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Algebraic Effects in Haskell using Implicit Parameters
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Implicit Effects: Algebraic Effects in Haskell using Implicit Parameters

Build Status

`implicit-effects` is currently work in progress and will soon be announced publicly. The code is mostly ready but documentation is being worked on. Thank you for your understanding looking at the preview of this project.


implicit-effects is a new library for using algebraic effects in Haskell. It uses the GHC language extension ImplicitParams to bind effect operations for a monad to the callee's context on call site. This contrasts with the usual typeclass approach for implementing effects, where instances of effect operations for a particular monad type is derived globally with guaranteed uniqueness. implicit-effects decouple effect definitions and interpretations from usage of effects on specific monad, allowing computations to use implicit effects with any monad, including Identity, IO, MTL monads, free monads, or generic forall m . (Monad m).

Although implicit parameters are used, implicit-effects hides the usage behind a single typeclass ImplicitOps. Other than declaring new instances for ImplicitOps when defining new effects, users are not exposed to implicit parameters and can use the effect constraints just like regular typeclass constraints. implicit-effects only requires free monad transformers for advanced algebraic effects interpretations that require access to the continuation. It is agnostic of the concrete free monad implementation, allowing effect interpretation through any free monad transformer implementing the FreeEff class. This allows users to switch between any free monad variants with the most optimized performance without getting locked in to any concrete implementation for their applications.

implicit-effects allows users to pay for the performance price of free monads and full algebraic effects only when needed. For lightweight effect interpretations that only wrap around other effects, e.g. MonadTime and Teletype, users can define the effect operation handlers directly without going through free monads. They can also make use of existing monads they have defined for existing applications, such as MTL monad transformers stack, and start with adding lightweight effects before moving to full algebraic effects. Since effect interpretations are decoupled from computations, users can mix and switch between lightweight interpretations, algebraic effect handlers, and concrete monads with little to no change to their core application logic.

Work In Progress

implicit-effects is an experimental effects library I developed after less than a year study on algebraic effects. I am publishing implicit-effects to share about different approaches I use to implement algebraic effects in Haskell, which I think is worth considering or explored further by the Haskell community. However considering this is my first serious personal Haskell project, and that I lacks professional experience in developing production quality Haskell applications, you may want to think twice before using implicit-effects in any serious Haskell projects. (At least not yet)

Operations and Co-Operations

An effect for implicit-effects is defined by declaring three datatypes and implementing a few typeclass instances. We first need a dummy datatype as effect signature, an operation datatype for consumption by computations, and a co-operation datatype for interpretation of algebraic effects.

Consider a simple example for a time effect. Traditionally the operations for time effect would be defined as a typeclass like MonadTime:

class Monad m => MonadTime m where
  currentTime :: m UTCTime

In implicit-effects, we define the time effect instead as follow:

data TimeEff
  -- empty body

data TimeOps eff = TimeOps {
  currentTimeOp :: eff UTCTime

instance EffOps TimeEff where
  type Operation TimeEff = TimeOps

We define a dummy TimeEff datatype with empty body for identifying the time effect. We then define the operation type TimeOps, parameterized by a Monad eff. (To make effect programming more friendly to beginners, in implicit-effects we define Effect as a less scary type alias to Monad and we name monadic type variables as eff instead of m) TimeOps will be bound to implicit parameters later for used in computations.

We then declare TimeEff as an instance of EffOps. The typeclass requires us to declare an Operation type for our effect TimeEff. Here we just put TimeOps as the effect operation type.

We then have to define how implicit-effects can bind TimeOps to a specific implicit parameter. This is done by implementing the ImplicitOps instance for TimeEff:

instance EffFunctor TimeEff where
  -- Required by ImplicitOps. We leave this undefined for now and will
  -- explain in the next section.
  effmap = undefined

instance ImplicitOps TimeEff where
  type OpsConstraint TimeEff eff = (?timeOps :: TimeOps eff)

  withOps :: forall eff r . (Effect eff)
    => TimeOps eff
    -> ((OpsConstraint TimeEff eff) => r)
    -> r
  withOps ops comp = let ?timeOps = ops in comp

  captureOps :: forall eff
     . (Effect eff, OpsConstraint TimeEff eff)
    => TimeOps eff
  captureOps = ?timeOps

Using the GHC extension ConstraintKinds, the OpsConstraint type family in ImplicitOps defines the unique name of the implicit parameter to bind the effect operation. Here we choose the name ?timeOps. Note that due to injectivity conditions imposed by TypeFamilyDependencies, there should be naming conventions for the implicit parameters to avoid any name clash which would result in compile time error.

The type signatures for withOps and captureOps are written here for illustrative purpose. withOps implements how we can bind a TimeOps into the ?timeOps implicit parameter for any computation comp of any type r that requires the implicit parameter ?timeOps in its context. Conversely captureOps is used to capture a TimeOps from the ?timeOps implicit parameter, if it is available in the current context. The implementation for withOps and captureOps are simply usage of the relevant implicit parameter expressions.

Note that with the types for withOps and captureOps, it is necessary for the following law to hold for any non trivial effect operations:

withOps ops captureOps = ops

Finally to make it easy for users to use TimeEff, we define the helper function currentTime to access the currentTimeOp field of TimeOps in the implicit parameter ?timeOps:

currentTime :: forall eff . (OpsConstraint TimeEff eff)
  => eff UTCTime
currentTime = currentTimeOp captureOps

With the above definitions, we can now define our first lightweight interpretation of TimeEff under the IO monad:

import Data.Time.Clock

ioTimeOps :: TimeOps IO
ioTimeOps = TimeOps getCurrentTime

For the trivial implementation, we just use the getCurrentTime function from the time package to implement a TimeOps that can work only under IO.

With our first interpretation of TimeEff implemented, we can write our example app as follow that makes use of it:

app :: forall eff
   . (EffConstraint (TimeEff  IoEff) eff)
  => eff ()
app = do
  time <- currentTime
  liftIo $ putStrLn $ "the current time is " ++ show time

app' :: IO ()
app' = withOps (ioTimeOps  ioOps) app

There are a few new more things introduced in the example above. EffConstraint is a type alias that include both Effect eff and OpsConstraint in a single constraint to reduce boilerplate. Without it we would otherwise write (Effect eff, OpsConstraint (TimeEff ∪ IoEff) eff).

IoEff is one of the built in effects offered by implicit-effects. It is the operation equivalent to the MonadIO typeclass, with a liftIo operation. ioOps is the trivial instance for IoOps IO (Operation IoEff IO) that offers liftIo under IO.

-- module Control.Effect.Implicit.Ops.Io

data IoOps eff = IoOps {
  liftIoOp :: forall a . IO a -> eff a

ioOps :: IoOps IO
ioOps = IoOps {
  liftIoOp = id

Our example application app is a generic computation that works under all monad/effect eff. It has the constraint that requires both TimeEff and IoEff be supported to run on the effect eff. By defining app generically, we can run app on different effects later on, such as on a monad transformer stack as the application grows, or use it with mock effects for testing.

(∪) is the union type operator that we can use to combine multiple effect operations. It is the type alias to Union, so if you can't figure how to type "∪", you can write TimeEff `Union` IoEff or Union TimeEff IoEff instead.

We can bind the effect operations with app using withOps and get app', which works under IO as both ioTimeOps and ioOps works under IO. The union operator (∪) at the term level is an alias to the UnionOps constructor. By passing both operations as ioTimeOps ∪ ioOps, withOps binds both constraints simultaneously with app and unify eff with IO. With that we get to run our app in main just as if it has been written to work with IO directly.

In the example above, we are just defining a simple time effect without touching more advanced concepts such as effect interpretation. The main takeaway is how simple it is to define an effect operation and use them. As we dive deeper into implicit-effects, we will learn that even advanced effects are defined similar to the above example.

One of the goals for implicit-effects is to avoid performance overhead if possible. For the example TimeEff, since we are just letting IO do bulk of the work, we don't need to pay for the performance cost of using free monads or advanced constructs in implicit-effects. There is still a little performance overhead for accessing the effect operations through implicit parameters over typeclasses, but hopefully there is room for optimization in GHC if enough people use implicit parameters.

We will also see later on more abstractions provided by implicit-effects, and how the performance tradeoff may worth it when we use them to structure more complex applications.


Following the previous example, let's say we want to add a state effect to store or update the fetched time. We can use StateEff provided by Control.Effect.Implicit.Ops.State, which have the same interface as MonadState.

app2 :: forall eff
   . (EffConstraint (TimeEff  IoEff   StateEff UTCTime) eff)
  => eff ()
app2 = do
  time1 <- get
  liftIo $ putStrLn $ "the previous recorded time is " ++ show time1

  time2 <- currentTime
  put time2
  liftIo $ putStrLn $ "the current time is " ++ show time2

With our updated app, we have to find a concrete monad for eff that supports all three effect operations we need. For instance we may try to implement StateOps UTCTime IO since we have already have IO instance for the other two operations. Or we can use the algebraic effects approach that we'll introduce in later section to implement state. But there is already a well tested and high performance implementation for the state effect, which is the StateT monad transformer provided by mtl, so why not use that instead?

In fact implicit-effects provides the stateTOps instance for any StateT eff:

-- module Control.Effect.Implicit.Transform.State

  :: forall eff s
   . (Effect eff, MonadState s eff)
  => StateOps s eff
stateTOps = StateOps {
  getOp = get,
  putOp = put

stateTOps can provide state operation on any MonadState instance by just delegating to mtl. With that we can for example run computations with StateEff on any StateT eff. Given that our previous two effect operations need to run on IO, it makes sense that we run our new app on StateT IO instead. But to do that we need to make new operation handlers for StateOps (StateT IO) and IoOps (StateT IO).

EffFunctor is a typeclass that support lifting computations running on a monad eff to a lifted monad t eff, similar to the MonadTrans class. It is more general that it can lift computations through natural transformation between any two effects eff1 and eff2, without requiring eff2 to be in the form of t eff1.

class EffFunctor (comp :: (Type -> Type) -> Type) where
  effmap :: forall eff1 eff2 .
    (Effect eff1, Effect eff2)
    => (eff1 ~> eff2) -- i.e. (forall x . eff1 x -> eff2 x)
    -> comp eff1
    -> comp eff2

Notice that EffFunctor is parameterized by a type variable comp, which is parameterized by an monad eff. Operation handlers are one kind of computation that can be an EffFunctor, but there are also more general use of EffFunctor which we will learn later on.

ImplicitOps requires the Operation type of its effect to be an EffFunctor. We will fill in our EffFunctor instance for TimeOps, which we skipped in earlier section:

instance EffFunctor TimeOps where
  effmap lifter ops = TimeOps {
    currentTimeOp = lifter $ currentTimeOp ops

With that we can now to lift both ioTimeOps and ioOps to work on StateT UTCTime IO using the lift method in MonadTrans.

stateTIoTimeOps :: TimeOps (StateT UTCTime IO)
stateTIoTimeOps = effmap lift ioTimeOps

stateTIoOps :: TimeOps (StateT UTCTime IO)
stateTIoOps = effmap lift ioOps

With all 3 operation handlers available, we can now bind our application and make it work on StateT UTCTime IO:

app2' :: StateT UTCTime IO ()
app2' = withOps (stateTIoTimeOps  stateTIoOps  stateTOps) app2

We can run our StatT monad with the usual evalStateT, but say if we need the initial state to be the time when the program starts, we'd once again need to get the current time. Fortunately we can reuse the ioTimeOps we defined earlier to do just that:

app3 :: IO ()
app3 = withOps ioTimeOps $
  currentTime >>= evalStateT app2'

Given the popularity and stability of mtl, we can expect common use of similar patterns as above to use monad transformers in conjunction with implicit-effects. As such the helper function withStateTAndOps is provided to help us do the same thing with much less boilerplate:

app4 :: forall eff
   . (EffConstraint (TimeEff  IoEff) eff)
  => eff ()
app4 = do
  start <- currentTime
  withStateTAndOps @(TimeEff  IoEff) start app2

withStateTAndOps automatically captures any operation handler specified in the type application, and automatically lift them to work on the lifted StateT monad. It then runs the generic computation app2 on StateT UTCTime eff with the liften operation handlers, then finally run evalStateT and return the result in the original monad eff.

Notice that both app2 and app4 are defined generically to work on any monad eff. This means unlike app3, app4 can run on deeper monad transformer stacks with no modification required.

So far we are still working on replicating the familiar patterns of mtl and make them work with implicit-effects. This may look redundant because if that is all implicit-effects can do, it might as well be enough for us to stick with just mtl. As we will learn in coming sections, the more interesting things for implicit-effects is that we can also run algebraic effects together with our regular mtl effects with minimal impact on compatibility and performance.


As we add more effects to our app, we may notice that binding an operation handler to a computation function is kind of like function application through implicit parameters. Since it is similar to function applications, we can also do partial application of effect operations to a computation as well. Consider an example app:

app1 :: forall eff
   . EffConstraint (TimeEff  EnvEff AppConfig  StateEff AppState) eff
  => eff ()
app1 = ...

Our app uses three effects, TimeEff for getting current time, EnvEff to reading the app config, and StateEff for storing states. Our app is free of IoEff, which makes it much easier to test with mock effects.

It may be cumbersome if we only bind all effect operations in our main program. For EnvEff and StateEff, we may still need to write some code to get the environment or initialize state. But for TimeEff, we pretty much know that our real app is going to use some IO to get the time. So why not bind it with ioTimeOps first:

app2 :: EffConstraint (EnvEff AppConfig  StateEff AppState) IO
  => IO ()
app2 = withOps ioTimeOps app1

By binding ioTimeOps with app1, we also unintentionally unified the effect variable eff with IO, since ioTimeOps is defined to run directly with IO. However with that binding we now have a problem: we now have to provide EnvEff and StateEff ops handlers that can run on IO, not ReaderT AppConfig IO or StateT AppState IO or ReaderT AppConfig StateT AppState IO. Because of that, we can't reuse our readerTOps and stateTOps that are defined to work only under lifted monads.

The problem is partial application of operation handlers have too eagerly bind the concrete monad for the entire computation. Instead we need some way to lazily hold on to both ioTimeOps and app1, and lift them to some other monad at later time is necessary. Fortunately implicit-effects solves this by providing the Computation datatype:

app3 :: forall eff . (Effect eff)
  => Computation
       (TimeEff  EnvEff AppConfig  StateEff AppState)
       (Return ())
app3 = genericReturn app1

The Computation type have the following signature:

newtype Computation ops comp eff1 = Computation {
  runComp :: forall eff2 .
    ( ImplicitOps ops
    , Effect eff1
    , Effect eff2
    => LiftEff eff1 eff2
    -> Operation ops eff2
    -> comp eff2

The detailed machinery is not too important at this moment, but the gist is that Computation provides a liftable computation wrapper around generic computation functions. The first type argument is the effect signatures of the required effect operations. The second type argument is the computation type parameterized by an effect eff. In normal function computations we use the Return wrapper type which is defined as:

newtype Return a eff = Return {
  returnVal :: eff a

Finally the third type argument to Computation is the base monad that is can run on, as well as the base monad of operation handlers that it can accept.

The genericReturn helper is provided by implicit-effects to wrap a plain function computation into a Computation:

genericReturn :: forall ops a . (ImplicitOps ops)
  => (forall eff . (EffConstraint ops eff)
      => eff a)
  -> (forall eff . (Effect eff)
      => Computation ops (Return a) eff)

Other than Return computation for plain functions, effect Operations are also computations since they are also parameterized by a monad type.

ioTimeHandler :: Computation NoEff TimeOps IO
ioTimeHandler = baseOpsHandler ioTimeOps

The baseOpsHandler helper is provided by implicit-effects to wrap an operation handler to a computation.

baseOpsHandler :: forall handler eff
   . (ImplicitOps handler, Effect eff)
  => Operation handler eff
  -> Computation NoEff (Operation handler) eff

NoEff is the empty effect signature, indicating that the operation handler computation defined does not depend on other effects. As you may have guess, soon after this we will talk about operation handlers that depend on other effects.

Given we have an ops handler computation and a return computation, we can bind the two together as follow:

app4 :: Computation
         (EnvEff AppConfig  StateEff AppState)
         (Return ())
app4 = bindOpsHandlerWithCast
  cast cast
  ioTimeHandler app3

bindOpsHandlerWithCast is a helper function provided by implicit-effects that binds an ops handler to a computation, at the same time perform safe "casting" of the effect union constraints to a suitable target type. We will go into details on ops casting in later sections, but the gist of it is that without it we'd have to write something like:

app4' :: Computation
         (NoEff  EnvEff AppConfig  StateEff AppState)
         (Return ())
app4' = bindExactOpsHandler ioTimeHandler app3

Notice that NoEff is appended to the front of app4''s effect dependencies, as the precise version bindExactOpsHandler merges the effect operations required by both ioTimeHandler and app3. But through some Haskell hacks called constraint casting, we can statically show proofs to Haskell that NoEff can be eliminated since it has a trivial constraint that can always be satisfied. We'll leave further explanation to the next sections and continue with our example.

The nice thing about Computation is that we can partially apply ops handlers as many times as we need, as long as the ops handlers can run on either the current monad or a lifted monad. With that we can for example further bind our app with a StateT handler:

app5 :: Computation
         (EnvEff AppConfig  StateEff AppState)
         (Return ())
         StateT AppState IO
app5 = liftComputation stateTLiftEff app4

app6 :: Computation
         (EnvEff AppConfig)
         (Return ())
         StateT AppState IO
app6 = bindOpsHandlerWithCast
  cast cast
  stateTHandler app5

The liftComputation function is used to lift a computation to run on a lifted monad, by providing it a LiftEff object. LiftEff is an opaque object that can be used to apply effmap to an EffFunctor, but with the optimization that if it is an identity idLift, it just skips the effmap and returns the original EffFunctor.

We first lift our app to work on StateT AppState IO, and then use bindOpsHandlerWithCast to bind it with stateTHandler, which is provided as the Computation version of stateTOps. Also notice that bindOpsHandlerWithCast allows reordering of effect operations, so we can still bind it even though StateEff appears in the last position in our original type for app3.

We can then similarly continue with binding our reader ops with ReaderT:

app7 :: Computation
         (Return ())
         ReaderT AppConfig StateT AppState IO
app7 = bindOpsHandlerWithCast
  cast cast
  readerTHandler $
  liftComputation readerTLiftEff app6

Now we have "fully applied" the effect operations of a computation, making it requiring only NoEff. With that we can use execComp to run our computation and get back the underlying function:

app8 :: ReaderT AppConfig StateT AppState IO ()
app8 = execComp app7

At this stage we can then execute our monad transformer stack as usually, and finally get back IO (). In practice, app4 through app8 can slowly be transformed in different parts of our codebase. We can essentially fully utilize the functional programming style and doing partial applications of named parameters to our computations like regular functions.


At this point you may be suspicious of the above roundabout way of using implicit-effects just to get back our favorite monad transformer stacks. There is actually even simplified abstractions provided by implicit-effects that lets us use mtl without touching the monad transformers like ReaderT and StateT.

app1 :: Computation
         (EnvEff AppConfig  StateEff AppState)
         (Return ())
app1 = ...

initialAppState :: AppState
initialAppState = ...

app2 :: Computation
         (EnvEff AppConfig)
         (Return ())
app2 = runPipelineWithCast
  cast cast
  (stateTPipeline initialAppState)

A Pipeline is simply generic functions that transforms computations, wrapped in a newtype. stateTPipeline is one of the pipelines provided by implicit-effects that given an initial state, it performs transformation that removes the StateEff operation from a Computation without changing the monad type. Here again we have to use some ops casting magic with runPipelineWithCast that reorder the effect operations of the original computation, and remove the NoEff noise from the result computation.

Notice here stateTPipeline completely encapsulates the fact that we are using StateT underneath. As far as the computation concerns, we can swap in different pipelines that implement StateEff, with performance characteristics being the only difference.


To Be Continued..

I am still working on writing the documentation and tutorial for implicit-effects. Thank you for taking the time to read until here. In the meanwhile, you can refer to the Haddock documentation for implicit-effects to learn more.

You can also look at the effect operation unit tests which has some example use of implicit-effects.


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