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Hierarchical State Transducer library","keywords":["state-machine","state machine","finite state machine","state-transducer","state transducer","automata","automaton","automata"],"repository":{"type":"git","url":"git+https://github.com/brucou/state-transducer.git"},"author":{"name":"brucou"},"license":"MIT","readme":"|Modelize your interface | Encode the graph | Run the generated machine! |\r\n|---|---|---|\r\n|![password submit fsm](assets/password%20submit%20fsm.png) |![password selector fsm transitions](assets/password%20selector%20transitions%20code.png)|![password selector](assets/password%20selector.png)\r\n\r\n[![npm version](https://badge.fury.io/js/state-transducer.svg)](https://badge.fury.io/js/state-transducer)\r\n![](https://img.shields.io/bundlephobia/minzip/state-transducer.svg)\r\n![](https://img.shields.io/github/license/brucou/state-transducer.svg)\r\n![Contributions welcome](https://img.shields.io/badge/contributions-welcome-orange.svg)\r\n\r\n# Table of Contents\r\n- [Features](#features)\r\n- [Examples](#examples)\r\n- [Motivation](#motivation)\r\n- [The link between state machines and user interfaces](#the-link-between-state-machines-and-user-interfaces)\r\n- [Install](#install)\r\n- [Tests](#tests)\r\n- [Integration with UI libraries](#integration-with-ui-libraries)\r\n- [API](#api)\r\n  * [API design](#api-design)\r\n  * [General concepts](#general-concepts)\r\n  * [Transducer semantics](#transducer-semantics)\r\n  * [`createStateMachine :: FSM_Def -> Settings -> FSM`](#-createstatemachine----fsm-def----settings----fsm-)\r\n  * [`traceFSM :: Env -> FSM_Def -> FSM_Def`](#-tracefsm----env----fsm-def----fsm-def-)\r\n  * [`makeWebComponentFromFsm :: ComponentDef -> FSM`](#-makewebcomponentfromfsm----componentdef----fsm-)\r\n- [Possible API extensions](#possible-api-extensions)\r\n- [Visualization tools](#visualization-tools)\r\n- [Credits](#credits)\r\n- [Roadmap](#roadmap)\r\n- [Who else uses state machines](#who-else-uses-state-machines)\r\n- [Annex](#annex)\r\n  * [So what is an Extended Hierarchical State Transducer ?](#so-what-is-an-extended-hierarchical-state-transducer--)\r\n  * [Terminology](#terminology)\r\n\r\n# Features\r\nThis library enables you to write user interfaces as state machines. You specify the machine as a\r\n graph. The library computes a function which implements that machine. You use that to drive \r\n your interface. It integrates easily with any or no framework. Tests can be automatically generated.\r\n\r\nSalient features :\r\n\r\n- **small size** : treeshakeable implementation, down from 8kB\r\n- **small API** : one function for the state machine, one function for tracing (and one function \r\nfor the [test generation](https://github.com/brucou/state-transducer-testing) available in a \r\nseparate package)\r\n- **just a function!** : easy to integrate into any framework\r\n- **[automatic test generation!](https://github.com/brucou/state-transducer-testing)** : write the machine, how to progress from one state to another, and let the computer generate hundreds of tests for you\r\n\r\n# Examples\r\n|Code playground | Demo | State Machine | \r\n|---|---|---|\r\n|[password meter component](https://codesandbox.io/s/73wy8jwk86)|![password meter demo](assets/password%20selector%20demo%20animated.png)|![password submit fsm](assets/password%20submit%20fsm.png)\r\n|[movie database search interface](https://codesandbox.io/s/mo2p97k7m8)|![movie app demo](assets/movie%20app%20demo%20init.png)|![movie app machine](https://github.com/brucou/movie-search-app/raw/specs-all/article/movie%20search%20good%20fsm%20corrected%20flowchart%20no%20emphasis%20switchMap.png) \r\n|[wizard forms](https://github.com/brucou/cycle-state-machine-demo/tree/first-iteration-fix)|![wizard form demo](https://github.com/brucou/cycle-state-machine-demo/raw/first-iteration-fix/public/assets/images/animated_demo.gif)|![wizard form machine](https://github.com/brucou/cycle-state-machine-demo/raw/first-iteration-fix/public/assets/images/graphs/sparks%20application%20process%20with%20comeback%20proper%20syntax%20-%20flat%20fsm.png)\r\n\r\n# Motivation\r\nThis library fundamentally implements computations which can be modelized by a type of state \r\nmachines called hierarchical extended [state transducer](https://en.wikipedia.org/wiki/Finite-state_transducer). This library offers a way to define, and use such transducers. \r\n\r\nNow, the whole thing can sound very abstract but the major motivation for this library has been the \r\nspecification and implementation of user interfaces. As a matter of fact, to [every user \r\ninterface can be associated a computation](https://brucou.github.io/posts/user-interfaces-as-reactive-systems/#reactive-systems-as-automata) \r\nrelating inputs to the user interface to an action to be performed on the interfaced systems. That \r\ncomputation often has a logic [organized around a limited set of control states](#base-example), \r\nand can be advantageously modelized by a state machine. \r\n\r\n[**Jump to the examples**](#general-concepts).\r\n\r\nThis library is born from :\r\n\r\n- the desire to apply such state machines for both specification and implementation of user \r\ninterfaces\r\n- the absence of existing javascript libraries which satisfy our [design criteria](https://github.com/brucou/state-transducer#api-design)\r\n  - mostly, we want the state machine library API design to be as close as possible from the \r\n  mathematical object denoting it. This should allow us to reason about it, compose and reuse \r\n  it easily. \r\n  - most libraries we found either do not feature hierarchy in their state machines, or use a \r\n  rather imperative API, or impose a concurrency model on top of the state machine's control flow\r\n\r\nThis is a [work in progress](#roadmap), however the main API for the v1.0 should be relatively \r\nstable.\r\n\r\nIt works nicely and have already been used succesfully for user-interfaces as well as in other \r\ncontexts:\r\n\r\n- in multi-steps workflows: see an example [here](https://github.com/brucou/component-combinators/tree/master/examples/volunteerApplication), a constant feature of enterprise software today\r\n- for ['smart' synchronous streams](https://github.com/brucou/partial-synchronous-streams), which\r\n tracks computation state to avoid useless re-computations\r\n- to implement cross-domain communication protocols, to coordinate iframes with a main window\r\n\r\nIn such cases, we were able to modelize our computation with an Extended Hierarchical State Transducer \r\nin a way that :\r\n\r\n- is economical (complexity of the transducer proportional to complexity of the computation)\r\n- is reasonably easy to reason about and communicate (the transducer can\r\n be visually represented, supporting both internal and external communication, and design \r\n specification and documentation)\r\n- supports step-wise refinement and iterative development (control states can be refined into a \r\nhierarchy of nested states)\r\n\r\n# The link between state machines and user interfaces\r\nIn short :\r\n\r\n- a user interface can be specified by a relation between events received by the user \r\ninterfaces and actions to be performed as a result on the interfaced system. \r\n- Because to the same triggering event, there may be different actions to perform on the \r\ninterfaced system (depending for instance on when the event did occur, or which other events \r\noccured before), we use state to represent that variability, and specify the user interface with \r\na function `f` such that `actions = f(state, event)`. We call here `f` the reactive function for the user interface.\r\n- The previous expression suffices to specify the user interface's behaviour, but is not enough \r\nto deduce an implementation. We then use a function `g` such that `(actions_n, state_{n+1} = g\r\n(state_n, event_n)`. That is, we explicitly include the modification of the state triggered by \r\nevents. Depending on the choice that is made for `state_n`, there is an infinite number of ways \r\nto specify the user interface.\r\n- a state machine specification is one of those ways with some nice properties (concise \r\nspecification, formal reasoning, easy visualization). It divides the state into control states and \r\nextended state. For each control state, it specifies a reactive sub-function which returns an \r\nupdated state (i.e. a new control state, and a new extended state) and the actions to perform on \r\nthe interfaced system.\r\n\r\nLet's take a very simple example to illustrate these equations. The user interface to \r\nspecify is a [password selector](https://cdn.dribbble.com/users/522131/screenshots/4467712/password_strength.png). Visually, the user interface consists of a password input field \r\nand a submit password button. Its behaviour is the following :\r\n- the user types\r\n- for each new value of the password input, the input is displayed in green if the password is \r\nstrong (that will be, to remain simple if there are both letters and numbers in the password), and\r\n in red otherwise\r\n- if the password is not strong, the user click on `set password` button is ignored, otherwise \r\nthe password is set to the value of the password input\r\n \r\nA `f` partial formulation :\r\n\r\n|State|Event|Actions|\r\n|---|---|---|\r\n|`{input: \"\"}`|*typed `a`*|display input in red|\r\n|`{input: \"a\"}`|*typed `2`*|display input in green|\r\n|`{input: \"a2\"}`|*clicked submit*|submit `a2` password|\r\n|`{input: \"a\"}`|*typed `b`*|display input in red|\r\n|`{input: \"ab\"}`|*clicked submit*|---|\r\n\r\nA `g` partial formulation :\r\n\r\n|state_n|event|actions_n|state_{n+1}|\r\n|---|---|---|---|\r\n|`{input: \"\"}`|*typed `a`*|display input in red|`{input: \"a\"}`|\r\n|`{input: \"a\"}`|*typed `2`*|display input in green|`{input: \"a2\"}`|\r\n|`{input: \"a2\"}`|*clicked submit*|submit `a2` password|`{input: \"a2\"}`|\r\n|`{input: \"a\"}`|*typed `b`*|display input in red|`{input: \"ab\"}`|\r\n|`{input: \"ab\"}`|*clicked submit*|---|`{input: \"ab\"`}|\r\n\r\nA state machine partial formulation :\r\n\r\n|Control state|Extended state|Event|Actions|New control state|New extended state|\r\n|---|---|---|---|---|---|\r\n|**Weak**|`input: \"\"`|typed `a`|display input in red|**Weak**|`input: \"a\"`|\r\n|**Weak**|`input: \"a\"`|typed `2`|display input in green|**Strong**|`input: \"a2\"`|\r\n|**Strong**|`input: \"a2\"`|clicked submit|submit `a2` password|**Done**|`input: \"a2\"`|\r\n|**Weak**|`input: \"a\"`|typed `b`|display input in red|**Weak**|`input: \"ab\"`|\r\n|**Weak**|`input: \"ab\"`|clicked submit| - |**Weak**| `input: \"ab\"` |\r\n\r\nThe corresponding implementation is by a function `fsm` with an encapsulated initial internal state\r\n of `{control state : weak, extended state: {input : ''}}` such that, if the user types 'a2' and \r\nclicks submit :\r\n\r\n```\r\nfsm(typed 'a') = nothing\r\nfsm(typed '2') = nothing\r\nfsm(clicked submit) = submit `a2` password\r\n```\r\n\r\nThe corresponding visualization (actions are not represented) :\r\n\r\n![password submit fsm](assets/password%20submit%20fsm.png)\r\n\r\nNote that we wrote only partial formulations in our table, as the sequence of inputs by the user \r\nis potentially infinite (while this article is not). Our tables do not for instance give a \r\nmapping for the following sequence of events : `[typed 'a', typed '2', typed \r\n <backspace>]`. Conversely, our state machine concisely represents the fact that whatever input\r\n  we receive in the `Weak` control state, it will only go to the `Strong` control state if some \r\n pre-configured condition are fulfilled (both numbers and letters in the password). It will \r\n only submit the password if the `clicked submit` event is received while it is in the `Strong` \r\n state.\r\n The starting state and these two assertions can be combined into a theorem : the machine will only \r\n submit a password if the password is strong. In short, we are able to reason formally about the \r\n machine and extract properties from its definition. This is just one of the many attractive properties of state \r\n  machines which makes it a tool of choice for **robust** and testable user interface's \r\n  implementation.\r\n\r\nFor the modelization of a [much more complex user interface](https://sarimarton.github.io/tmdb-ui-cyclejs/dist/#/), and more details on the benefits of state machine, I'll refer the reader to a [detailed article](https://github.com/brucou/movie-search-app/blob/specs-all/article/article.md) I wrote on the subject.\r\n \r\n# Install\r\n`npm install state-transducer --save`\r\n\r\n# Tests\r\nTo run the current automated tests : `npm run test`\r\n\r\n# Integration with UI libraries\r\nThe machine implementation is just a function. As such it is pretty easy to integrate in any \r\nframework. In fact, we have implemented the same interface behaviour over [React](https://codesandbox.io/s/ym8vpqm7m9), [Vue](https://codesandbox.io/s/4p1nnywy0), [Svelte*](https://github.com/brucou/movie-search-app-svelte), [Inferno](https://codesandbox.io/s/9zjo5yx8po), [Nerv](https://codesandbox.io/s/o4vkwmw7y), [Ivi](https://codesandbox.io/s/3x9x5v4kq5) with \r\n the exact same fsm. By isolating your component behaviour in a fsm, you can delay the UI library \r\n choice to the last moment.\r\n \r\n[*]: Svelte has a specific build process which I haven't mastered yet. As a result, the CSS files somewhat clash together, which makes the demo a bit less appealing visually. As this is not so important for our purposes, I decided not to spend time solving the framework-specific build issues.\r\n \r\nAs of April 2019, we officially provide the following integrations :\r\n\r\n- [integration with React](https://github.com/brucou/react-state-driven)\r\n  - using state machines allows to use React mostly as a DOM library and eliminates the need for \r\n  state management, hooks and other react paraphernalia.\r\n- [integration with Vue](https://github.com/brucou/vue-state-driven) \r\n  - using state machines allows to use Vue mostly as a DOM library and eliminates the need for \r\n  state management, hooks and other Vue advanced concepts.\r\n- integration with framework supporting webcomponents (only supported in [browsers which support \r\ncustom elements v1](https://caniuse.com/#feat=custom-elementsv1))\r\n  - provided by the factory function `makeWebComponentFromFsm`\r\n  - I am investigating whether the dependency on custom elements could be removed with the \r\n  excellent [wicked elements](https://github.com/WebReflection/wicked-elements/tree/master/esm)\r\n\r\n# API\r\n## API design\r\nThe key objectives for the API was :\r\n\r\n- **generality**, **reusability** and **simplicity** \r\n  - there is no explicit provision made to accommodate specific use cases or frameworks\r\n  - it must be possible to add a [concurrency and/or communication mechanism](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.92.6145&rep=rep1&type=pdf) on top of the current design\r\n  - it must be possible to integrate smoothly into React, Angular and your popular framework\r\n  - support for both interactive and reactive programming\r\n- parallel and sequential composability of transducers\r\n\r\nAs a result of this, the following choices were made :\r\n\r\n- **functional interface** : the transducer is just a function. As such, the \r\ntransducer is a black-box, and only its computed outputs can be observed\r\n- **complete encapsulation** of the state of the transducer\r\n- **no effects** performed by the machine\r\n- no exit and entry actions, or activities as in other state machine formalisms\r\n  - there is no loss of generality as both entry and exit actions can be implemented with our \r\n  state transducer. There is simply no syntactic support for it in the core API. This can however be\r\n   provided through standard functional programming patterns (higher-order functions, etc.)\r\n- every computation performed is synchronous (asynchrony is an effect)\r\n- action factories return the **updates** to the extended state to avoid any \r\nunwanted direct modification of the extended state (API user must provide such update function, \r\nwhich in turn allows him to use any formalism to represent state - for instance `immutable.js`)\r\n- no restriction is made on output of transducers, but inputs must follow some conventions (if a\r\n machine's output match those conventions, two such machines can be sequentially composed\r\n- parallel composition naturally occurs by feeding two state machines the same input(s))\r\n  - as a result, reactive programming is naturally enabled. If `inputs` is a stream of \r\nwell-formatted machine inputs, and `f` is the fsm, then the stream of outputs will be `inputs.map\r\n(f)`. It is so simple that we do not even surface it at the API level.\r\n\r\nConcretely, our state transducer will be created by the factory function `createStateMachine`, \r\nwhich returns a state transducer which :\r\n\r\n- immediately positions itself in its configured initial state (as defined by its initial control\r\n state and initial extended state) \r\n- will compute an output for any input that is sent to it since that\r\n\r\nLet us insist again on the fact that the state transducer is not, in general, a pure function of \r\nits inputs. However, a given output of the transducer depends exclusively on the sequence of inputs \r\nit has received so far ([causality property](https://en.wikipedia.org/wiki/Causal_system)). This means that it is possible to associate to a state transducer another function which takes a sequence of inputs into a \r\n sequence of outputs, in a way that **that** function is pure. This is what enables \r\n simple and automated testing.\r\n\r\n## General concepts\r\nThere are a few things to be acquainted with :\r\n- the basic state machine formalism\r\n- its extension, including hierarchy (compound states), and history states\r\n- the library API\r\n\r\nTo familiarize the reader with these, we will be leveraging two examples. The first example is \r\nthe aforementioned password selector. This pretty simple example will serve to showcase the API \r\nof the library, and standard state machine terminology. The second example modelizes the \r\nbehaviour of a CD player. It is more complex, and will feature a hierarchical state machine. For \r\nthis example, we will show a run of the machine, and by doing so, illustrate advanced concepts \r\nsuch as compound states, and history states. We will not indigate into the implementation however. For a very advanced example, I invite the reader to refer to [the wizard form demo](https://github.com/brucou/cycle-state-machine-demo).\r\n\r\nWe then present into more details the semantics of a state transducer and how it relates to its \r\nconfiguration. Finally we present our API whose documentation relies on all previously introduced\r\n concepts.\r\n\r\n### Base example\r\nWe will be using as our base example the password selector we discussed previously. As a \r\nreminder, its behaviour was described by the following state machine : \r\n\r\n![password submit fsm](assets/password%20submit%20fsm.png)\r\n\r\nTo specify our machine, we need :\r\n- a list of control states the machine can be in\r\n- a list of events accepted by the machine\r\n- to describe transitions from a control state to another \r\n- the initial state of the machine (initial control state, initial extended state)\r\n\r\nThe first three are clear from the graph. The initial control state can also be deduced from the \r\ngraph. The initial exxtended state can be derived from the mapping table [above](#the-link-between-state-machines-and-user-interfaces) describing the \r\nbehaviour of the password selector. \r\n\r\nThe fsm ends up being defined by:\r\n\r\n```javascript\r\nconst initialExtendedState = {\r\n  input: \"\"\r\n};\r\nconst states = {\r\n  [INIT]: \"\",\r\n  [STRONG]: \"\",\r\n  [WEAK]: \"\",\r\n  [DONE]: \"\"\r\n};\r\nconst initialControlState = INIT;\r\nconst events = [TYPED_CHAR, CLICKED_SUBMIT, START];\r\nconst transitions = [\r\n  { from: INIT, event: START, to: WEAK, action: displayInitScreen },\r\n  { from: WEAK, event: CLICKED_SUBMIT, to: WEAK, action: NO_ACTIONS },\r\n  {\r\n    from: WEAK,\r\n    event: TYPED_CHAR,\r\n    guards: [\r\n      { predicate: isPasswordWeak, to: WEAK, action: displayInputInRed },\r\n      { predicate: isPasswordStrong, to: STRONG, action: displayInputInGreen }\r\n    ]\r\n  },\r\n  {\r\n    from: STRONG,\r\n    event: TYPED_CHAR,\r\n    guards: [\r\n      { predicate: isPasswordWeak, to: WEAK, action: displayInputInRed },\r\n      { predicate: isPasswordStrong, to: STRONG, action: displayInputInGreen }\r\n    ]\r\n  },\r\n  {\r\n    from: STRONG,\r\n    event: CLICKED_SUBMIT,\r\n    to: DONE,\r\n    action: displaySubmittedPassword\r\n  }\r\n];\r\n\r\nconst pwdFsmDef = {\r\n  initialControlState,\r\n  initialExtendedState,\r\n  states,\r\n  events,\r\n  transitions\r\n};\r\n```\r\n\r\nwhere action factories mapped to a transition compute two things : \r\n- a list of updates to apply internally to the extended state\r\n- an external output for the consumer of the state transducer \r\n\r\nFor instance :\r\n\r\n```javascript\r\nfunction displayInitScreen() {\r\n  return {\r\n    updates: NO_STATE_UPDATE,\r\n    outputs: [\r\n      { command: RENDER, params: { screen: INIT_SCREEN, props: void 0 } }\r\n    ]\r\n  };\r\n}\r\n\r\n```\r\n\r\nThe full runnable code is [available here](https://codesandbox.io/s/73wy8jwk86).\r\n\r\n### CD drawer example\r\nThis example is taken from Ian Horrock's seminal book on statecharts and is the specification of\r\n a CD player. The behaviour of the CD player is pretty straight forward and understandable \r\n immediately from the visualization. From a didactical point of view, the example serves to feature \r\n advanced characteristics of hierarchical state machines, including history states, composite states, \r\n transient states, automatic transitions, and entry points. For a deeper understanding of how the\r\n  transitions work in the case of a hierarchical machine, you can have a look at the \r\n  [terminology](https://github.com/brucou/state-transducer#terminology) and \r\n  [sample run](https://github.com/brucou/state-transducer#example-run) for the CD player machine.\r\n \r\n![cd player state chart](http://i.imgur.com/ygsOVi9.jpg)\r\n\r\nThe salient facts are :\r\n- `NO Cd loaded`, `CD_Paused` are control states which are composite states : they are themselves state machines comprised on control states.\r\n- The control state `H` is a pseudo-control state called shallow history state\r\n- All composite states feature an entry point and an automatic transition. For instance \r\n`CD_Paused` has the sixth control state as entry point, and the transition from `CD_Paused` into \r\nthat control state is called an automatic transition. Entering the `CD_Paused` control state \r\nautomatically triggers that transition.\r\n- `Closing CD drawer` is a transient state. The machine will automatically transition away from \r\nit, picking a path according to the guards configured on the available exiting transitions\r\n\r\n### Example run\r\nTo illustrate the previously described transducer semantics, let's run the CD player example.\r\n\r\n| Control state      | Internal event | External event|\r\n|--------------------|:-----------:|------------------|\r\n| INIT_STATE         |     INIT_EVENT |                  |\r\n| No Cd Loaded       |     INIT    |                  |\r\n| CD Drawer Closed   |      --     |                  |\r\n| CD Drawer Closed   |             | Eject            |\r\n| CD Drawer Open     |             | Eject (put a CD) |\r\n| Closing CD Drawer  |  eventless  |                  |\r\n| CD Loaded          |     INIT    |                  |\r\n| CD Loaded subgroup |     INIT    |                  |\r\n| CD Stopped         |      --     |                  |\r\n| CD stopped         |             | Play             |\r\n| CD playing         |             | Forward down     |\r\n| Stepping forwards  |             | Forward up       |\r\n| **CD playing**     |      --     |                  |\r\n\r\nNote :\r\n\r\n- the state entry semantics -- entering `No Cd Loaded` leads to enter `CD Drawer Closed`\r\n- the guard -- because we put a CD in the drawer, the machine transitions from `Closing CD Drawer` to `CD Loaded` \r\n- the eventless transition -- the latter is an eventless transition : the guards are \r\nautomatically evaluated to select a transition to progress the state machine (by contract, there \r\nmust be one)\r\n- the hierarchy of states -- the `Forward down` event transitions the state machines to `Stepping\r\n forwards`, as it applies to all atomic states nested in the `CD Loaded subgroup` control state\r\n- the history semantics -- releasing the forward key on the CD player returns to `CD Playing` the\r\n last atomic state for compound state `CD Loaded subgroup`.\r\n \r\n\r\n## Transducer semantics\r\nWe give here a quick summary of the behaviour of the state transducer :\r\n\r\n**Preconditions**\r\n\r\n- the machine is configured with a set of control states, an initial extended state, \r\ntransitions, guards, action factories, and user settings. \r\n- the machine configuration is valid (cf. contracts)\r\n- Input events have the shape `{{[event_label]: event_data}}`\r\n\r\n**Event processing**\r\n\r\n- Calling the machine factory creates a machine according to specifications and triggers the \r\nreserved `INIT_EVENT` event which advances the state machine out of the reserved **internal** \r\ninitial control state towards the relevant **user-configured** initial control state\r\n  - the `INIT_EVENT` event carries the initial extended state as data\r\n  - if there is no initial transition, it is required to pass an initial control state\r\n  - if there is no initial control state, it is required to configure an initial transition\r\n  - an initial transition is a transition from the reserved `INIT_STATE` initial control state, \r\n  triggered by the reserved initial event `INIT_EVENT`\r\n- **Loop**\r\n- Search for a feasible transition in the configured transitions\r\n  - a feasible transition is a transition which is configured to deal with the received event, and \r\n  for which there is a fulfilled guard \r\n- If there is no feasible transition :\r\n  - issue memorized output (`NO_OUTPUT` if none), extended state and control state do not change.\r\n   **Break** away from the loop\r\n- If there is a feasible transition, select the first transition according to what follows :\r\n  - if there is an INIT transition, select that\r\n  - if there is an eventless transition, select that\r\n  - otherwise select the first transition whose guard is fulfilled (as ordered per array index)\r\n- evaluate the selected transition\r\n  - if the target control state is an history state, replace it by the control state it \r\n  references (i.e. the last seen nested state for that compound state)\r\n  - **update the extended state** (with the updates produced by the action factory)\r\n  - aggregate and memorize the outputs (produced by the action factory)\r\n  - update the control state to the target control state\r\n  - update the history for the control state (applies only if control state is compound state)\r\n- iterate on **Loop**\r\n- **_THE END_**\r\n\r\nA few interesting points : \r\n\r\n- a machine always transitions towards an atomic state at the end of event processing\r\n- on that path towards an atomic target state, all intermediary extended state updates are \r\nperformed. Guards and action factories on that path are thus receiving a possibly evolving extended \r\nstate. The computed outputs will be aggregated in an array of outputs.\r\n \r\nThe aforedescribed behaviour is loosely summarized here :\r\n\r\n![event processing](assets/FSM%20event%20processing%20semantics.png)\r\n\r\n**History states semantics**\r\n\r\nAn history state relates to the past configuration a compound state. There \r\nare two kinds of history states : shallow history states (H), and deep history states (H*). A \r\npicture being worth more than words, thereafter follows an illustration of both history states :\r\n\r\n![deep and shallow history](test/assets/history%20transitions,%20INIT%20event%20CASCADING%20transitions.png)\r\n\r\nAssuming the corresponding machine has had the following run `[INIT, EVENT1, EVENT3, EVENT5, \r\nEVENT4]`:\r\n \r\n- the configurations for the `OUTER` control state will have been `[OUTER.A, INNER, INNER.S, INNER.T]`\r\n - the shallow history state for the `OUTER` control state will correspond to the `INNER` control\r\n  state (the last direct substate of `OUTER`), leading to an automatic transition to INNER_S  \r\n - the deep history state for the `OUTER` control state will correspond to the `INNER.T` control\r\n     state (the last substate of `OUTER` before exiting it)\r\n\r\nIn short the history state allows to short-circuit the default entry behaviour for a compound \r\nstate, which is to follow the transition triggered by the INIT event. When transitioning to the \r\nhistory state, transition is towards the last seen state for the entered compound state.\r\n\r\n### Contracts\r\n\r\n#### Format\r\n- state names (from `fsmDef.states`) must be unique and be JavaScript strings\r\n- event names (from `fsmDef.events`) must be unique and be JavaScript strings\r\n- reserved states (like `INIT_STATE`) cannot be used when defining transitions\r\n- at least one control state must be declared in `fsmDef.states`\r\n- all transitions must be valid :\r\n  - the transition syntax must be followed (cf. types)\r\n  - all states referenced in the `transitions` data structure must be defined in the `states` data \r\n  structure\r\n  - all transitions must define an action (even if that action does not modify the extended state\r\n   or returns `NO_OUTPUT`)\r\n- all action factories must fill in the `updates` and `outputs` property (no syntax sugar) (**NOT\r\n ENFORCED**)\r\n  - NO_OUTPUT must be used to indicate the absence of outputs\r\n- all transitions for a given origin control state and triggering event must be defined in one \r\nrow of `fsmDef.transitions`\r\n- `fsmDef.settings` must include a `updateState` function covering the state machine's extended \r\nstate update concern.\r\n\r\n#### Initial event and initial state\r\nBy initial transition, we mean the transition with origin the machine's default initial state.\r\n\r\n- An initial transition must be configured :\r\n  - by way of a starting control state defined at configuration time\r\n  - by way of a initial transition at configuration time\r\n- ~~the init event has the initial extended state as event data~~\r\n- ~~The machine cannot stay blocked in the initial control state. This means that at least one \r\ntransition must be configured and be executed between the initial control state and another state\r\n.   This is turn means :~~\r\n  - ~~at least one non-reserved control state must be configured~~\r\n  - ~~at least one transition out of the initial control state must be configured~~\r\n  - ~~of all guards for such transitions, if any, at least one must be fulfilled to enable a \r\n  transition away from the initial control state~~\r\n- there is exactly one initial transition, whose only effect is to determine the starting \r\ncontrol state for the machine\r\n  - the action on any such transitions is the *identity* action\r\n  - the control state resulting from the initial transition may be guarded by configuring \r\n  `guards` for the initial transition\r\n- there are no incoming transitions to the reserved initial state\r\n\r\nAdditionally the following applies :\r\n- the initial event can only be sent internally (external initial events will be ignored, and the \r\nmachine will return `NO_OUTPUT`)\r\n- the state machine starts in the reserved initial state\r\n\r\n#### Coherence\r\n- the initial control state (`fsmDef.initialControlState`) must be a state declared in `fsmDef.\r\nstates`\r\n- transitions featuring the initial event (`INIT_EVENT`) are only allowed for transitions involving \r\ncompound states\r\n  - e.g. A -INIT_EVENT-> B iff A is a compound state or A is the initial state\r\n- all states declared in `fsmDef.states` must be used as target or origin of transitions in \r\n`fsmDef.transitions`\r\n- all events declared in `fsmDef.events` must be used as triggering events of transitions in \r\n`fsmDef.transitions`\r\n- history pseudo states must be target states and refer to a given declared compound state\r\n- there cannot be two transitions with the same `(from, event, predicate)` - sameness defined for\r\n predicate by referential equality (**NOT ENFORCED**)\r\n\r\n#### Semantical contracts\r\n- The machine behaviour is as explicit as possible\r\n  - if a transition is taken, and has guards configured, one of those guards must be fulfilled, i\r\n  .e. guards must cover the entire state space when they exist\r\n- A transition evaluation must end\r\n  - eventless transitions must progress the state machine\r\n    - at least one guard must be fulfilled, otherwise we would remain forever in the same state\r\n  - eventless self-transitions are forbidden (while theoretically possible, the feature is of \r\n  little practical value, though being a possible source of ambiguity or infinite loops)\r\n  - ~~eventless self-transitions must modify the extended state~~\r\n    - ~~lest we loop forever (a real blocking infinite loop)~~\r\n    - ~~note that there is not really a strong rationale for eventless self-transition, I recommend \r\n      just staying away from it~~\r\n- the machine is deterministic and unambiguous\r\n  - to a (from, event) couple, there can only correspond one row in the `transitions` array of the \r\n  state machine (but there can be several guards in that row)\r\n      - (particular case) eventless transitions must not be contradicted by event-ful transitions\r\n      - e.g. if there is an eventless transition `A -eventless-> B`, there cannot be a competing \r\n      `A -ev-> X`\r\n  - A -ev> B and A < OUTER_A with OUTER_A -ev>C !! : there are two valid transitions triggered by\r\n     `ev`. Such transitions would unduely complicate the input testing generation, and decrease \r\n     the readability of the machine so we forbid such transitions[^x]\r\n- no transitions from the history state (history state is only a target state)\r\n- A transition evaluation must always end (!), and end in an atomic state\r\n  - Every compound state must have eactly one inconditional (unguarded) INIT transition, i.e. a \r\n  transition whose triggering event is `INIT_EVENT`. That transition must have a target state \r\n  which is a substate of the compound state (no hierarchy crossing), and which is not a history \r\n  pseudo state\r\n  - Compound states must not have eventless transitions defined on them (would introduce \r\n  ambiguity with the INIT transition)\r\n  - (the previous conditions ensure that there is always a way down the hierarchy for compound \r\n  states, and that way is always taken when entering the compound state, and the descent \r\n  process always terminate)\r\n- the machine does not perform any effects\r\n  - guards, action factories are pure functions\r\n    - as such exceptions while running those functions are fatal, and will not be caught\r\n  - `updateState :: ExtendedState -> ExtendedStateUpdates -> ExtendedState` must be a pure function\r\n   (this is important in particular for the tracing mechanism which triggers two execution of this \r\n   function with the same parameters)\r\n\r\n[^x]: There are however semantics which allow such transitions, thus possibilitating event bubbling.\r\n\r\nThose contracts ensure a good behaviour of the state machine. and we recommend that they all be \r\nobserved. However, some of them are not easily enforcable :\r\n\r\n- we can only check at runtime that transition with guards fulfill at least one of those guards. \r\nIn these cases, we only issue a warning, as this is not a fatal error. This leaves some \r\nflexibility to have a shorter machine configuration. Note that we recommend explicitness and \r\ndisambiguity vs. conciseness. \r\n- purity of functions cannot be checked, even at runtime\r\n\r\nContracts enforcement can be parameterized with `settings.debug.checkContracts`.\r\n \r\n## `createStateMachine :: FSM_Def -> FSM`\r\n### Description\r\nThis FSM factory function takes the parameters defining the behaviour of the state transducer, \r\nand returns the created state transducer. The created state transducer is a regular function called \r\nwith inputs which are passed to the encapsulated state machine, which computes the function's \r\noutput. The syntax for an input is `{{[eventLabel] : eventData}}`, i.e. an input is an object \r\nwith exactly one key, which is the event identifier, and the value matching the key is the event data.\r\n\r\nThe machine additionnally may carry over environment variables, which are accessible in guards, \r\nand action factories. This helps maintaining such functions pure and testable. Environment \r\nvariables can also be used to parameterize the state machine's behaviour.\r\n\r\nHistory pseudo states are generated by a helper function `historyState :: \r\nHistoryType -> ControlState -> HistoryPseudoState`. An history state is coupled to a \r\ncompound control state, and has a type (deep or shallow). Passing this information to the factory \r\nprodudces the sought history state. \r\n\r\nThe `settings.updateState` property is mandatory, and specify how to update a model from the `\r\n.updates` produced by an action factory. We used successfully [JSON patch](http://jsonpatch.com/) operations for model updates, but you can choose to use the inmutable library of your choice or a simple reducer. The \r\nimportant point is that the extended state should not be modified in place, i.e. `updateState` is\r\n a pure function. \r\n\r\nThe `settings.debug.checkContracts`, when set, represent contracts that the state machine must \r\nfulfill. The `state-transducer` library comes by default with a set of contracts enforcing most \r\nof the syntax and semantics of the state machine format chosen.\r\n\r\nThe `settings.debug.console`, when set, represent a `console` object through which tracing and \r\ndebug info will flow. This is useful in development and can be turned off in production.   \r\n\r\n### Contracts\r\n- All [previously mentioned](https://github.com/brucou/state-transducer#contracts) contracts apply.\r\n- [Type contracts](https://github.com/brucou/state-transducer/blob/master/src/types.js)\r\n- The `settings.updateState` property is mandatory!\r\n- The `settings` property **should not be modified** after being passed as parameter (i.e. should\r\n be a constant): it is not cloned and is passed to all relevant functions (guards, etc.)\r\n\r\n### Implementation example\r\nWe are going to show the definition for the following hierrchical state machine :\r\n\r\n![state machine under test](test/assets/history%20transitions,%20INIT%20event%20CASCADING%20transitions.png)\r\n\r\nThe definition is as follows :\r\n\r\n```javascript\r\nconst states = { [OUTER]: { [INNER]: { [INNER_S]: '', [INNER_T]: '' }, [OUTER_A]: '', [OUTER_B]: '' }, [Z]: '' };\r\n  const fsmDef = {\r\n    states,\r\n    events: [EVENT1, EVENT2, EVENT3, EVENT4],\r\n    initialExtendedState: { history: SHALLOW, counter: 0 },\r\n    transitions: [\r\n      { from: INIT_STATE, event: INIT_EVENT, to: OUTER, action: ACTION_IDENTITY },\r\n      { from: OUTER, event: INIT_EVENT, to: OUTER_A, action: ACTION_IDENTITY },\r\n      { from: OUTER_A, event: EVENT1, to: INNER, action: ACTION_IDENTITY },\r\n      { from: INNER, event: INIT_EVENT, to: INNER_S, action: ACTION_IDENTITY },\r\n      { from: INNER_S, event: EVENT3, to: INNER_T, action: ACTION_IDENTITY },\r\n      { from: INNER_T, event: EVENT3, to: INNER_S, action: ACTION_IDENTITY },\r\n      { from: INNER, event: EVENT2, to: OUTER_B, action: ACTION_IDENTITY },\r\n      { from: OUTER, event: EVENT1, to: Z, action: ACTION_IDENTITY },\r\n      {\r\n        from: Z, event: EVENT4, guards: [\r\n          {\r\n            predicate: function isDeep(x, e) {return x.history === DEEP},\r\n            to: historyState(DEEP, OUTER),\r\n            action: incCounter\r\n          },\r\n          {\r\n            predicate: function isShallow(x, e) {return x.history !== DEEP},\r\n            to: historyState(SHALLOW, OUTER),\r\n            action: incCounter\r\n          }\r\n        ]\r\n      },\r\n    ],\r\n    settings : { updateState : applyJSONpatch }\r\n  };\r\n```\r\n\r\nNote in particular :\r\n- the nesting of states in `states`\r\n- the use of `ACTION_IDENTITY` when there is no action to be applied\r\n  - that action does not modify the extended state of the machine, and returns `NO_OUTPUT`\r\n- how history states are included in the machine definition with `historyState`\r\n\r\nThere are plenty of additional examples in the [test directory](https://github.com/brucou/state-transducer/blob/master/test/hierarchy.specs.js).\r\n\r\n## `traceFSM :: Env -> FSM_Def -> FSM_Def`\r\n### Description\r\nThis function converts a state machine `A` into a traced state machine `T(A)`. The traced state \r\nmachine, on receiving an input `I` outputs an object with the following information :\r\n\r\n- `outputs` : the outputs `A(I)` \r\n- `updates` : the update of the extended state of `A` to be performed as a consequence of receiving the input `I` \r\n- `extendedState` : the extended state of `A` **prior** to receiving the input `I`\r\n- `newExtendedState` : the extended state of `A` **after** receiving the input `I` and computing \r\nthe outputs\r\n- `controlState` : the control state in which the machine is when receiving the input `I`\r\n- `event::{eventLabel, eventData}` : the event label and event data corresponding to `I` \r\n- `settings` : settings passed at construction time to `A`\r\n- `targetControlState` : the target control state the machine has transitioned to as a consequence of receiving the input `I`\r\n- `predicate` : the predicate (guard) corresponding to the transition that was taken to \r\n`targetControlState`, as a consequence of receiving the input `I`\r\n- `actionFactory` : the action factory which was executed as a consequence of receiving the \r\ninput `I`\r\n- `guardIndex` : the index for the guard in the `.guards` array of a transition away from a \r\ncontrol state, triggered by an event\r\n- `transitionIndex` : the index for the transition in the `.transitions` array which contain the \r\nspecification for the machine's transition\r\n\r\nNote that the trace functionality is obtained by decorating the action factories in `A`. As \r\nsuch, all action factories will see their output wrapped. This means :\r\n\r\n- transitions which do not lead to the execution of action factories are not traced\r\n- when the machine cannot find any transition for an event, hence any action to execute, \r\nthe traced machine will simply return `null`.\r\n\r\nNote also that `env` is not used for now, and will be used to parameterize the tracing in future \r\nversions of the library.\r\n\r\n### Contracts\r\n- [Type contracts](https://github.com/brucou/state-transducer/blob/master/src/types.js)\r\n\r\n### Implementation example\r\nCf. [tests](https://github.com/brucou/state-transducer/blob/master/test/fsm_trace.specs.js)\r\n\r\n## `makeWebComponentFromFsm :: ComponentDef -> FSM`\r\n### Description\r\nThis factory function creates a web component which takes no observed attributes or properties. The \r\nbehaviour or logic of the component is parameterized by the machine passed as parameter. The \r\ncommunication capability of the component is parameterized by subjects generated from a subject\r\n factory passed as parameter. The command handling capability are provided by command handlers \r\n and effect handlers passed as parameters. An initial event, terminal event (unused for now), and\r\n  a moniker indicating absence of actions to perform can be passed as options. \r\n\r\nThe web component receives input through its input subject, passes to the encapsulated machine \r\nwhich computes outputs and the component subsequently process those outputs via the command \r\nhandlers. The web component may or may not use the output subject to emit events. At the moment, \r\nwe do not have any example or test covering this use case.\r\n\r\nComponent whose behaviour is defined by a machine can be seamlessly integrated into any framework\r\n by converting to web component. Note however that the portion of the web component \r\n specification used, custom elements v1, is only supported in modern browsers. In the web \r\n component scenario, communication betwween the web component and other framework's component \r\n occurs through the input and output subject or DOM events. It is not possible to use any \r\n facility provided by the framework. \r\n\r\n### Contract\r\n- Type contracts\r\n- web component name must fulfill web component's specifications i.e. include an hyphen in its name\r\n\r\n### Implementation example\r\nWe have implemented a [movie search app](https://github.com/brucou/movie-search-app-nerv) with \r\n[Nerv](https://github.com/NervJS/nerv), a lightweight React clone which works with browsers down to \r\nIE8. The entry file can be found [here](https://github.com/brucou/movie-search-app-nerv/blob/master/src/index.js).\r\n\r\n```javascript\r\nconst fsm = createStateMachine(movieSearchFsmDef, {\r\n  updateState: applyJSONpatch,\r\n  debug: { console }\r\n});\r\n\r\nfunction subjectFromEventEmitterFactory() {\r\n  const eventEmitter = emitonoff();\r\n  const DUMMY_NAME_SPACE = \"_\";\r\n  const _ = DUMMY_NAME_SPACE;\r\n  const subscribers = [];\r\n\r\n  return {\r\n    next: x => eventEmitter.emit(_, x),\r\n    complete: () => subscribers.forEach(f => eventEmitter.off(_, f)),\r\n    subscribe: f => (subscribers.push(f), eventEmitter.on(_, f))\r\n  };\r\n}\r\n\r\nconst nervRenderCommandHandler = {\r\n  [COMMAND_RENDER]: (next, params, effectHandlers, el) => {\r\n    const { screen, query, results, title, details, cast } = params;\r\n    const props = params;\r\n    render(screens(next)[screen](props), el);\r\n  }\r\n};\r\nconst commandHandlersWithRender = Object.assign(\r\n  {},\r\n  commandHandlers,\r\n  nervRenderCommandHandler\r\n);\r\n\r\nconst options = { initialEvent: { [events.USER_NAVIGATED_TO_APP]: void 0 } };\r\n\r\nmakeWebComponentFromFsm({\r\n  name: \"movie-search\",\r\n  eventSubjectFactory: subjectFromEventEmitterFactory,\r\n  fsm,\r\n  commandHandlers: commandHandlersWithRender,\r\n  effectHandlers,\r\n  options\r\n});\r\n\r\nrender(h(\"movie-search\"), document.getElementById(\"root\"));\r\n```\r\n\r\n# Possible API extensions\r\nBecause of the API design choices, it is possible to realize the possible extensions without \r\nmodifying the state chart library (open/closed principle):\r\n\r\n- entry and exit actions\r\n  - decorating action factories : entry actions are already implemented and will be documented in\r\n   a future version of the library. Examples can be found in the []test directory](https://github.com/brucou/state-transducer/blob/master/test/entry-actions.specs.js).\r\n- logging/tracing/monitoring\r\n  - achieved through decorating both guards and action factories\r\n- contract checking (preconditions, postconditions and probably invariants - to be investigated) \r\nfor both states and transitions\r\n  - can be done by inserting in first position extra guards which either fail or throw, and \r\n  decorating exising guards\r\n- overriding initial control state and extended state\r\n  - can be achieved by modifying the `INIT` transition (by contract there is exactly one such \r\n  transition) and the `initial_extended_state`; and leaving everything else intact\r\n\r\nNote that some extensions may perform effects (logs, ...), meaning that the \r\norder of evaluation and application of operations would then become significant in general. \r\nExtension performing effects should only be used in development.\r\n\r\nEquipped with a history of inputs and the corresponding history of outputs, it is also possible to\r\n do property-based testing (for instance checking that a pattern in a sequence of outputs occurs only \r\nwhen a pattern occurs in the matching sequence of inputs).\r\n\r\nSome extensions may be useful to check/test the **design** of the automata, i.e. checking that the \r\nautomata which acts as modelization of requirements indeed satisfies the requirements. When \r\nsufficient confidence is acquired, those extensions can be safely removed or deactivated.\r\n\r\n# Visualization tools\r\nWe have included two helpers for visualization of the state transducer :\r\n\r\n- conversion to plantUML : `toPlantUml :: FSM_Def -> PlantUml`.\r\n  - the resulting chain of characters can be pasted in [plantText](`https://www.planttext.com/`) \r\n  or [plantUML previewer](http://sujoyu.github.io/plantuml-previewer/) to get an automated graph \r\n  representation. Both will produce the exact same visual representation.\r\n- conversion to [online visualizer](https://github.com/brucou/state-transducer-visualizer) \r\nformat (dagre layout engine) : for instructions, cf. github directory : `toDagreVisualizerFormat \r\n:: FSM_Def -> JSON`\r\n\r\n![visualization example](https://github.com/brucou/state-transducer-visualizer/raw/master/assets/cd-player-automatic-dagre-visualization.png)\r\n\r\nAutomated visualization works well with simple graphs, but seems to encounter trouble to generate\r\n optimally satisfying complex graphs. The Dagre layout seems to be a least worse option. I\r\n believe the best option for visualization is to use professional specialized tooling such as \r\n `yed`. In a future version, we will provide a conversion to `yed` graph format to facilitate \r\n such workflow. The [`yed`](https://www.yworks.com/products/yed) orthogonal and flowchart layout \r\n seem to give pretty good results.\r\n\r\n# Credits\r\n- Credit to [Pankaj Parashar](https://css-tricks.com/password-strength-meter/) for the password \r\nselector\r\n- Credit to [Sari Marton](https://github.com/sarimarton/) for the [original version](https://github.com/sarimarton/tmdb-ui-cyclejs) of the movie search app\r\n\r\n# Roadmap\r\n## Roadmap v1.0\r\n- [x] stabilise core API\r\n  - state machine as an effectless, impure function with causality properties\r\n  - expose only the factory, keep internal state fully encapsulated\r\n- [x] test [integration with React](https://github.com/brucou/react-state-driven)\r\n- [x] test [integration with Vue](https://github.com/brucou/vue-state-driven)\r\n- [x] support [model-based testing, and test input generation](https://pdfs.semanticscholar.org/f8e6/b3019c0d5422f35d2d98c242f149184992a3.pdf)\r\n  - [x] *all-transitions* coverage test case generator\r\n- [x] add tracing support\r\n  - obtained by decorating the machine definition\r\n- [x] add entry actions\r\n\r\n## Roadmap v1.X\r\n- [ ] support for visualization in third-party tools \r\n  - yed format conversion\r\n  - trace emitter\r\n- [ ] document entry actions\r\n- [ ] showcase property-based testing\r\n- [ ] decide definitively on tricky semantic cases\r\n  - transitionning to history states when there is no history\r\n  - ~~event delegation~~ \r\n\r\n## Roadmap v1.Y\r\n- [ ] support for live, interactive debugging\r\n\r\n## Roadmap v1.Z\r\n- [ ] add cloning API\r\n- [ ] add reset API\r\n- [ ] add and document exit actions\r\n- [ ] turn the test generation into an iterator(ES6 generator) : this allows it to be composed with \r\ntransducers and manipulate the test cases one by one as soon as they are produced. Will be useful\r\n for both example-based and property-based testing. When the generators runs through thousands of\r\n  test cases, we often have to wait a long time before seeing any result, which is pretty \r\n  damageable when a failure is located toward the ends of the generated input sequences.\r\n- [ ] add other searches that DFS, BFS (add probability to transitions, exclude some transitions,\r\n etc.). HINT : `store.pickOne` can be used to select the next transition\r\n   - pick a random transition\r\n   - pick next transition according to ranking (probability-based, prefix-based or else) \r\n\r\n# Who else uses state machines\r\nThe use of state machines is not unusual for safety-critical software for embedded systems. \r\nNearly all safety-critical code on the Airbus A380 is implemented with a [suite of tools](https://www.ansys.com/products/embedded-software/ansys-scade-suite/scade-suite-capabilities#cap1) which \r\nproduces state machines both as [specification](https://www.youtube.com/watch?list=PL0lZXwHtV6Ok5s-iSkBjHirM1fu53_Phv&v=EHP_spl5xU0) and [implementation](https://www.youtube.com/watch?v=523bJ1vZZmw&index=5&list=PL0lZXwHtV6Ok5s-iSkBjHirM1fu53_Phv) \r\ntarget. The driver here is two-fold. On the one hand is productivity : writing highly reliable code\r\n by hand can be done but it is painstakingly slow, while state machines allow to **generate the code** \r\nautomatically. On the other hand is reliability. Quoting Gerard Berry, founder of Esterel \r\ntechnologies, [<< low-level programming techniques will not remain acceptable for large \r\nsafety-critical programs, since they make behavior understanding and analysis almost \r\nimpracticable >>](https://ptolemy.berkeley.edu/projects/chess/design/2010/discussions/Pdf/synclang.pdf), in a harsh regulatory context \r\nwhich may require that every single system requirement \r\nbe traced to the code that implements it (!). Requirements modeled by state-machines are amenable\r\n to formal verification and validation. \r\n\r\nState machines have also been used extensively in [games of reasonable complexity](http://howtomakeanrpg.com/a/state-machines.html), and [tutorials](https://www.gamedev.net/articles/programming/general-and-gameplay-programming/state-machines-in-games-r2982/) abound\r\n on the subject. Fu and Houlette, in \r\n [AI Game Programming Wisdom 2](https://www.researchgate.net/publication/284383920_The_Ultimate_Guide_to_FSMs_in_Games)\r\n  summarized the rationale : \"Behavior modeling techniques based on state-machines are very \r\n  popular in the gaming industry because they are easy to implement, computationally efficient, \r\n  an intuitive representation of behavior, accessible to subject matter experts in addition to programmers, relatively easy to maintain, and can be developed in a number of commercial integrated development environments\". \r\n\r\nMore prosaically, did you know that ES6 generators compile down to ES5 state machines where no \r\nnative option is available? Facebook's [`regenerator`](https://github.com/facebook/regenerator) \r\nis a good example of such.\r\n\r\nSo state machines are nothing like a new, experimental tool, but rather one with a fairly extended \r\nand proven track in both industrial and consumer applications. \r\n\r\n# Annex\r\n## So what is an Extended Hierarchical State Transducer ? \r\nNot like it matters so much but anyways. Feel free to skip that section if you have little \r\ninterest in computer science.\r\n\r\nAlright, let's build the concept progressively.\r\n\r\nAn [automaton](https://en.wikipedia.org/wiki/Automata_theory) is a construct made of states \r\ndesigned to determine if a sequence of inputs should be accepted or rejected. It looks a lot like a \r\nbasic board game where each space on the board represents a state. Each state has information about what to do when an input is received by the machine (again, rather like what to do when you land on the Jail spot in a popular board game). As the machine receives a new input, it looks at the state and picks a new spot based on the information on what to do when it receives that input at that state. When there are no more inputs, the automaton stops and the space it is on when it completes determines whether the automaton accepts or rejects that particular set of inputs.\r\n\r\nState machines and automata are essentially interchangeable terms. Automata is the favored term \r\nwhen connoting automata theory, while state machines is more often used in the context of the \r\nactual or practical usage of automata.\r\n\r\nAn extended state machine is a state machine endowed with a set of variables, predicates (guards)\r\nand instructions governing the update of the mentioned set of variables. To any extended state \r\nmachines it corresponds a standard state machine (albeit often one with a far greater number of \r\nstates) with the same semantics.\r\n\r\nA hierarchical state machine is a state machine whose states can be themselves state machines. \r\nThus instead of having a set of states as in standard state machines, we have a hierarchy (tree) of \r\nstates describing the system under study.\r\n\r\nA [state transducer](https://en.wikipedia.org/wiki/Finite-state_transducer) is a state \r\nmachine, which in addition to accepting inputs, and modifying its state accordingly, may also \r\ngenerate outputs.\r\n\r\nWe propose here a library dealing with extended hierarchical state transducers, i.e. a state machine\r\nwhose states can be other state machines (hierarchical part), which (may) associate an output to an \r\ninput (transducer part), and whose input/output relation follows a logic guided by \r\npredefined control states (state machine part), and an encapsulated memory which can be \r\nmodified through actions guarded by predicates (extended part).\r\n\r\nNote that if we add concurrency and messaging to extended hierarchical state transducers, we get\r\n a statechart. We made the design decision to remain at the present level, and not to incorporate \r\n any concurrency mechanism.[^2]\r\n\r\n[^2]: Our rationale is as follows :  \r\n - statecharts include activities and actions which may produce effects, and concurrency. We are \r\n seeking an purely computational approach (i.e effect-less) to facilitate **composition, reuse and \r\n  testing**. \r\n - In the absence of concurrency (i.e. absence of parallel regions), a statechart can be turned \r\n into a hierarchical state transducer. That is often enough! \r\n - there is no difference in terms of \r\n expressive power between statecharts and hierarchical transducers[^4], just as there is no \r\n difference in expressive power between extended state machines and regular state machines. The \r\n difference lies in naturalness and convenience : a 5-state extended state machine is \r\n easier to read and maintain than the equivalent 50-state regular state machine. \r\n - we argue that convenience here is on the side of being able to freely plug in any [concurrent \r\n or communication model](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.92.6145&rep=rep1&type=pdf) fitting the problem space. In highly concurrent systems, programmers may have it hard to elaborate a mental model of the statecharts solely from the visualization of \r\n concurrent statecharts.\r\n - some [statecharts practitioners](http://sismic.readthedocs.io/en/master/communication.html#) \r\n favor having separate state charts communicating[^5] in an ad-hoc way rather than an integrated \r\n statechart model where concurrent state charts are gathered in nested states of a single \r\n statechart. We agree.\r\n \r\n[^3]: As a matter of fact, more than 20 different semantics have been proposed to define \r\nprecisely the concurrency model for statecharts, e.g Rhapsody, Statemate, VisualMate, StateFlow, \r\nUML, etc. do not share a single concurrency model.\r\n[^4]: David Harel, Statecharts.History.CACM : Speaking in the strict mathematical sense of power \r\nof expression, hierarchy and orthogonality are but helpful abbreviations and can be eliminated\r\n[^5]: David Harel, Statecharts.History.CACM : <<I definitely do not recommend having a single \r\nstatechart for an entire system. (...) concurrency occurs on a higher level.)>>\r\n\r\n## Terminology\r\nIn this section, we seek to define quickly the meaning of the key terms which will be commonly \r\nused when referring to state machines.\r\n\r\n<dl>\r\n  <dt>control state</dt>\r\n  <dd>Control states, in the context of an extended state machine is a piece of the internal state\r\n   of the state machine, which serves to determine the transitions to trigger in response to \r\n   events. Transitions only occur between control states. Cf. base example illustration. </dd>\r\n  <dt>extended state</dt>\r\n  <dd>We refer by extended state the piece of internal state of the state machine which can be \r\n  modified on transitioning to another state. That piece of internal state **must** be \r\n  initialized upon creating the state machine. In this context, the extended state will simply \r\n  take the form of a regular object. The shape of the extended state is largely \r\n  application-specific. In the context of our multi-steps workflow, extended state could for \r\n  instance be the current application data, which varies in function of the state of the \r\n  application.</dd>\r\n  <dt>input</dt>\r\n  <dd>In the context of our library, we will use interchangeable input for events. An automata \r\n  receives inputs and generated outputs. However, as a key intended use case for this\r\n   library is user interface implementation, inputs will often correspond to events generated by a \r\n   user. We thus conflate both terms in the context of this documentation.\r\n  </dd>\r\n  <dt>external event</dt>\r\n  <dd>External events are events which are external and uncoupled to the state machine at hand. \r\n  Such events could be, in the context of an user interface, a user click on a button.\r\n  </dd>\r\n  <dt>internal event</dt>\r\n  <dd>Internal events are events coupled to a specific state machine. Depending on the semantics \r\n  of a particular state machine, internal events may be generated to realize those semantics. In \r\n  the context of our library, we only generate internal events to trigger automatic transitions. \r\n  </dd>\r\n  <dt>initial event</dt>\r\n  <dd>In the context of our library, the initial event (<b>INIT_EVENT</b>) is fired automatically\r\n   upon starting a state machine. The initial event \r\n  can be used to configure the initial machine transition, out from the initial control state. \r\n  However it is often simpler to just configure an initial control state for the machine.\r\n  </dd>\r\n  <dt>automatic event</dt>\r\n  <dd>This is an internally triggered event which serves to triggers transitions from control \r\n  states for which no triggering events are configured. Such transitions are called automatic \r\n  transitions. Not firing an automatic event would mean that the state machine would be forever  \r\n  stuck in the current control state.\r\n  </dd>\r\n  <dt>transition</dt>\r\n  <dd>Transitions are changes in tne control state of the state machine under study. Transitions \r\n  can be configured to be taken only when predefined conditions are fulfilled (guards). \r\n  Transitions can be triggered by an event, or be automatic when no triggering event is specified.\r\n  </dd>\r\n  <dt>automatic transition</dt>\r\n  <dd>Transitions between control states can be automatically evaluated if there are no \r\n  triggering events configured. The term is a bit confusing however, as it is possible in theory \r\n  that no transition is actually executed, if none of the configured guard is fulfilled. We \r\n  forbid this case by contract, as failing to satisfy any such guard would mean that \r\n   the machine never progress to another state! In our CD player example, an automatic transition\r\n    is defined for control state 3 (`Closing CD drawer`). According to the extended state of our \r\n    machine, the transition can have as target either the `CD Drawer Closed` or `CD Loaded` \r\n    control states.\r\n  </dd>\r\n  <dt>self transition</dt>\r\n  <dd>Transitions can also occur with origin and destination the same conrol state. When \r\n  that happens, the transition is called a self transition.\r\n  </dd>\r\n  <dt>transition evaluation</dt>\r\n  <dd>Given a machine in a given control state, and an external event occuring, the transitions \r\n  configured for that event are evaluated. This evaluation ends up in identifying a valid \r\n  transition, which is executed (e.g. taken) leading to a change in the current control state ; \r\n  or with no satisfying transition in which case the machine remains in the same control state, \r\n  with the same extended state.\r\n  </dd>\r\n  <dt>guards</dt>\r\n  <dd>Guards associated to a transition are predicates which must be fulfilled for that \r\n  transition to be executed. Guards play an important role in connecting extended state to the  \r\n  control flow for the computation under specification. As a matter of fact, in our context, guards \r\n  are pure functions of both the occurring event and extended state.\r\n  </dd>\r\n  <dt>action factory</dt>\r\n  <dd>This is a notion linked to our implementation. An action factory is a function which \r\n  produces information about two actions to be performed upon executing a transition : update the\r\n   encapsulated extended state for the state transducer, and possibly generate an output to its \r\n   caller. \r\n  </dd>\r\n  <dt>output</dt>\r\n  <dd>An output of the transducer is simply the value returned by the transducer upon receiving \r\n  an input (e.g. event). We will sometimes use the term *action* for output, as in the context of\r\n   user interface specification, the output generated by our transducers will be actions on the \r\n   interfaced systems. Actions is quite the overloaded and polysemic terms though, so we will try\r\n    as much as possible to use output when necessary to avoid confusion.\r\n  </dd>\r\n  <dt>composite state</dt>\r\n  <dd>As previously presented, an hierarchical state machine may feature control states which may \r\n  themselves be hierarchical state machines. When that occurs, such control state will be called \r\n  a composite state. In our CD player example, the control state `CD loaded` is a composite state.\r\n  </dd>\r\n  <dt>compound state</dt>\r\n  <dd>exact synonim of *composite state*\r\n  </dd>\r\n  <dt>nested state</dt>\r\n  <dd>A control state which is part of a composite state\r\n  </dd>\r\n  <dt>atomic state</dt>\r\n  <dd>An atomic state is a control state which is not itself a state machine. In other words, it \r\n  is a control state like in any standard state machine. In our base example, all states are \r\n  atomic states. In our CD player example, the control state 5 is an atomic state. The `CD \r\n  loaded` control state is not.\r\n  </dd>\r\n  <dt>transient state</dt>\r\n  <dd>transient states are control states which are ephemeral. They are meant to be immediately \r\n  transitioned from. Transient state thus feature no external triggering event (but necessitates \r\n  of internal automatic event), and may have associated guards. By contract, one of these guards,\r\n   if any, must be fulfilled to prevent the machine for eternally remain in the same control \r\n   state.   In our CD player example, the control state 3 is a transient state. Upon entering \r\n   that state, the machine will immediately transition to either control state 1, or composite \r\n   state `CD loaded`.\r\n  </dd>\r\n  <dt>terminal state</dt>\r\n  <dd>the terminal state is a control state from which the machine is not meant to transition \r\n  from. This corresponds to a designed or anticipated end of run of the state machine.\r\n  <dt>history state</dt>\r\n  <dd>Semantics for the history state may vary according to the intended application of \r\n  hierarchical automata. In our restrictive context, the history state allows to transition back \r\n  to the previou","readmeFilename":"README.md","homepage":"https://github.com/brucou/state-transducer#readme","bugs":{"url":"https://github.com/brucou/state-transducer/issues"}}