mealy-arrow: Monadic Mealy machines with Arrow, ArrowChoice, and ArrowLoop

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A monadic Mealy machine in the coalgebraic (continuation-passing) representation: . newtype Auto m a b = Auto { step :: a -> m (b, Auto m a b) } . Each step consumes an input, produces an output in some monad m, and returns the next state as a continuation. The monad parameter controls the effect discipline: Identity for pure machines, IO for effectful ones. . Instances: Category, Arrow, ArrowChoice, ArrowLoop, Profunctor, Functor. Smart constructors: stateless, stateful, constAuto. Natural transformation: hoistAuto. . == How is this different from the mealy package? . The Hackage package mealy provides a pure, existentially-quantified inject/step/extract triple designed for online statistics (moving averages, regression). It has Category and Profunctor instances but no Arrow, no ArrowChoice, no ArrowLoop, and no monadic effects. . mealy-arrow provides the Nu (greatest fixpoint) representation with full Arrow instances and a monad parameter. It is designed for interactive systems: terminal UIs, protocol handlers, game logic, API clients — anything where each step may have effects and the machine's control flow may branch.

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- Arrow
  - Control.Arrow.Mealy

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mealy-arrow-0.1.0.0.tar.gz [browse] (Cabal source package)
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Versions [RSS]	0.1.0.0
Change log	CHANGELOG.md
Dependencies	base (>=4.14 && <5), mealy-arrow, profunctors (>=5.0 && <6) [details]
Tested with	ghc ==9.10.3
License	BSD-3-Clause
Author	mealy-arrow contributors
Maintainer	mealy-arrow contributors
Uploaded	by kaol at 2026-05-05T08:28:08Z
Category	Control, Arrows
Source repo	head: git clone https://github.com/mealy-arrow/mealy-arrow
Distributions
Executables	mealy-arrow-example
Downloads	3 total (3 in the last 30 days)
Rating	(no votes yet) [estimated by Bayesian average]
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Status	Docs available [build log] Last success reported on 2026-05-05 [all 1 reports]

Readme for mealy-arrow-0.1.0.0

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mealy-arrow

Monadic Mealy machines with Category, Arrow, ArrowChoice, ArrowLoop, and Profunctor instances.

The type

newtype Auto m a b = Auto { step :: a -> m (b, Auto m a b) }

Each step consumes an input, produces an output in monad m, and returns the continuation. The state is the closure — there is no external state type. This is the Nu (greatest fixpoint / final coalgebra) encoding of a Mealy machine.

At Identity it is a pure state machine. At IO it can do effects. The full Arrow stack lets you branch (Either-routing via ArrowChoice), fan (&&&), parallelise (***), and feed back (ArrowLoop with MonadFix).

Quick example

import Control.Arrow.Mealy
import Data.Functor.Identity

counter :: Auto Identity Int Int
counter = stateful 0 $ \total x -> let s = total + x in (s, s)

>>> runIdentity $ stepN counter [1,2,3,4,5]
[1,3,6,10,15]

How is this different from the `mealy` package?

The Hackage package mealy is a pure, existentially-quantified fold triple for online statistics. It has Category and Profunctor but no Arrow, no effects, no branching. mealy-arrow is for interactive systems where each step may have effects and the control flow may branch.