiers, collectB and collectBs. collectB waits on two blip streams and emits after it has received something from both. collectBs is like collectN, except emits after every n emitted values received with the past n emitted values.
  • Control.Auto.Collection: “Intervaled” counterparts to mux and muxMany, muxI and muxManyI. They store Intervals instead of Autos…and when the Intervals turned “off”, they are removed from the collection.
  • Control.Auto.Switch: A new “count-down” switcher, switchIn, which acts a bit like (-->) and (-?>), except the switch happens deterministically after a pre-set given number of steps. Act like the first Auto for a given number of steps, and then act like the second ever after. Basically a direct implementation of the common onFor n a1 --> a2 idiom.

  • Adapted to more consistent semantic versioning scheme, where the third number is a new update, and the fourth number is reserved for bug fixes.

  • Control.Auto.Blip: foldrB and foldlB' officially deprecated in their current forms. From version 0.5, they will have corrected functionality and a new type signature. The current functionality doesn’t really make sense, and was a mistake during their implementation. You can begin using the new versions now, with:

    foldrB  = foldr  (merge f) mempty
    foldlB' = foldl' (merge f) mempty
  • Control.Auto.Effects: New “sealing” mechanisms for underlying Reader: sealReaderMVar and sealReaderM. sealReaderMVar allows things like “hot swapping” configuration data; at every step, the Auto asks for its environment from an MVar, that could be changed/modified from a different thread with new configuration data. sealReaderM is a more general/potentially dangerous version where the environment is retrieved through an arbitrary action in the underlying monad.

  • Control.Auto.Run: New powerful combinator throughT, letting you “lift” an Auto to run over/through any Traversable. Can replace during, perBlip, accelOverList, etc. The specialized versions will remain more performant, though.

  • Control.Auto.Run: In the spirit of the hip and current Foldable Traversable Proposal, overTraversable added to complement overList, so you can now “stream” Autos over IntMaps, Maybes, Consts…or any Traversable. Not replacing overList completely, though, for performance reasons.

  • Control.Auto.Blip: Removed unnecessary Monad constraints on became_, became', noLonger_, and noLonger'.

  • Control.Auto.Interval: Bug fix on holdFor and holdFor_, where they had the potential to overflow Int and begin “holding” forever when given specifically malformed input.

  • Control.Auto.Time: Performance boost on accelOverList by using strict Writer over lazy.

  • Bug fix version reverting breaking changes from 0.4.x should be able to run all 0.2.x programs with full backwards compatibility.
  • Control.Auto.Effects: Reverted back to lazy StateT and WriterT, because of situations where auto cannot resolve fixed points for recursive bindings.
  • Control.Auto.Blip: forkB renamed to splitB to prevent confusion with “fork”, usually used in Haskell to refer to concurrency. Also anticipating adding concurrency-based Autos, so this is a move to clear the way for any possible conflicts.

DEPRECATED: Please use!

  • Control.Auto.Effects: Breaking change: switched to strict StateT and WriterT.
  • Control.Auto.Effects: Added readerA and writerA, for convenience in “creating” Autos under ReaderT and WriterT; also added stateA and accumA for completeness.

  • Control.Auto.Run: As a part of an effort to provide integration with disciplined effectful streaming, introduced streamAutoEffects and toEffectStream, which convert Auto m a b’s to streams of effects in m that can be processed and manipulated and integrated with any ListT-compatible library, like pipes. See documentation for more details. These were also added to the exports of Control.Auto.
  • Control.Auto.Interval: New Auto holdJusts, which stretches the last seen “on”/Just value over the duration of a “off”/Nothing interval.
  • Documentation fixes to emphasize auto’s focus on value streams, not effect streams, in contrast to pipes, conduit, etc.
  • Version restrictions on some packages relaxed on profunctors, semigroups, and base.

  • Control.Auto.Process.Random: Added combinators and sealers dealing for working with an underlying Rand or RandT monad.
  • Because of this, committed to adding MonadRandom as a dependency.

  • Control.Auto: Added unserialize, delay, and delay_ to Control.Auto’s exports.
  • Control.Auto.Blip: New blip stream manipulator: forkB, which forks a blip stream into to separate ones based on whether or not the emitted values match a predicate.
  • Control.Auto.Time: Added a generalized version of stretch, stretchAccumBy which allows access to the “skipped” inputs during the stretched periods, as well as the ability to control the outputs during the stretched periods.

  • Control.Auto.Collection: Bug for dynZipF fixed, where newly added Autos would overwrite ones alreay stored.
  • Control.Auto: fromInterval added to Control.Auto’s exports.

DEPRECATED: Please use!

  • Control.Auto.Collection: dynZipF and dynMapF, implicit-serialization dynamic collections.

  • Control.Auto.Effects: catchA added to Control.Auto.Effects, allowing explicit catching of runtime exceptions thrown in underlying IO.

  • First official release. No backwards-incompatible changes until