A fast, flexible, fused effect system for Haskell

• Overview
  • Algebraic effects
  • Higher-order effects
  • Fusion
• Usage
  • Using built-in effects
  • Invoking effects
  • Running effects
  • Required compiler extensions
  • Defining new effects
  • Defining effect handlers
• Project overview
  • Development
  • Versioning
• Benchmarks
• Related work
  • Contributed packages
  • Projects using fused-effects
  • Comparison to mtl
  • Comparison to freer-simple
  • Comparison to polysemy
  • Comparison to eff
• Acknowledgments

Overview

fused-effects is an effect system for Haskell that values expressivity, efficiency, and rigor. It provides an encoding of algebraic, higher-order effects, includes a library of the most common effects, and generates efficient code by fusing effect handlers through computations. It is suitable for use in hobbyist, research, and industrial contexts.

Readers already familiar with effect systems may wish to start with the usage instead. For those interested, this talk at Strange Loop outlines the history of and motivation behind effect systems and fused-effects itself.

Algebraic effects

In fused-effects and other systems with algebraic (or, sometimes, extensible) effects, effectful programs are split into two parts: the specification (or syntax) of the actions to be performed, and the interpretation (or semantics) given to them.

In fused-effects, effect types provide syntax and carrier types provide semantics. Effect types are datatypes with one constructor for each action, invoked using the send builtin. Carriers are monads, with an Algebra instance specifying how an effect’s constructors should be interpreted. Carriers can handle more than one effect, and multiple carriers can be defined for the same effect, corresponding to different interpreters for the effect’s syntax.

Higher-order effects

Unlike some other effect systems, fused-effects offers higher-order (or scoped) effects in addition to first-order algebraic effects. In a strictly first-order algebraic effect system, operations like local or catchError, which specify some action limited to a given scope, must be implemented as interpreters, hard-coding their meaning in precisely the manner algebraic effects were designed to avoid. By specifying effects as higher-order functors, this limitation is removed, meaning that these operations admit a variety of interpretations. This means, for example, that you can introspect and redefine both the local and ask operations provided by the Reader effect, rather than solely ask (as is the case with certain formulations of algebraic effects).

As Nicolas Wu et al. showed in Effect Handlers in Scope, this has implications for the expressiveness of effect systems. It also has the benefit of making effect handling more consistent, since scoped operations are just syntax which can be interpreted like any other, and are thus simpler to reason about.

Fusion

In order to maximize efficiency, fused-effects applies fusion laws, avoiding the construction of intermediate representations of effectful computations between effect handlers. In fact, this is applied as far as the initial construction as well: there is no representation of the computation as a free monad parameterized by some syntax type. As such, fused-effects avoids the overhead associated with constructing and evaluating any underlying free or freer monad.

Instead, computations are performed in a carrier type for the syntax, typically a monad wrapping further monads, via an instance of the Carrier class. This carrier is specific to the effect handler selected, but since it isn’t described until the handler is applied, the separation between specification and interpretation is maintained. Computations are written against an abstract effectful signature, and only specialized to some concrete carrier when their effects are interpreted.

Since the interpretation of effects is written as a typeclass instance which ghc is eager to inline, performance is excellent: approximately on par with mtl.

Finally, since the fusion of carrier algebras occurs as a result of the selection of the carriers, it doesn’t depend on complex RULES pragmas, making it easy to reason about and tune.

Usage

Package organization

The fused-effects package is organized into two module hierarchies:

• those under Control.Effect, which provide effects and functions that invoke these effects’ capabilities.
• those under Control.Carrier, which provide carrier types capable of executing the effects described by a given effect type.

An additional module, Control.Algebra, provides the Algebra interface that carrier types implement to provide an interpretation of a given effect. You shouldn’t need to import it unless you’re defining your own effects.

Invoking effects

Each module under the Control.Effect hierarchy provides a set of functions that invoke effects, each mapping to a constructor of the underlying effect type. These functions are similar to, but more powerful than, those provided by mtl. In this example, we invoke the get and put functions provided by Control.Effect.State, first extracting the state and then updating it with a new value:

action1 :: Has (State String) sig m => m ()
action1 = get >>= \ s -> put ("hello, " ++ s)

The Has constraint requires a given effect (here State) to be present in a signature (sig), and relates that signature to be present in a carrier type (m). We generally, but not always, program against an abstract carrier type, usually called m, as carrier types always implement the Monad typeclass.

To add effects to a given computation, add more Has constraints to the signature/carrier pair sig and m. For example, to add a Reader effect managing an Int, we would write:

action2 :: (Has (State String) sig m, Has (Reader Int) sig m) => m ()
action2 = do
  i <- ask
  put (replicate i '!')

Running effects

Effects are run with effect handlers, specified as functions (generally starting with run…) unpacking some specific monad with a Carrier instance. For example, we can run a State computation using runState, imported from the Control.Carrier.State.Strict carrier module:

example1 :: Algebra sig m => [a] -> m (Int, ())
example1 list = runState 0 $ do
  i <- get
  put (i + length list)

runState returns a tuple of both the computed value (the ()) and the final state (the Int), visible in the result of the returned computation. The get function is resolved with a visible type application, due to the fact that effects can contain more than one state type (in contrast with mtl’s MonadState, which limits the user to a single state type).

Since this function returns a value in some carrier m, effect handlers can be chained to run multiple effects. Here, we get the list to compute the length of from a Reader effect:

example2 :: Algebra sig m => m (Int, ())
example2 = runReader "hello" . runState 0 $ do
  list <- ask
  put (length (list :: String))

(Note that the type annotation on list is necessary to disambiguate the requested value, since otherwise all the typechecker knows is that it’s an arbitrary Foldable. For more information, see the comparison to mtl.)

When all effects have been handled, a computation’s final value can be extracted with run:

example3 :: (Int, ())
example3 = run . runReader "hello" . runState 0 $ do
  list <- ask
  put (length (list :: String))

run is itself actually an effect handler for the Lift Identity effect, whose only operation is to lift a result value into a computation.

Alternatively, arbitrary Monads can be embedded into effectful computations using the Lift effect. In this case, the underlying Monadic computation can be extracted using runM. Here, we use the MonadIO instance for the LiftC carrier to lift putStrLn into the middle of our computation:

example4 :: IO (Int, ())
example4 = runM . runReader "hello" . runState 0 $ do
  list <- ask
  liftIO (putStrLn list)
  put (length list)

(Note that we no longer need to give a type annotation for list, since putStrLn constrains the type for us.)

Required compiler extensions

When defining your own effects, you may need -XKindSignatures if GHC cannot correctly infer the type of your constructor; see the documentation on common errors for more information about this case.

When defining carriers, you’ll need -XTypeOperators to declare a Carrier instance over (:+:), -XFlexibleInstances to loosen the conditions on the instance, -XMultiParamTypeClasses since Carrier takes two parameters, and -XUndecidableInstances to satisfy the coverage condition for this instance.

The following invocation, taken from the teletype example, should suffice for most use or construction of effects and carriers:

{-# LANGUAGE FlexibleInstances, GeneralizedNewtypeDeriving, MultiParamTypeClasses, TypeOperators, UndecidableInstances #-}

Defining new effects

The process of defining new effects is outlined in docs/defining_effects.md, using the classic Teletype effect as an example.

Project overview

This project builds a Haskell package named fused-effects. The library’s sources are in src. Unit tests are in test, and library usage examples are in examples. Further documentation can be found in docs.

This project adheres to the Contributor Covenant code of conduct. By participating, you are expected to uphold this code.

Finally, this project is licensed under the BSD 3-clause license.

Development

Development of fused-effects is typically done using cabal v2-build:

cabal v2-build # build the library
cabal v2-test  # build and run the examples and tests

The package is available on hackage, and can be used by adding it to a component’s build-depends field in your .cabal file.

Testing

fused-effects comes with a rigorous test suite. Each law or property stated in the Haddock documentation is checked using generative tests powered by the hedgehog library.

Versioning

fused-effects adheres to the Package Versioning Policy standard.

Benchmarks

To run the provided benchmark suite, use cabal v2-bench. You may wish to provide the -O2 compiler option to view performance under aggressive optimizations. fused-effects has been benchmarked against a number of other effect systems. See also @patrickt’s benchmarks.

Related work

fused-effects is an encoding of higher-order algebraic effects following the recipes in Effect Handlers in Scope (Nicolas Wu, Tom Schrijvers, Ralf Hinze), Monad Transformers and Modular Algebraic Effects: What Binds Them Together (Tom Schrijvers, Maciej Piróg, Nicolas Wu, Mauro Jaskelioff), and Fusion for Free—Efficient Algebraic Effect Handlers (Nicolas Wu, Tom Schrijvers).

Contributed packages

Though we aim to keep the fused-effects core minimal, we encourage the development of external fused-effects-compatible libraries. If you’ve written one that you’d like to be mentioned here, get in touch!

• fused-effects-lens provides combinators to use the lens library fluently inside effectful computations.
• fused-effects-exceptions provides handlers for exceptions thrown in the IO monad.
• fused-effects-resumable provides resumable exceptions, which can also serve as a limited form of coroutines.
• fused-effects-mwc-random provides a performant, high-quality source of random data, as well as values from common numerical distributions.
• fused-effects-readline provides a REPL effect that interfaces with haskeline for its UI.
• fused-effects-parser provides parser-combinator style effects similar to parsing libraries such as trifecta.

Projects using fused-effects

• semantic, a program analysis toolkit
• now-haskell, a client library for AWS Lambda

Comparison to other effect libraries

Comparison to mtl

Like mtl, fused-effects provides a library of monadic effects which can be given different interpretations. In mtl this is done by defining new instances of the typeclasses encoding the actions of the effect, e.g. MonadState. In fused-effects, this is done by defining new instances of the Carrier typeclass for the effect.

Also like mtl, fused-effects allows scoped operations like local and catchError to be given different interpretations. As with first-order operations, mtl achieves this with a final tagless encoding via methods, whereas fused-effects achieves this with an initial algebra encoding via Carrier instances.

In addition, mtl and fused-effects are similar in that they provide instances for the monad types defined in the transformers package (Control.Monad.Reader, Control.Monad.Writer, etc). This means that applications using mtl can migrate many existing transformers-based monad stacks to fused-effects with minimal code changes. fused-effects provides its own hierarchy of carrier monads (under the Control.Carrier namespace) that provide a more fluent interface for new code, though it may be useful to use transformers types when working with third-party libraries.

Unlike mtl, effects are automatically available regardless of where they occur in the signature; in mtl this requires instances for all valid orderings of the transformers (O(n²) of them, in general).

Also unlike mtl, there can be more than one State or Reader effect in a signature. This is a tradeoff: mtl is able to provide excellent type inference for effectful operations like get, since the functional dependencies can resolve the state type from the monad type.

Unlike fused-effects, mtl provides a ContT monad transformer; however, it’s worth noting that many behaviours possible with delimited continuations (e.g. resumable exceptions) are directly encodable as effects.

Finally, thanks to the fusion and inlining of carriers, fused-effects is only marginally slower than equivalent mtl code (see benchmarks).

Comparison to freer-simple

Like freer-simple, fused-effects uses an initial encoding of library- and user-defined effects as syntax which can then be given different interpretations. In freer-simple, this is done with a family of interpreter functions (which cover a variety of needs, and which can be extended for more bespoke needs), whereas in fused-effects this is done with Carrier instances for newtypes.

Unlike fused-effects, in freer-simple, scoped operations like catchError and local are implemented as interpreters, and can therefore not be given new interpretations.

Unlike freer-simple, fused-effects has relatively little attention paid to compiler error messaging, which can make common (compile-time) errors somewhat more confusing to diagnose. Similarly, freer-simple’s family of interpreter functions can make the job of defining new effect handlers somewhat easier than in fused-effects. Further, freer-simple provides many of the same effects as fused-effects, plus a coroutine effect, but minus resource management and random generation.

Finally, fused-effects has been benchmarked as faster than freer-simple.

Comparison to polysemy

Like polysemy, fused-effects is a batteries-included effect system capable of scoped, reinterpretable algebraic effects.

As of GHC 8.8, fused-effects outperforms polysemy, though new effects take more code to define in fused-effects than polysemy (though the Control.Carrier.Interpret module provides a low-friction API for rapid prototyping of new effects). Like freer-simple and unlike fused-effects, polysemy provides custom type errors if a given effect invocation is ambigous or invalid in the current context.

Comparison to eff

eff is similar in many ways to fused-effects, but is slightly more performant due to its representation of effects as typeclasses. This approach lets GHC generate better code in exchange for sacrificing the flexibility associated with effects represented as data types. eff also uses the monad-control package to lift effects between contexts rather than implementing an Algebra-style class itself.

Acknowledgements

The authors of fused-effects would like to thank:

• Tom Schrijvers, Nicholas Wu, and all their collaborators for the research that led to fused-effects;
• Alexis King for thoughtful discussions about and suggestions regarding our methodology;
• the authors of other effect libraries, including eff, polysemy, and capabilities, for their exploration of the space.