Heftia: higher-order algebraic effects done right

Heftia is an extensible effects library for Haskell that generalizes "Algebraic Effects and Handlers" to higher-order effects, providing users with maximum flexibility and delivering standard and reasonable speed. In its generalization, the focus is on ensuring predictable results based on simple, consistent semantics, while preserving soundness.

Please refer to the Haddock documentation for usage and semantics. For information on performance, please refer to performance.md.

This library is inspired by the paper:

• Casper Bach Poulsen and Cas van der Rest. 2023. Hefty Algebras: Modular Elaboration of Higher-Order Algebraic Effects. Proc. ACM Program. Lang. 7, POPL, Article 62 (January 2023), 31 pages. https://doi.org/10.1145/3571255

The elaboration approach proposed in the above paper allows for a straightforward treatment of higher-order effects.

Heftia's data structure is an extension of the Freer monad, designed to be theoretically straightforward by eliminating ad-hoc elements.

Key Features

• Correct Semantics for Higher-Order Effects & Continuations

  This library provides the following features simultaneously, which existing libraries could not support together:

  • Higher-order effects
  • Delimited continuations (algebraic effects)
    • Coroutines (non-scoped resumptions)
    • Non-deterministic computations
  • MonadUnliftIO
    • Code example: heftia-effects/Example/UnliftIO/Main.hs

  All of these interact through a simple, consistent, and predictable semantics based on algebraic effects.

• Easy and Concise Implementation for Custom Effect Interpreters

  As you can see from the implementations of basic effect interpreters such as State, Throw/Catch, Writer, NonDet, and Coroutine, they can be implemented in just a few lines, or even a single line. Even for effects like NonDet and Coroutine, which involve continuations and might seem difficult to implement at first glance, this is exactly how simple it can be. This is the power of algebraic effects. Users can quickly define experimental and innovative custom effects using continuations.

• Standard and Reasonable Performance

  It operates at a speed positioned roughly in the middle between faster libraries (like effectful or eveff) and relatively slower ones (like polysemy or fused-effects): performance.md.

• Purity

  • Does not depend on the IO monad and can use any monad as the base monad.
  • Semantics are isolated from the IO monad, meaning that aspects like asynchronous exceptions and threads do not affect the behavior of effects.

Heftia should be a good substitute for mtl, polysemy, fused-effects, and freer-simple. Additionally, if performance is not a top priority, it should also be a good alternative for effectful. If performance is particularly important, effectful would be the best alternative to this library.

Downsides

This library has notable semantic differences, particularly compared to libraries like effectful, polysemy, and fused-effects. The semantics of this library are almost equivalent to those of freer-simple and are also similar to Alexis King's eff library. This type of semantics is often referred to as continuation-based semantics. Additionally, unlike recent libraries such as effectful, which have an IO-fused effect system, the semantics of this library are separated from IO. Due to these differences, people who are already familiar with the semantics of other major libraries may find it challenging to transition to this library due to the mental model differences.

For those who have not used an extensible effects library in Haskell before, this should not be a problem. Particularly, if you are already somewhat familiar with the semantics of algebraic effects through languages like koka or eff-lang, you likely already have the mental model needed for this library, and everything should go smoothly.

Status

This library is currently in the beta stage. There may be significant changes and potential bugs.

We are looking forward to your feedback!

Getting Started

1. $ cabal update
   

2. Add heftia-effects ^>= 0.4 and ghc-typelits-knownnat ^>= 0.7 to the build dependencies. Enable the ghc-typelits-knownnat plugin, GHC2021, and the following language extensions as needed:

   • LambdaCase
   • DerivingStrategies
   • DataKinds
   • TypeFamilies
   • BlockArguments
   • FunctionalDependencies
   • RecordWildCards
   • DefaultSignatures
   • PatternSynonyms

Example .cabal:

...
    build-depends:
        ...
        heftia-effects ^>= 0.4,
        ghc-typelits-knownnat ^>= 0.7,

    default-language: GHC2021

    default-extensions:
        ...
        LambdaCase,
        DerivingStrategies,
        DataKinds,
        TypeFamilies,
        BlockArguments,
        FunctionalDependencies,
        RecordWildCards,
        DefaultSignatures,
        PatternSynonyms,
        TemplateHaskell,
        PartialTypeSignatures,
        AllowAmbiguousTypes
...

If you encounter an error like the following, add the pragma:

{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-}

to the header of your source file.

Could not deduce ‘GHC.TypeNats.KnownNat (1 GHC.TypeNats.+ ...)’

The supported versions are GHC 9.4.1 and later. This library has been tested with GHC 9.8.2 and 9.4.1.

Example

Compared to existing Effect System libraries in Haskell that handle higher-order effects, this library's approach allows for a more effortless and flexible handling of higher-order effects. Here are some examples:

Extracting Multi-shot Delimited Continuations

In handling higher-order effects, it's easy to work with multi-shot delimited continuations. For more details, please refer to the example code.

Two interpretations of the censor effect for Writer

Let's consider the following Writer effectful program:

hello :: (Tell String <: m, Monad m) => m ()
hello = do
    tell "Hello"
    tell " world!"

censorHello :: (Tell String <: m, WriterH String <<: m, Monad m) => m ()
censorHello =
    censor
        ( \s ->
            if s == "Hello" then
                "Goodbye"
            else if s == "Hello world!" then
                "Hello world!!"
            else
                s
        )
        hello

For censorHello, should the final written string be "Goodbye world!" (Pre-applying behavior) ? Or should it be "Hello world!!" (Post-applying behavior) ? With Heftia, you can freely choose either behavior depending on which higher-order effect interpreter (which we call an elaborator) you use.

main :: IO ()
main = runEff do
    (sPre, _) <-
        runTell
            . runWriterHPre @String
            $ censorHello

    (sPost, _) <-
        runTell
            . runWriterHPost @String
            $ censorHello

    liftIO $ putStrLn $ "Pre-applying: " <> sPre
    liftIO $ putStrLn $ "Post-applying: " <> sPost

Using the runWriterHPre elaborator, you'll get "Goodbye world!", whereas with the runWriterHPost elaborator, you'll get "Hello world!!".

Pre-applying: Goodbye world!
Post-applying: Hello world!!

For more details, please refer to the complete code and the implementation of the elaborator.

Semantics Zoo

To run the SemanticsZoo example:

$ git clone https://github.com/sayo-hs/heftia
$ cd heftia/heftia-effects
$ cabal run exe:SemanticsZoo
...
# State & Except
( evalState . runThrow . runCatch $ action ) = Right True
( runThrow . evalState . runCatch $ action ) = Right True

# NonDet & Except
( runNonDet . runThrow . runCatch . runChooseH $ action1 ) = [Right True,Right False]
( runThrow . runNonDet . runCatch . runChooseH $ action1 ) = Right [True,False]
( runNonDet . runThrow . runCatch . runChooseH $ action2 ) = [Right False,Right True]
( runThrow . runNonDet . runCatch . runChooseH $ action2 ) = Right [False,True]

# NonDet & Writer
( runNonDet . runTell . runWriterH . runChooseH $ action ) = [(3,(3,True)),(4,(4,False))]
( runTell . runNonDet . runWriterH . runChooseH $ action ) = (6,[(3,True),(4,False)])

# https://github.com/hasura/eff/issues/12
interpret SomeEff then runCatch : ( runThrow . runCatch . runSomeEff $ action ) = Right "caught"
runCatch then interpret SomeEff : ( runThrow . runSomeEff . runCatch $ action ) = Left "not caught"

[Note] All other permutations will cause type errors.
$

Documentation

A detailed explanation of usage and semantics is available in Haddock. The example codes are located in the heftia-effects/Example/ directory. Also, the following HeftWorld example (outdated): https://github.com/sayo-hs/HeftWorld

About the internal elaboration mechanism: https://sayo-hs.github.io/jekyll/update/2024/09/04/how-the-heftia-extensible-effects-library-works.html

Comparison

• Higher-Order Effects: Does it support higher-order effects?

• Delimited Continuation: The ability to manipulate delimited continuations.

• Effect System: For a term representing an effectful program, is it possible to statically decidable a type that enumerates all the effects the program may produce?

• Purely Monadic: Is an effectful program represented as a transparent data structure that is a monad, and can it be interpreted into other data types using only pure operations without side effects or unsafePerformIO?

• Dynamic Effect Rewriting: Can an effectful program have its internal effects altered afterwards (by functions typically referred to as handle with, intercept, interpose, transform, translate, or rewrite) ?

  For example, would it be possible to apply interpose as many times as the number of values input by the user at runtime?

• Semantics: Classification of behaviors resulting from the interpretation of effects.

  • Algebraic Effects: The same as Algebraic Effects and Handlers.
  • IO-fused: IO + ReaderT pattern.
  • Carrier dependent: The behavior depends on the specific type inference result of the monad. Tagless-final style.

Library or Language	Higher-Order Effects	Delimited Continuation	Effect System	Purely Monadic	Dynamic Effect Rewriting	Semantics
heftia	Yes	Multi-shot	Yes	Yes	Yes	Algebraic Effects
freer-simple	No	Multi-shot	Yes	Yes	Yes	Algebraic Effects
polysemy	Yes	No	Yes	Yes	Yes	Weaving-based (functorial state)
effectful	Yes	No	Yes	No (based on the IO monad)	Yes	IO-fused
eff	Yes	Multi-shot	Yes	No (based on the IO monad)	Yes	Algebraic Effects & IO-fused 1
speff	Yes	Multi-shot (restriction: 2)	Yes	No (based on the IO monad)	Yes	Algebraic Effects & IO-fused
in-other-words	Yes	Multi-shot?	Yes	Yes	No?	Carrier dependent
mtl	Yes	Multi-shot (ContT)	Yes	Yes	No	Carrier dependent
fused-effects	Yes	No?	Yes	Yes	No	Carrier dependent & Weaving-based (functorial state)
Koka-lang	No	Multi-shot	Yes	No (language built-in)	Yes	Algebraic Effects
OCaml-lang 5	?	One-shot	No 3	No (language built-in)	?	Algebraic Effects?

Heftia can simply be described as a higher-order version of freer-simple. This is indeed true in terms of its internal mechanisms as well.

Additionally, this library provides a consistent algebraic effects semantics that is independent of carriers and effects. On the other hand, in libraries like in-other-words, mtl, and fused-effects, the semantics of the code depend on the effect and, in part, the carrier inferred by type inference. Fixing the semantics to a algebraic effects model helps improve the predictability of the behavior (interpretation result) of the code without losing flexibility.

Carrier-dependent semantics can lead to unexpected behavior for code readers, particularly in situations where the types become implicit. Particularly, attention should be given to the fact that due to type inference, semantic changes may propagate beyond the blocks enclosed by interpret or interpose. In the case of carrier-independent semantics, especially with Freer-based effects, interpret and interpose do not alter the semantics by intervening in type inference or instance resolution of the carrier. Instead, they function as traditional functions, simply transforming the content of the data structure. This results in minimal surprise to the mental model of the code reader.

Performance

Overall, the performance of this library is positioned roughly in the middle between the fast (effectful, eveff, etc.) and slow (polysemy, fused-effects, etc.) libraries, and can be considered average. In all benchmarks, the speed is nearly equivalent to freer-simple, only slightly slower.

For more details, please refer to performance.md.

Compatibility with other libraries

About mtl

• Since the representation of effectful programs in Heftia is simply a monad (Eff), it can be used as the base monad for transformers. This means you can stack any transformer on top of it.

• The Eff monad is an instance of MonadIO, MonadError, MonadRWS, MonadUnliftIO, Alternative, etc., and these behave as the senders for the embedded IO or the effect GADTs defined in data-effects.

Representation of effects

• Heftia relies on data-effects for the definitions of standard effects such as Reader, Writer, and State.

• It is generally recommended to use effects defined with automatic derivation provided by data-effects-th.

• The representation of first-order effects is compatible with freer-simple. Therefore, effects defined for freer-simple can be used as is in this library. However, to avoid confusion between redundantly defined effects, it is recommended to use the effects defined in data-effects.

• GADTs for higher-order effects are formally similar to Polysemy and fused-effects, but they need to be instances of the HFunctor type class. While it's not impossible to manually derive HFunctor for effect types based on these libraries and use them, it's inconvenient, so it's better to use data-effects. Also, it is not compatible with Effectful and eff.

Future Plans

• Increase effects and nurture the ecosystem
  • async/await, concurrent/parallel programming, streaming, co-log, file system, Subprocesses, POSIX, and so on...
• Write practical software using Heftia
• Support for Applicative effects
• (Support for Linear effects?)

License

The license is MPL 2.0. Please refer to the NOTICE. Additionally, the code from freer-simple has been modified and used internally within this library. Therefore, some modules are licensed under both MPL-2.0 AND BSD-3-Clause. For details on licenses and copyrights, please refer to the module's Haddock documentation.

Your contributions are welcome!

Please see CONTRIBUTING.md.

Acknowledgements, citations, and related work

The following is a non-exhaustive list of people and works that have had a significant impact, directly or indirectly, on Heftia’s design and implementation:

• Oleg Kiselyov, Amr Sabry, and Cameron Swords — Extensible Effects: An alternative to monad transfomers
• Oleg Kiselyov and Hiromi Ishii — Freer Monads, More Extensible Effects
• Rob Rix, Patrick Thomson, and other contributors — fused-effects
• Sandy Maguire and other contributors — polysemy
• Alexis King and other contributors — freer-simple, eff
• Casper Bach Poulsen and Cas van der Rest — Hefty Algebras: Modular Elaboration of Higher-Order Algebraic Effects

---

1. https://github.com/hasura/eff/issues/12 ↩︎

2. Scoped Resumption only. e.g. Coroutines are not supported. ↩︎

3. Effects do not appear in the type signature and can potentially cause unhandled errors at runtime ↩︎