Polysemy

Core Types

data Sem r a

The Sem monad handles computations of arbitrary extensible effects. A value of type Sem r describes a program with the capabilities of r. For best results, r should always be kept polymorphic, but you can add capabilities via the Member constraint.

The value of the Sem monad is that it allows you to write programs against a set of effects without a predefined meaning, and provide that meaning later. For example, unlike with mtl, you can decide to interpret an Error effect traditionally as an Either, or instead as (a significantly faster) IO Exception. These interpretations (and others that you might add) may be used interchangeably without needing to write any newtypes or Monad instances. The only change needed to swap interpretations is to change a call from runError to errorToIOFinal.

The effect stack r can contain arbitrary other monads inside of it. These monads are lifted into effects via the Embed effect. Monadic values can be lifted into a Sem via embed.

Higher-order actions of another monad can be lifted into higher-order actions of Sem via the Final effect, which is more powerful than Embed, but also less flexible to interpret.

A Sem can be interpreted as a pure value (via run) or as any traditional Monad (via runM or runFinal). Each effect E comes equipped with some interpreters of the form:

runE :: Sem (E ': r) a -> Sem r a

which is responsible for removing the effect E from the effect stack. It is the order in which you call the interpreters that determines the monomorphic representation of the r parameter.

Order of interpreters can be important - it determines behaviour of effects that manipulate state or change control flow. For example, when interpreting this action:

>>> :{
  example :: Members '[State String, Error String] r => Sem r String
  example = do
    put "start"
    let throwing, catching :: Members '[State String, Error String] r => Sem r String
        throwing = do
          modify (++"-throw")
          throw "error"
          get
        catching = do
          modify (++"-catch")
          get
    catch @String throwing (\ _ -> catching)
:}

when handling Error first, state is preserved after error occurs:

>>> :{
  example
    & runError
    & fmap (either id id)
    & evalState ""
    & runM
    & (print =<<)
:}
"start-throw-catch"

while handling State first discards state in such cases:

>>> :{
  example
    & evalState ""
    & runError
    & fmap (either id id)
    & runM
    & (print =<<)
:}
"start-catch"

A good rule of thumb is to handle effects which should have "global" behaviour over other effects later in the chain.

After all of your effects are handled, you'll be left with either a Sem '[] a, a Sem '[ Embed m ] a, or a Sem '[ Final m ] a value, which can be consumed respectively by run, runM, and runFinal.

Examples

As an example of keeping r polymorphic, we can consider the type

Member (State String) r => Sem r ()

to be a program with access to

get :: Sem r String
put :: String -> Sem r ()

methods.

By also adding a

Member (Error Bool) r

constraint on r, we gain access to the

throw :: Bool -> Sem r a
catch :: Sem r a -> (Bool -> Sem r a) -> Sem r a

functions as well.

In this sense, a Member (State s) r constraint is analogous to mtl's MonadState s m and should be thought of as such. However, unlike mtl, a Sem monad may have an arbitrary number of the same effect.

For example, we can write a Sem program which can output either Ints or Bools:

foo :: ( Member (Output Int) r
       , Member (Output Bool) r
       )
    => Sem r ()
foo = do
  output @Int  5
  output True

Notice that we must use -XTypeApplications to specify that we'd like to use the (Output Int) effect.

Since: 0.1.2.0

Instances

Monad (Sem f)

Defined in Polysemy.Internal

Methods

(>>=) :: Sem f a -> (a -> Sem f b) -> Sem f b

(>>) :: Sem f a -> Sem f b -> Sem f b

return :: a -> Sem f a

fail :: String -> Sem f a

Functor (Sem f)

Defined in Polysemy.Internal

Methods

fmap :: (a -> b) -> Sem f a -> Sem f b

(<$) :: a -> Sem f b -> Sem f a

Member Fixpoint r => MonadFix (Sem r)

Defined in Polysemy.Internal

Methods

mfix :: (a -> Sem r a) -> Sem r a

Member (Fail :: (Type -> Type) -> Type -> Type) r => MonadFail (Sem r)

Since: 1.1.0.0

Defined in Polysemy.Internal

Methods

fail :: String -> Sem r a

Applicative (Sem f)

Defined in Polysemy.Internal

Methods

pure :: a -> Sem f a

(<*>) :: Sem f (a -> b) -> Sem f a -> Sem f b

liftA2 :: (a -> b -> c) -> Sem f a -> Sem f b -> Sem f c

(*>) :: Sem f a -> Sem f b -> Sem f b

(<*) :: Sem f a -> Sem f b -> Sem f a

Member (Embed IO) r => MonadIO (Sem r)

This instance will only lift IO actions. If you want to lift into some other MonadIO type, use this instance, and handle it via the embedToMonadIO interpretation.

Defined in Polysemy.Internal

Methods

liftIO :: IO a -> Sem r a

Member NonDet r => Alternative (Sem r)

Defined in Polysemy.Internal

Methods

empty :: Sem r a

(<|>) :: Sem r a -> Sem r a -> Sem r a

some :: Sem r a -> Sem r [a]

many :: Sem r a -> Sem r [a]

Member NonDet r => MonadPlus (Sem r)

Since: 0.2.1.0

Defined in Polysemy.Internal

Methods

mzero :: Sem r a

mplus :: Sem r a -> Sem r a -> Sem r a

type Member e r = MemberNoError e r

A proof that the effect e is available somewhere inside of the effect stack r.

type MemberWithError e r = (MemberNoError e r, WhenStuck (IndexOf r (Found r e)) (AmbiguousSend r e))

Like Member, but will produce an error message if the types are ambiguous.

@since TODO

type family Members es r :: Constraint where ...

Makes constraints of functions that use multiple effects shorter by translating single list of effects into multiple Member constraints:

foo :: Members '[ Output Int
                , Output Bool
                , State String
                ] r
    => Sem r ()

translates into:

foo :: ( Member (Output Int) r
       , Member (Output Bool) r
       , Member (State String) r
       )
    => Sem r ()

Since: 0.1.2.0

Equations

Members '[] r = ()

Members (e ': es) r = (Member e r, Members es r)

Running Sem

run :: Sem '[] a -> a

Run a Sem containing no effects as a pure value.

runM :: Monad m => Sem '[Embed m] a -> m a

Lower a Sem containing only a single lifted Monad into that monad.

runFinal :: Monad m => Sem '[Final m] a -> m a

Lower a Sem containing only a single lifted, final Monad into that monad.

If you also need to process an Embed m effect, use this together with embedToFinal.

Since: 1.2.0.0

Type synonyms for user convenience

type InterpreterFor e r = forall a. Sem (e ': r) a -> Sem r a

Type synonym for interpreters that consume an effect without changing the return value. Offered for user convenience.

r Is kept polymorphic so it's possible to place constraints upon it:

teletypeToIO :: Member (Embed IO) r
             => InterpreterFor Teletype r

Interoperating With Other Monads

Embed

newtype Embed m (z :: Type -> Type) a where

An effect which allows a regular Monad m into the Sem ecosystem. Monadic actions in m can be lifted into Sem via embed.

For example, you can use this effect to lift IO actions directly into Sem:

embed (putStrLn "hello") :: Member (Embed IO) r => Sem r ()

That being said, you lose out on a significant amount of the benefits of Sem by using embed directly in application code; doing so will tie your application code directly to the underlying monad, and prevent you from interpreting it differently. For best results, only use Embed in your effect interpreters.

Consider using trace and traceToIO as a substitute for using putStrLn directly.

Since: 1.0.0.0

Constructors

Embed

Fields

• :: { unEmbed :: m a
•    } -> Embed m z a

embed :: Member (Embed m) r => m a -> Sem r a

Embed a monadic action m in Sem.

Since: 1.0.0.0

embedToFinal :: (Member (Final m) r, Functor m) => Sem (Embed m ': r) a -> Sem r a

Transform an Embed m effect into a Final m effect

Since: 1.2.0.0

Final

For advanced uses of Final, including creating your own interpreters that make use of it, see Polysemy.Final

data Final m z a

An effect for embedding higher-order actions in the final target monad of the effect stack.

This is very useful for writing interpreters that interpret higher-order effects in terms of the final monad.

Final is more powerful than Embed, but is also less flexible to interpret (compare runEmbedded with finalToFinal). If you only need the power of embed, then you should use Embed instead.

Beware: Final actions are interpreted as actions of the final monad, and the effectful state visible to withWeavingToFinal / withStrategicToFinal / interpretFinal is that of all interpreters run in order to produce the final monad.

This means that any interpreter built using Final will not respect local/global state semantics based on the order of interpreters run. You should signal interpreters that make use of Final by adding a -Final suffix to the names of these.

State semantics of effects that are not interpreted in terms of the final monad will always appear local to effects that are interpreted in terms of the final monad.

State semantics between effects that are interpreted in terms of the final monad depend on the final monad. For example, if the final monad is a monad transformer stack, then state semantics will depend on the order monad transformers are stacked.

Since: 1.2.0.0

Instances

type DefiningModule Final

Defined in Polysemy.Final

type DefiningModule Final = "Polysemy.Final"

embedFinal :: (Member (Final m) r, Functor m) => m a -> Sem r a

withWeavingToFinal admits an implementation of embed.

Just like embed, you are discouraged from using this in application code.

Since: 1.2.0.0

Lifting

raise :: forall e r a. Sem r a -> Sem (e ': r) a

Introduce an effect into Sem. Analogous to lift in the mtl ecosystem

raiseUnder :: forall e2 e1 r a. Sem (e1 ': r) a -> Sem (e1 ': (e2 ': r)) a

Like raise, but introduces a new effect underneath the head of the list.

raiseUnder can be used in order to turn transformative interpreters into reinterpreters. This is especially useful if you're writing an interpreter which introduces an intermediary effect, and then want to use an existing interpreter on that effect.

For example, given:

fooToBar :: Member Bar r => Sem (Foo ': r) a -> Sem r a
runBar   :: Sem (Bar ': r) a -> Sem r a

You can write:

runFoo :: Sem (Foo ': r) a -> Sem r a
runFoo =
    runBar     -- Consume Bar
  . fooToBar   -- Interpret Foo in terms of the new Bar
  . raiseUnder -- Introduces Bar under Foo

Since: 1.2.0.0

raiseUnder2 :: forall e2 e3 e1 r a. Sem (e1 ': r) a -> Sem (e1 ': (e2 ': (e3 ': r))) a

Like raise, but introduces two new effects underneath the head of the list.

Since: 1.2.0.0

raiseUnder3 :: forall e2 e3 e4 e1 r a. Sem (e1 ': r) a -> Sem (e1 ': (e2 ': (e3 ': (e4 ': r)))) a

Like raise, but introduces two new effects underneath the head of the list.

Since: 1.2.0.0

Trivial Interpretation

subsume :: Member e r => Sem (e ': r) a -> Sem r a

Interprets an effect in terms of another identical effect.

This is useful for defining interpreters that use reinterpretH without immediately consuming the newly introduced effect. Using such an interpreter recursively may result in duplicate effects, which may then be eliminated using subsume.

Since: 1.2.0.0

Creating New Effects

Effects should be defined as a GADT (enable -XGADTs), with kind (* -> *) -> * -> *. Every primitive action in the effect should be its own constructor of the type. For example, we can model an effect which interacts with a tty console as follows:

data Console m a where
  WriteLine :: String -> Console m ()
  ReadLine  :: Console m String

Notice that the a parameter gets instantiated at the desired return type of the actions. Writing a line returns a (), but reading one returns String.

By enabling -XTemplateHaskell, we can use the makeSem function to generate smart constructors for the actions. These smart constructors can be invoked directly inside of the Sem monad.

makeSem ''Console

results in the following definitions:

writeLine :: Member Console r => String -> Sem r ()
readLine  :: Member Console r => Sem r String

Effects which don't make use of the m parameter are known as "first-order effects."

Higher-Order Effects

Every effect has access to the m parameter, which corresponds to the Sem monad it's used in. Using this parameter, we're capable of writing effects which themselves contain subcomputations.

For example, the definition of Error is

data Error e m a where
  Throw :: e -> Error e m a
  Catch :: m a -> (e -> m a) -> Error e m a

where Catch is an action that can run an exception handler if its first argument calls throw.

makeSem ''Error

throw :: Member (Error e) r => e -> Sem r a
catch  :: Member (Error e) r => Sem r a -> (e -> Sem r a) -> Sem r a

As you see, in the smart constructors, the m parameter has become Sem r.

makeSem :: Name -> Q [Dec]

If T is a GADT representing an effect algebra, as described in the module documentation for Polysemy, $(makeSem ''T) automatically generates a smart constructor for every data constructor of T. This also works for data family instances. Names of smart constructors are created by changing first letter to lowercase or removing prefix : in case of operators. Fixity declaration is preserved for both normal names and operators.

Since: 0.1.2.0

makeSem_ :: Name -> Q [Dec]

Like makeSem, but does not provide type signatures and fixities. This can be used to attach Haddock comments to individual arguments for each generated function.

data Output o m a where
  Output :: o -> Output o m ()

makeSem_ ''Output

-- | Output the value @o@.
output :: forall o r
       .  Member (Output o) r
       => o         -- ^ Value to output.
       -> Sem r ()  -- ^ No result.

Because of limitations in Template Haskell, signatures have to follow some rules to work properly:

• makeSem_ must be used before the explicit type signatures
• signatures have to specify argument of Sem representing union of effects as r (e.g. Sem r ())
• all arguments in effect's type constructor have to follow naming scheme from data constructor's declaration:

data Foo e m a where
  FooC1 :: Foo x m ()
  FooC2 :: Foo (Maybe x) m ()

should have x in type signature of fooC1:

fooC1 :: forall x r. Member (Foo x) r => Sem r ()

and Maybe x in signature of fooC2:

fooC2 :: forall x r. Member (Foo (Maybe x)) r => Sem r ()

• all effect's type variables and r have to be explicitly quantified using forall (order is not important)

These restrictions may be removed in the future, depending on changes to the compiler.

Change in (TODO(Sandy): version): in case of GADTs, signatures now only use names from data constructor's type and not from type constructor declaration.

Since: 0.1.2.0

Combinators for Interpreting First-Order Effects

interpret

Arguments

:: FirstOrder e "interpret"

=> (forall x m. e m x -> Sem r x)

A natural transformation from the handled effect to other effects already in Sem.

-> Sem (e ': r) a

-> Sem r a

The simplest way to produce an effect handler. Interprets an effect e by transforming it into other effects inside of r.

intercept

Arguments

:: (Member e r, FirstOrder e "intercept")

=> (forall x m. e m x -> Sem r x)

A natural transformation from the handled effect to other effects already in Sem.

-> Sem r a

Unlike interpret, intercept does not consume any effects.

-> Sem r a

Like interpret, but instead of handling the effect, allows responding to the effect while leaving it unhandled. This allows you, for example, to intercept other effects and insert logic around them.

reinterpret

Arguments

:: FirstOrder e1 "reinterpret"

=> (forall m x. e1 m x -> Sem (e2 ': r) x)

A natural transformation from the handled effect to the new effect.

-> Sem (e1 ': r) a

-> Sem (e2 ': r) a

Like interpret, but instead of removing the effect e, reencodes it in some new effect f. This function will fuse when followed by runState, meaning it's free to reinterpret in terms of the State effect and immediately run it.

reinterpret2

Arguments

:: FirstOrder e1 "reinterpret2"

=> (forall m x. e1 m x -> Sem (e2 ': (e3 ': r)) x)

A natural transformation from the handled effect to the new effects.

-> Sem (e1 ': r) a

-> Sem (e2 ': (e3 ': r)) a

Like reinterpret, but introduces two intermediary effects.

reinterpret3

Arguments

:: FirstOrder e1 "reinterpret3"

=> (forall m x. e1 m x -> Sem (e2 ': (e3 ': (e4 ': r))) x)

A natural transformation from the handled effect to the new effects.

-> Sem (e1 ': r) a

-> Sem (e2 ': (e3 ': (e4 ': r))) a

Like reinterpret, but introduces three intermediary effects.

rewrite :: forall e1 e2 r a. (forall m x. e1 m x -> e2 m x) -> Sem (e1 ': r) a -> Sem (e2 ': r) a

Rewrite an effect e1 directly into e2, and put it on the top of the effect stack.

Since: 1.2.3.0

transform :: forall e1 e2 r a. Member e2 r => (forall m x. e1 m x -> e2 m x) -> Sem (e1 ': r) a -> Sem r a

Transform an effect e1 into an effect e2 that is already somewhere inside of the stack.

Since: 1.2.3.0

Combinators for Interpreting Higher-Order Effects

interpretH

Arguments

:: (forall x m. e m x -> Tactical e m r x)

A natural transformation from the handled effect to other effects already in Sem.

-> Sem (e ': r) a

-> Sem r a

Like interpret, but for higher-order effects (ie. those which make use of the m parameter.)

See the notes on Tactical for how to use this function.

interceptH

Arguments

:: Member e r

=> (forall x m. e m x -> Tactical e m r x)

A natural transformation from the handled effect to other effects already in Sem.

-> Sem r a

Unlike interpretH, interceptH does not consume any effects.

-> Sem r a

Like interceptH, but for higher-order effects.

See the notes on Tactical for how to use this function.

reinterpretH

Arguments

:: (forall m x. e1 m x -> Tactical e1 m (e2 ': r) x)

A natural transformation from the handled effect to the new effect.

-> Sem (e1 ': r) a

-> Sem (e2 ': r) a

Like reinterpret, but for higher-order effects.

See the notes on Tactical for how to use this function.

reinterpret2H

Arguments

:: (forall m x. e1 m x -> Tactical e1 m (e2 ': (e3 ': r)) x)

A natural transformation from the handled effect to the new effects.

-> Sem (e1 ': r) a

-> Sem (e2 ': (e3 ': r)) a

Like reinterpret2, but for higher-order effects.

See the notes on Tactical for how to use this function.

reinterpret3H

Arguments

:: (forall m x. e1 m x -> Tactical e1 m (e2 ': (e3 ': (e4 ': r))) x)

A natural transformation from the handled effect to the new effects.

-> Sem (e1 ': r) a

-> Sem (e2 ': (e3 ': (e4 ': r))) a

Like reinterpret3, but for higher-order effects.

See the notes on Tactical for how to use this function.

Combinators for Interpreting Directly to IO

withLowerToIO

Arguments

:: Member (Embed IO) r

=> ((forall x. Sem r x -> IO x) -> IO () -> IO a)

A lambda that takes the lowering function, and a finalizing IO action to mark a the forked thread as being complete. The finalizing action need not be called.

-> Sem r a

Run an effect stack all the way down to IO by running it in a new thread, and temporarily turning the current thread into an event poll.

This function creates a thread, and so should be compiled with -threaded.

Since: 0.5.0.0

Kind Synonyms

type Effect = (Type -> Type) -> Type -> Type

The kind of effects.

Since: 0.5.0.0

type EffectRow = [Effect]

The kind of effect rows.

Since: 0.5.0.0

Composing IO-based Interpreters

(.@) infixl 8

Arguments

:: Monad m

=> (forall x. Sem r x -> m x)

The lowering function, likely runM.

-> (forall y. (forall x. Sem r x -> m x) -> Sem (e ': r) y -> Sem r y)

-> Sem (e ': r) z

-> m z

Some interpreters need to be able to lower down to the base monad (often IO) in order to function properly --- some good examples of this are lowerError and lowerResource.

However, these interpreters don't compose particularly nicely; for example, to run lowerResource, you must write:

runM . lowerError runM

Notice that runM is duplicated in two places here. The situation gets exponentially worse the more intepreters you have that need to run in this pattern.

Instead, .@ performs the composition we'd like. The above can be written as

(runM .@ lowerError)

The parentheses here are important; without them you'll run into operator precedence errors.

Warning: This combinator will duplicate work that is intended to be just for initialization. This can result in rather surprising behavior. For a version of .@ that won't duplicate work, see the .@! operator in polysemy-zoo.

Interpreters using Final may be composed normally, and avoid the work duplication issue. For that reason, you're encouraged to use -Final interpreters instead of lower- interpreters whenever possible.

(.@@) infixl 8

Arguments

:: Monad m

=> (forall x. Sem r x -> m x)

The lowering function, likely runM.

-> (forall y. (forall x. Sem r x -> m x) -> Sem (e ': r) y -> Sem r (f y))

-> Sem (e ': r) z

-> m (f z)

Like .@, but for interpreters which change the resulting type --- eg. lowerError.

Tactics

Higher-order effects need to explicitly thread other effects' state through themselves. Tactics are a domain-specific language for describing exactly how this threading should take place.

The first computation to be run should use runT, and subsequent computations in the same environment should use bindT. Any first-order constructors which appear in a higher-order context may use pureT to satisfy the typechecker.

type Tactical e m r x = forall f. Functor f => Sem (WithTactics e f m r) (f x)

Tactical is an environment in which you're capable of explicitly threading higher-order effect states. This is provided by the (internal) effect Tactics, which is capable of rewriting monadic actions so they run in the correct stateful environment.

Inside a Tactical, you're capable of running pureT, runT and bindT which are the main tools for rewriting monadic stateful environments.

For example, consider trying to write an interpreter for Resource, whose effect is defined as:

data Resource m a where
  Bracket :: m a -> (a -> m ()) -> (a -> m b) -> Resource m b

Here we have an m a which clearly needs to be run first, and then subsequently call the a -> m () and a -> m b arguments. In a Tactical environment, we can write the threading code thusly:

Bracket alloc dealloc use -> do
  alloc'   <- runT  alloc
  dealloc' <- bindT dealloc
  use'     <- bindT use

where

alloc'   ::         Sem (Resource ': r) (f a1)
dealloc' :: f a1 -> Sem (Resource ': r) (f ())
use'     :: f a1 -> Sem (Resource ': r) (f x)

The f type here is existential and corresponds to "whatever state the other effects want to keep track of." f is always a Functor.

alloc', dealloc' and use' are now in a form that can be easily consumed by your interpreter. At this point, simply bind them in the desired order and continue on your merry way.

We can see from the types of dealloc' and use' that since they both consume a f a1, they must run in the same stateful environment. This means, for illustration, any puts run inside the use block will not be visible inside of the dealloc block.

Power users may explicitly use getInitialStateT and bindT to construct whatever data flow they'd like; although this is usually unnecessary.

type WithTactics e f m r = Tactics f m (e ': r) ': r

getInitialStateT :: forall f m r e. Sem (WithTactics e f m r) (f ())

Get the stateful environment of the world at the moment the effect e is to be run. Prefer pureT, runT or bindT instead of using this function directly.

pureT :: a -> Tactical e m r a

Lift a value into Tactical.

runT

Arguments

:: m a

The monadic action to lift. This is usually a parameter in your effect.

-> Sem (WithTactics e f m r) (Sem (e ': r) (f a))

Run a monadic action in a Tactical environment. The stateful environment used will be the same one that the effect is initally run in. Use bindT if you'd prefer to explicitly manage your stateful environment.

bindT

Arguments

:: (a -> m b)

The monadic continuation to lift. This is usually a parameter in your effect.

Continuations lifted via bindT will run in the same environment which produced the a.

-> Sem (WithTactics e f m r) (f a -> Sem (e ': r) (f b))

Lift a kleisli action into the stateful environment. You can use bindT to get an effect parameter of the form a -> m b into something that can be used after calling runT on an effect parameter m a.

getInspectorT :: forall e f m r. Sem (WithTactics e f m r) (Inspector f)

Get a natural transformation capable of potentially inspecting values inside of f. Binding the result of getInspectorT produces a function that can sometimes peek inside values returned by bindT.

This is often useful for running callback functions that are not managed by polysemy code.

Example

We can use the result of getInspectT to "undo" pureT (or any of the other Tactical functions):

ins <- getInspectorT
fa <- pureT "hello"
fb <- pureT True
let a = inspect ins fa   -- Just "hello"
    b = inspect ins fb   -- Just True

newtype Inspector f

A container for inspect. See the documentation for getInspectorT.

Constructors

Inspector

Fields

• inspect :: forall x. f x -> Maybe x

  See the documentation for getInspectorT.