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Motivation

Time and again we have to implement computations which, while they cannot be modelized by pure functions, however have the following interesting properties :

  • they transform an input into an output, depending only on the present and past inputs
  • they do not perform any effects
  • the algorithm for the computation involves a finite, parameterizable set of rules, coalescing
    around a finite, fixed set of control states

These computations can often be modelized advantageously1 by a class of state machines called hierarchical extended state transducer. This library offers a way to define, and use such class of state machines. We will come back on the meaning of the fancy name, but in short a state transducer is a state machine which may produce outputs. Most of the time, we will call them just state machine anyways, but keep in mind that every word in hierarchical extended state transducer has a reason to be.

Now, the whole thing can sound very abstract but the major motivation for this library has been the specification and implementation of user interfaces. As a matter of fact, to every user interface can be associated a computation relating a user input to an action to be performed on the interfaced systems. That computation often has a logic organized around a limited set of control states. Exactly what we just wrote about. Jump to the examples.

The use of state machines is not unusual for safety-critical software for embedded systems. Nearly all safety-critical code on the Airbus A380 is implemented with a suite of tools which produces state machines both as specification and implementation target. The driver here is two-fold. On the one hand is productivity : writing highly reliable code by hand can be done but it is painstakingly slow, while state machines allow to generate the code automatically. On the other hand is reliability. Quoting Gerard Berry, founder of Esterel technologies, << low-level programming techniques will not remain acceptable for large safety-critical programs, since they make behavior understanding and analysis almost impracticable >>, in a harsh regulatory context which may require that every single system requirement be traced to the code that implements it (!). Requirements modeled by state-machines are amenable to formal verification and validation.

State machines have also been used extensively in games of reasonable complexity, and tutorials abound on the subject. The driving factors are again two. First, the basic problem for AI to solve here is : given the state of the world, what should I do? Because game character behavior can be modeled (in most cases) as a sequence of different character "mental states", where change in state is driven by the actions of the player or other characters, or possibly some features of the game world, game programmers often find that state machines are a natural choice for defining character AI. Second, it is a very accessible and affordable tool vs. alternatives. The "decision-action" model is straightforward enough to appeal to the nonprogrammers on the game development team (such as level designers), yet impressively powerful. FSMs also lend themselves to being quickly sketched out during design and prototyping, and even better, they can be easily and efficiently implemented.

More prosaically, did you know that ES6 generators compile down to ES5 state machines where no native option is available? Facebook's regenerator is a good example of such.

So state machines are nothing like a new, experimental tool, but rather one with a fairly extended and proven track in both industrial and consumer applications. Actually, old people like me will remember SproutCore, an ancient framework by any means (2010 was it?) when javascript was still young and nimble, and jQuery was a baby. The Ki library already offered then an interface to use hierarchical state machines (concretely statecharts). However, it has to be said that, when it comes to graphical user interfaces, it is a tool fairly unknown to developers. Our current assessment is that state machines are another useful tool in our toolbox to write more reliable, maintainable UIs, with a short distance between specification and implementation, just as it is the case with embedded software.

This library is born from :

  • the desire to investigate further the extent of the applicability of such tool both for specification and implementation of user interfaces
    • the reliability factor driving the use of state machines for safety-critical software is moot in the human-machine interface space. Errors in graphical user interfaces have lower significance than in airplane systems. Moreover, because of the potential subtle interactions between UI components, it may be difficult to exercise an extensive and realistic simulation of user interaction. But wouldn't the productivity factor still hold? Given that user interface programming is highly iterative, wouldn't the maintainability benefits be significant ?
    • the experience with gaming shows that, passed a given level of AI complexity, other techniques are better suited (behaviour trees, etc.). How does this translate to the graphical user interfaces problem space? What would be a sweet spot?
  • the absence of existing javascript libraries which satisfy our design criteria
    • mostly, we want the state machine library API design to be as close as possible from the mathematical object denoting it. This should allow us to reason about it, compose and reuse it easily.
    • most libraries we found either do not feature hierarchy in their state machines, or use a rather imperative API, or impose a concurrency model on top of the state machine's control flow

Needless to say, this library is written because of a substantiated belief that there are serious benefits today in using a more formalized approach to user interface design. It should also be obvious that this is a work in progress, the current version is taken from statechart code written two/three years ago and adjusted to the current API design. It works nicely though and have already been used succesfully :

  • in multi-steps workflows, a constant feature of enterprise software today
  • for 'smart' synchronous streams, which tracks computation state to avoid useless re-computations
  • to implement cross-domain communication protocols, to coordinate iframes with a main window

In such cases, we were able to modelize our computation with an Extended Hierarchical State Transducer in a way that :

  • is economical (complexity of the transducer proportional to complexity of the computation)
  • is reasonably easy to reason about and communicate (the transducer can be visually represented, supporting both internal and external communication, and design specification and documentation)
  • supports step-wise refinement and iterative development (control states can be refined into a hierarchy of nested states)

I guess we live in interesting times.

So what is an Extended Hierarchical State Transducer ?

Not like it matters so much but anyways. Feel free to skip that section if you have little interest in computer science.

Alright, let's build the concept progressively.

An automaton is a construct made of states designed to determine if a sequence of inputs should be accepted or rejected. It looks a lot like a basic 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.

State machines and automata are essentially interchangeable terms. Automata is the favored term when connoting automata theory, while state machines is more often used in the context of the actual or practical usage of automata.

An extended state machine is a state machine endowed with a set of variables, predicates (guards) and instructions governing the update of the mentioned set of variables. To any extended state machines it corresponds a standard state machine (albeit often one with a far greater number of states) with the same semantics.

A hierarchical state machine is a state machine whose states can be themselves state machines. Thus instead of having a set of states as in standard state machines, we have a hierarchy (tree) of states describing the system under study.

A state transducer is a state machine, which in addition to accepting inputs, and modifying its state accordingly, may also generate outputs.

We propose here a library dealing with extended hierarchical state transducers, i.e. a state machine whose states can be other state machines (hierarchical part), which (may) associate an output to an input (transducer part), and whose input/output relation follows a logic guided by predefined control states (state machine part), and an encapsulated memory which can be modified through actions guarded by predicates (extended part).

Note that if we add concurrency and messaging to extended hierarchical state transducers, we get a statechart. We made the design decision to remain at the present level, and not to incorporate any concurrency mechanism.2

  • statecharts include activities and actions which may produce effects, and concurrency. We are seeking an purely computational approach (i.e effect-less) to facilitate composition, reuse and testing.
  • In the absence of concurrency (i.e. absence of parallel regions), a statechart can be turned into a hierarchical state transducer. That is often enough!
  • there is no difference in terms of expressive power between statecharts and hierarchical transducers3, just as there is no difference in expressive power between extended state machines and regular state machines. The difference lies in naturalness and convenience : a 5-state extended state machine is easier to read and maintain than the equivalent 50-state regular state machine.
  • we argue that convenience here is on the side of being able to freely plug in any concurrent or communication model 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 concurrent statecharts.
  • some statecharts practitioners favor having separate state charts communicating4 in an ad-hoc way rather than an integrated statechart model where concurrent state charts are gathered in nested states of a single statechart. We agree.

Install

npm install state-transducer

API

API design

The key objectives for the API was :

  • generality and reusability (there is no provision made to accommodate specific use cases or frameworks)
    • it must be possible to add a concurrency and/or communication mechanism on top of the current design
    • it must be possible to integrate smoothly into React, Angular and your popular framework
    • support for both interactive and reactive programming
  • parallel and sequential composability of transducers

As a result of this, the following choices were made :

  • complete encapsulation of the state of the transducer
  • single public method : the transducer is used through a sole yield function (though a start syntactic sugar is provided for yielding the mandatory INIT event). As such, the transducer is a black-box, and only its injected outputs can be observed
  • no effects performed by the machine
  • no exit and entry actions, or activities as in other state machine formalisms
    • there is no loss of generality as both entry and exit actions can be implemented with our state transducer, there is simply no API or syntactic support for it
  • every computation performed is synchronous (asynchrony is an effect)
  • action factories return the updates to the extended state (JSON patch format) to avoid any unwanted direct modification of the extended state
  • no restriction is made on output of transducers, but inputs must follow some conventions (if a machine's output match those conventions, two such machines can be sequentially composed ; parallel composition naturally occurs by feeding two state machines the same input(s))
  • reactive programming is enabled by exposing a pure function of an input stream, which runs the transducer for each incoming input, thus generating a sequence of outputs
  • library is decoupled from any concrete implementation of streams : an interface is chosen, and the implementation of that interface must be passed through settings

Concretely, our state transducer will be created by the factory function create_state_machine, which returns a state transducer which :

  • must be started manually (with .start()), and configured with an initial event and transition
  • will compute an output for any input that is sent to it (with .yield(input))

The state transducer is not, in general, a pure function of its inputs. However, a given output of the transducer depends exclusively on the sequence of inputs it has received so far (causality property). This means that it is possible to
associate to a state transducer another function which takes a sequence of inputs into a sequence of outputs, in a way that that function is pure.

General concepts

Our state transducer is an object which encapsulates state, and exposes a single function by which input is received. That function, based on the transducer's encapsulated state and configuration, and the received input produces two things :

  • a list of updates to apply internally to the extended state
  • an external output for the consumer of the state transducer

To help illustrate further the concepts, and the terminology, we will use two examples, featuring basic and advanced features on the hierarchical state transducer model :

  • a real use case of non-hierarchical extended state machine applied to a web application user interface
  • the specification of the behaviour for a cd player as a hierarchical extended state machine

We will subsequently precise here the vocabulary which will be used throughout the documentation. We then describe how the behaviour of a transducer relates to its configuration. In particular we detail the concepts and semantics associated to hierarchical states. Finally we present our API whose documentation relies on all previously introduced concepts.

Base example

This example is taken from an actual project in which this library was used. It will be used in this paragraph to illustrate the core terminology defined in subsequent sections, and illustrate somewhat abstract notions. It does not feature hierarchical states, and as such can be seen as a regular extended state machine.

This example deals with a typical multi-step application process, whose user interface is made of a sequence of screens. In each screen, the user is required to introduce or review some information, and navigate through the application process up to completion.

That application process concretely consists of 5 screens whose flow is defined by the UX team as follows :

User flow

This in turn was turned into a non-trivial state machine (7 states, ~20 transitions) orchestrating the screens to display in function of the user inputs. The machine does not display the screen itself (it performs no effects), it computes a representation of the screen to display according to the sequence of inputs performed by the user and its encapsulated state (user-entered data, data validation, etc.). The action display screen in the graph below must be understood as a regular piece of data (virtual DOM tree) whose meaning is to be interpreted down the road by the portion of the program in charge of realizing effects (DOM patch library). The state machine can be visualized as follows :

illustration of basic terminology

In our example, the encapsulated state has the following shape :

{
  user,
  opportunity,
  project,
  userApplication,
  teams,
  errorMessage: null,
  validationMessages: {}
}

CD drawer example

This example is taken from Ian Horrock's seminal book on statecharts and is the specification of a CD player. The behaviour of the CD player is pretty straight forward and understandable immediately from the visualization. From a didactical point of view, the example serve to feature advanced characteristics of hierarchical state machines, including history states, composite states, transient states, automatic transitions, and entry points. For a deeper understanding of how the transitions work in the case of a hierarchical machine, you can have a look at the sample run for the CD player machine.

cd player state chart

Terminology

In this section, we seek to define quickly the meaning of the key terms which will be commonly used when referring to state machines.

control state
Control states, in the context of an extended state machine is a piece of the internal state of the state machine, which serves to determine the transitions to trigger in response to events. Transitions only occur between control states. Cf. base example illustration.
extended state
We refer by extended state the piece of internal state of the state machine which can be modified on transitioning to another state. That piece of internal state **must** be initialized upon creating the state machine. In this context, the extended state will simply take the form of a regular object. The shape of the extended state is largely application-specific. In the context of our multi-steps workflow, extended state could for instance be the current application data, which varies in function of the state of the application.
input
In the context of our library, we will use interchangeable input for events. An automata receives inputs and generated outputs. However, as a key intended use case for this library is user interface implementation, inputs will often correspond to events generated by a user. We thus conflate both terms in the context of this documentation.
external event
External events are events which are external and uncoupled to the state machine at hand. Such events could be, in the context of an user interface, a user click on a button.
internal event
Internal events are events coupled to a specific state machine. Depending on the semantics of a particular state machine, internal events may be generated to realize those semantics. In the context of our library, we only generate automatic events to trigger automatic transitions ; INIT events to jump start a state machine
initial event
In the context of our library, the initial event (INIT in the base example illustration) is fired automatically and only upon starting a state machine. The initial event can be used to configure the initial machine transition, out from the initial control state.
automatic event
This is an internally triggered event which serves to triggers transitions from control states for which no triggering events are configured. Such transitions are called automatic transitions. Not firing an automatic event would mean that the state machine would be forever stuck in the current control state.
transition
Transitions are changes in tne control state of the state machine under study. Transitions can be configured to be taken only when predefined conditions are fulfilled (guards). Transitions can be triggered by an event, or be automatic when no triggering event is specified.
automatic transition
Transitions between control states can be automatically evaluated if there are no triggering events configured. The term is a bit confusing however, as it is possible in theory that no transition is actually executed, if none of the configured guard is fulfilled. We forbid this case by contract, as failing to satisfy any such guard would mean that the machine never progress to another state! In our CD player example, an automatic transition is defined for control state 3 (`Closing CD drawer`). According to the extended state of our machine, the transition can have as target either the `CD Drawer Closed` or `CD Loaded` control states.
self transition
Transitions can also occur with origin and destination the same conrol state. When that happens, the transition is called a self transition. In our base example, the `Team Detail Screen` control state features 2 self-transitions.
transition evaluation
Given a machine in a given control state, and an external event occuring, the transitions configured for that event are evaluated. This evaluation ends up in identifying a valid transition, which is executed (e.g. taken) leading to a change in the current control state ; or with no satisfying transition in which case the machine remains in the same control state, with the same extended state.
guards
Guards associated to a transition are predicates which must be fulfilled for that transition to be executed. Guards play an important role in connecting extended state to the control flow for the computation under specification. As a matter of fact, in our context, guards are pure functions of both the occurring event and extended state.
action factory
This is a notion linked to our implementation. An action factory is a function which produces information about two actions to be performed upon executing a transition : update the encapsulated extended state for the state transducer, and possibly generate an output to its caller.
output
An output of the transducer is simply the value returned by the transducer upon receiving an input (e.g. event). We will sometimes use the term *action* for output, as in the context of user interface specification, the output generated by our transducers will be actions on the interfaced systems. Actions is quite the overloaded and polysemic terms though, so we will try as much as possible to use output when necessary to avoid confusion.
composite state
As previously presented, an hierarchical state machine may feature control states which may themselves be hierarchical state machines. When that occurs, such control state will be called a composite state. In our CD player example, the control state `CD loaded` is a composite state.
compound state
exact synonim of *composite state*
nested state
A control state which is part of a composite state
atomic state
An atomic state is a control state which is not itself a state machine. In other words, it is a control state like in any standard state machine. In our base example, all states are atomic states. In our CD player example, the control state 5 is an atomic state. The `CD loaded` control state is not.
transient state
transient states are control states which are ephemeral. They are meant to be immediately transitioned from. Transient state thus feature no external triggering event (but necessitates of internal automatic event), and may have associated guards. By contract, one of these guards, if any, must be fulfilled to prevent the machine for eternally remain in the same control state. In our CD player example, the control state 3 is a transient state. Upon entering that state, the machine will immediately transition to either control state 1, or composite state `CD loaded`.
terminal state
the terminal state is a control state from which the machine is not meant to transition from. This corresponds to a designed or anticipated end of run of the state machine.
history state
Semantics for the history state may vary according to the intended application of hierarchical automata. In our restrictive context, the history state allows to transition back to the previous control state that was previously transitioned away from. This makes sense mostly in the context of composite states, which are themselves state machines and hence can be in one of several control states. In our CD player example, there are a few examples of history states in the `CD loaded` composite state. For instance, if while being paused (atomic control state 6), the user request the previous CD track, then the machine will transition to... the same control state 6. The same is true if prior to the user request the machine was in control state 4, 5, or 7. History state avoids having to write individual transitions to each of those states from their parent composite state.
entry point
Entry points are the target of transitions which are taken when entering a given composite state. This naturally only applies to transitions with origin a control state not included in the composite state and destination a control state part of the composite state. An history state can also be used as an entry point. In our CD player example, control state 1 is an entry point for the composite state `No CD loaded`. The same stands for `H` (history state) in `CD Loaded` composite state. Similarly a transition from `No CD loaded` to `CD loaded` will result in the machine ending in control state 4 (`CD stopped`) by virtue of a chain of entry points leading to that control state.

Transducer semantics

We give here a quick summary of the behaviour of the state transducer :

Preconditions

  • the machine is configured with a set of control states, an initial extended state, transitions, guards, action factories, and user settings.
  • the machine configuration is valid (cf. contracts)
  • the machine is in a fixed initial control state at starting time
  • Input events ({{[event_label]: event_data}}), including the initial INIT event are passed to the transducer by call of the exposed yield method

Event processing

  • Starting the machine (.start()) triggers the reserved INIT event which advances the state machine out of the initial control state towards the relevant user-configured control state
    • note that the INIT event carries the initial extended state as data
  • 1
  • Search for a feasible transition in the configured transitions
  • If there is no feasible transition :
    • issue memorized output (NO_OUTPUT if none), extended state and ocntrol state do not change. THE END
  • If there is a feasible transition, select the first transition according to what follows :
    • if there is an INIT transition, select that
    • if there is an eventless transition, select that
    • otherwise select the first transition whose guard is fulfilled (as ordered per array index)
  • evaluate the selected transition
    • if the target control state is an history state, replace it by the control state it references (i.e. the last seen nested state for that compound state)
    • update the extended state (with the updates produced by the action factory)
    • memorize the outputs (produced by the action factory)
    • update the control state to the target state
    • update the history for the control state (applies only if control state is compound state)
  • return to 1

A few interesting points :

  • a machine always transitions towards an atomic state at the end of event processing
  • on that path towards an atomic target state, all intermediary extended state updates are performed. Guards and action factories on that path are thus receiving a possibly evolving extended state. The injected outputs will be aggregated in an array of outputs.

The aforedescribed behaviour is summarized here :

event processing

History states semantics An history state relates to the past configuration a compound state. There are two kinds of history states : shallow history states (H), and deep history states (H*). A picture being worth more than words, thereafter follows an illustration of both history states :

deep and shallow history

Assuming the corresponding machine has had the following run [INIT, EVENT1, EVENT3, EVENT5, EVENT4]:

  • the configurations for the OUTER control state will have been [OUTER.A, INNER, INNER.S, INNER.T]
  • the shallow history state for the OUTER control state will correspond to the INNER control state (the last direct substate of OUTER), leading to an automatic transition to INNER_S
  • the deep history state for the OUTER control state will correspond to the INNER.T control state (the last substate of OUTER before exiting it)

In short the history state allows to short-circuit the default entry behaviour for a compound state, which is to follow the transition triggered by the INIT event. When transitioning to the history state, transition is towards the last seen state for the entered compound state.

Example run

To illustrate the previously described transducer semantics, let's run the CD player example.

Control state Internal event User event
INIT INIT
No Cd Loaded INIT
CD Drawer Closed --
CD Drawer Closed Eject
CD Drawer Open Eject (put a CD)
Closing CD Drawer eventless
CD Loaded INIT
CD Loaded subgroup INIT
CD Stopped --
CD stopped Play
CD playing Forward down
Stepping forwards Forward up
CD playing --

Note :

  • the state entry semantics -- entering No Cd Loaded leads to enter CD Drawer Closed
  • the guard -- because we put a CD in the drawer, the machine transitions from Closing CD Drawer to CD Loaded
  • the eventless transition -- the latter is an eventless transition : the guards are automatically evaluated to select a transition to progress the state machine (by contract, there must be one)
  • the hierarchy of states -- the Forward down event transitions the state machines to Stepping forwards, as it applies to all atomic states nested in the CD Loaded subgroup control state
  • the history semantics -- releasing the forward key on the CD player returns to CD Playing the last atomic state for compound state CD Loaded subgroup.

Contracts

Format

  • state names must be unique and conform to the same nomenclature than javascript variable identifiers (cannot be empty strings, cannot start with a number, etc.)
  • all transitions must be valid :
    • all states referenced in the transitions data structure must be defined in the states data structure
    • the transition syntax must be followed (cf. types)
    • all transitions must define an action (even if that action does not modify the extended state or returns NO_OUTPUT)
  • all action factories must fill in the updates and outputs property (no syntax sugar)
    • NO_OUTPUT must be used to indicate the absence of outputs

Initial event and initial state

By initial transition, we mean the transition with origin the machine's default initial state.

  • the first event processed by the state machine must be the init event
  • the init event has the initial extended state as event data
  • the init event can only be sent once (further init events will be ignored, and the machine will return NO_OUTPUT)
  • the state machine starts in the initial state
  • there are no incoming transitions to the initial state
  • The machine cannot stay blocked in the initial control state. This means that at least one transition must be configured and be executed between the initial control state and another state . This is turn means :
    • at least one non-reserved control state must be configured
    • at least one transition out of the initial control state must be configured
    • of all guards for such transitions, if any, at least one must be fulfilled to enable a transition away from the initial control state
  • there is exactly one initial transition, with unambiguous target state, with only effect to determine the initial control state for the machine
    • there is no guard on that transition
    • the action on that transition is the identity action

Semantical contracts

  • the machine cannot block on receiving an input
    • eventless transitions must progress the state machine
      • at least one guard must be fulfilled, otherwise we would remain forever in the same state
    • eventless self-transitions must modify the extended state
      • lest we loop forever (a real blocking infinite loop)
      • note that there is not really a strong rationale for eventless self-transition, I recommend just staying away from it.
  • the machine is deterministic and unambiguous
    • NOTE TO SELF: absolutely enforce that contract
    • to a (from, event) couple, there can only correspond one row in the transitions array of the state machine (but there can be several guards in that row)
      • (particular case) eventless transitions must not be contradicted by event-ful transitions
    • A -ev> B and A < OUTER_A with OUTER_A -ev>C !! : there are two valid transitions triggered by ev. Such transitions would unduely complicate the input testing generation, and decrease the readability of the machine so we forbid such transitions5
    • there cannot be two transitions with the same (from, event, predicate) - sameness defined for predicate by referential equality
  • no transitions from the history state (history state is only a target state)
  • A transition evaluation must end in an atomic state
    • Initial states must be defined for every compound state
    • Every compound state must have eactly one INIT transition, i.e. a transition whose triggering event is INIT_EVENT. That transition must have a target state which is a substate of the compound state (no hierarchy crossing)
    • Compound states must not have eventless transitions defined on them (would introduce ambiguity with the INIT transition)
    • (the previous conditions ensure that there is always a way down the hierarchy for compound states, and that way is always taken when entering the compound state, and the descent process always terminate)
  • the machine does not perform any effects
    • guards, action factories are pure functions
      • as such exceptions while running those functions are fatal, and will not be caught
    • updateState :: ExtendedState -> ExtendedStateUpdates -> ExtendedState must be a pure function (this is important in particular for the tracing mechanism which triggers two execution of this function with the same parameters)

create_state_machine :: FSM_Def -> Settings -> FSM

Description

This FSM factory function takes the parameters defining the behaviour of the state transducer, and returns the created state transducer. That transducer has a method yield by which an input is passed to the state machine, and in return the injected output is received. The syntax for an input is {{[eventLabel] : eventData}}, i.e. an input is an object with exactly one key, which is the event identifier, and the value matching the key is the event data.

Note that by contract the state machine must be started by sending the INIT event. We provide the syntatic sugar .start() to do so.

The machine additionnally can carry over environment variables, which are accessible in guards, and action factories. This helps maintaining such functions pure and testable.

History states are generated by a factory returned by a helper makeHistoryStates :: FSM_States -> HistoryStateFactory. An history state is coupled to a compound state, and has a type (deep or shallow). Passing this information to the factory produdces the sought history state.

The settings.updateState property is mandatory, and specify how to update a model from the .updates produced by an action factory. We used successfully JSON patch operations for model updates, but you can choose to use the inmutable library of your choice or else. The important point is that the extended state should not be modified in place, i.e. updateState is a pure function.

Contracts

  • All previously mentioned contracts apply.
  • The settings.updateState property is mandatory.
  • The settings property should not be modified after being passed as parameter (i.e. should be a constant): it is not cloned and is passed to all relevant functions (guards, etc.)
  • The key types contracts are summarized here :
/**
 * @typedef {Object} FSM_Def
 * @property {FSM_States} states Object whose every key is a control state admitted by the
 * specified state machine. The value associated to that key is unused in the present version of the library. The
 * hierarchy of the states correspond to property nesting in the `states` object
 * @property {Array<EventLabel>} events A list of event monikers the machine is configured to react to
 * @property {Array<Transition>} transitions An array of transitions the machine is allowed to take
 * @property {*} initialExtendedState The initial value for the machine's extended state
 */
/**
 * @typedef {Object.<ControlState, *>} FSM_States
 */
/**
 * @typedef {InconditionalTransition | ConditionalTransition} Transition
 */
/**
 * @typedef {{from: ControlState, to: ControlState|HistoryState, event: EventLabel, action: ActionFactory}} InconditionalTransition
 *   Inconditional_Transition encodes transition with no guards attached. Every time the specified event occurs, and
 *   the machine is in the specified state, it will transition to the target control state, and invoke the action
 *   returned by the action factory
 */
/**
 * @typedef {{from: ControlState, event: EventLabel, guards: Array<Condition>}} ConditionalTransition Transition for the
 * specified state is contingent to some guards being passed. Those guards are defined as an array.
 */
/**
 * @typedef {{predicate: FSM_Predicate, to: ControlState|HistoryState, action: ActionFactory}} Condition On satisfying the
 * specified predicate, the received event data will trigger the transition to the specified target control state
 * and invoke the action created by the specified action factory, leading to an update of the internal state of the
 * extended state machine and possibly an output to the state machine client.
 */
/**
 * @typedef {function(ExtendedState, EventData, FSM_Settings) : Actions} ActionFactory
 */
/**
 * @typedef {{updates: ExtendedStateUpdate, outputs: Array<MachineOutput> | NO_OUTPUT}} Actions The actions
 * to be performed by the state machine in response to a transition. `updates` represents the state update for
 * the variables of the extended state machine. `output` represents the output of the state machine passed to the
 * API caller.
 */
/** @typedef {function (ExtendedState, EventData) : Boolean} FSM_Predicate */
/** @typedef {{updateState :: Function(ExtendedState, ExtendedStateUpdate) : ExtendedState, ...}} FSM_Settings */
/** @typedef {{merge: MergeObsFn, from: FromObsFn, filter: FilterObsFn, map: MapObsFn, share:ShareObsFn, ...}} FSM$_Settings */
/**
 * @typedef {function (Array<Observable>) : Observable} MergeObsFn Similar to Rxjs v4's `Rx.Observable.merge`. Takes
 * an array of observables and return an observable which passes on all outputs emitted by the observables in the array.
 */
/**
 * @typedef {function (value) : Observable} FromObsFn Similar to Rxjs v4's `Rx.Observable.from`. Takes
 * a value and lift it into an observable which completes immediately after emitting that value.
 */
/**
 * @typedef {function (value) : Observable} FilterObsFn Similar to Rxjs v4's `Rx.Observable.filter`. Takes
 * a value and lift it into an observable which completes immediately after emitting that value.
 */
/**
 * @typedef {function (value) : Observable} MapObsFn Similar to Rxjs v4's `Rx.Observable.map`. Takes
 * a value and lift it into an observable which completes immediately after emitting that value.
 */
/**
 * @typedef {function (value) : Observable} ShareObsFn Similar to Rxjs v4's `Rx.Observable.share`. Takes
 * a value and lift it into an observable which completes immediately after emitting that value.
 */
/**
 * @typedef {Object.<EventLabel, EventData>} LabelledEvent extended state for a given state machine
 */
/**
 * @typedef {Object} FsmTraceData
 * @property {ControlState} controlState
 * @property {{EventLabel, EventData}} eventLabel
 * @property {ControlState} targetControlState
 * @property {FSM_Predicate} predicate
 * @property {ExtendedStateUpdate} updates
 * @property {ExtendedState} extendedState
 * @property {ActionFactory} actionFactory
 * @property {Number} guardIndex
 * @property {Number} transitionIndex
 */
/**
 * @typedef {function(historyType: HistoryType, controlState: ControlState): HistoryState} HistoryStateFactory
 */
/**
 * @typedef {{type:{}, [HistoryType]: ControlState}} HistoryState
 */
/**
 * @typedef {Object.<HistoryType, HistoryDict>} History history object containing deeep and shallow history states
 * for all relevant control states
 */
/**
 * @typedef {Object.<ControlState, ControlState>} HistoryDict Maps a compound control state to its history state
 */
/**
 * @typedef {DEEP | SHALLOW} HistoryType
 */
/** @typedef {String} ControlState Name of the control state */
/** @typedef {String} EventLabel */
/**
 * @typedef {*} EventData
 */
/**
 * @typedef {*} ExtendedState extended state for a given state machine
 */
/**
 * @typedef {*} ExtendedStateUpdate
 */
/** @typedef {* | NO_OUTPUT} MachineOutput well it is preferrable that that be an object instead of a primitive */

Implementation example

We are going to show the definition for the following state machine :

state machine under test

The definition is as follows :

  const states = { [OUTER]: { [INNER]: { [INNER_S]: '', [INNER_T]: '' }, [OUTER_A]: '', [OUTER_B]: '' }, [Z]: '' };
  const hs = makeHistoryStates(states);
  const fsmDef = {
    states,
    events: [EVENT1, EVENT2, EVENT3, EVENT4, EVENT5],
    initialExtendedState: { history: DEEP, counter: 0 },
    transitions: [
      { from: INIT_STATE, event: INIT_EVENT, to: OUTER, action: ACTION_IDENTITY },
      { from: OUTER, event: INIT_EVENT, to: OUTER_A, action: ACTION_IDENTITY },
      { from: OUTER_A, event: EVENT1, to: INNER, action: ACTION_IDENTITY },
      { from: INNER, event: INIT_EVENT, to: INNER_S, action: ACTION_IDENTITY },
      { from: INNER_S, event: EVENT3, to: INNER_T, action: ACTION_IDENTITY },
      { from: INNER_T, event: EVENT3, to: INNER_S, action: ACTION_IDENTITY },
      { from: INNER, event: EVENT2, to: OUTER_B, action: ACTION_IDENTITY },
      { from: OUTER, event: EVENT5, to: Z, action: ACTION_IDENTITY },
      {
        from: Z, event: EVENT4, guards: [
          {
            predicate: function isDeep(x, e) {return x.history === DEEP},
            to: hs.deep(OUTER),
            action: incCounter
          },
          {
            predicate: function isShallow(x, e) {return x.history !== DEEP},
            to: hs.shallow(OUTER),
            action: incCounter
          }
        ]
      },
    ],
  };

Note in particular :

  • the nesting of states in states
  • the use of ACTION_IDENTITY when there is no action to be applied
    • that action does not modify the extended state of the machine, and returns NO_OUTPUT
  • how history states are included in the machine definition

There are plenty of additional examples in the test directory.

traceFSM :: Env -> FSM_Def -> FSM_Def

Description

This function converts a state machine A into a traced state machine T(A). The traced state machine, on receiving an input I outputs the following information :

  • outputs : the output A.yield(I)
  • updates : the update of the extended state of A to be performed as a consequence of receiving the input I
  • extendedState : the extended state of A prior to receiving the input I
  • controlState : the control state in which the machine is when receiving the input I
  • event::{eventLabel, eventData} : the event label and event data corresponding to I
  • settings : settings passed at construction time to A
  • targetControlState : the target control state the machine has transitioned to as a consequence of receiving the input I
  • predicate : the predicate (guard) corresponding to the transition that was taken to targetControlState, as a consequence of receiving the input I
  • actionFactory : the action factory which was executed as a consequence of receiving the input I
  • guardIndex : the index for the guard in the .guards array of a transition away from a control state, triggered by an event
  • transitionIndex : the index for the transition in the .transitions array which contain the specifications for the machine's transition

Note that the trace functionality is obtained by wrapping over the action factories in A. As such, all action factories will see their output wrapped. This means :

  • transitions which do not lead to the execution of action factories are not traced
  • when the machine cannot find any transition for an event, hence any action to execute, the traced machine will simply return null.

Note also that env is not used for now, and could be used to parameterize the tracing.

Contracts

Types contracts, nothing special.

Implementation example

Cf. tests

generateTestSequences :: FSM_Def -> Generators -> GenSettings -> Array<TestCase>

Description

The generateTestSequences method produce test cases from a state machine definition, and input generators associated to each transition defined in the machine. The test generation strategy is specified in genSettings.strategy (two common strategies are already defined in graph-adt library and can be reused). Additionally the genSettings parameter can contain any relevant parameter to be passed to the machine when it is created.

Input generators (Generators) are coupled to a given state machine for which they generate an input sequence. The structure of Generators hence replicates the structure of the transitions of the state machine under test. Typically we recommend copy pasting transitions from FSM_Def,
and add a gen property for each transition definition. That gen property is a function, which will either generate an input which progresses the state machine to the transition's target state, or declare itself incapable of doing so. That function will receive the extended state for the state machine, and must generate event data for the event defined in the embedding transition, or signal impossibility of such generation. If the input generate does generate event data, then we have a candidate input for inclusion in the test input sequence.

The generation strategy is determined by two predicates : isGoalReached, isTraversableEdge with the same signature. isGoalReached answers the question of whether an input sequence is finalized, and should be wrapped as a test case; or if alternatively the search should continue, possibly increasing the input sequence or possibly failing to generate an input sequence. Commonly, this function will test if a target control state is reached, as we often seek to generate input sequences driving the machine to a given state. isTraversableEdge answers the question of whether a transition (edge of the graph corresponding to the machine) should be taken, adding the generated input to the current input sequence. isTraversableEdge is commonly used to fulfill a coverage criteria, for instance All-transition (No test case can lead to a transition to be taken twice). As a matter of fact, the input generation is an exhaustive enumeration of edge paths in the state machine graph, which isTraversableEdge filters down through its criteria.

Any generated test case fulfills the goal specified by isGoalReached, and fulfills the conditions imposed by isTraversableEdge. The test case gathers information about the input sequence for the test case, the output and control state sequence (the latter for reporting purposes) corresponding to running that input sequence through the state machine.

Semantics

  • the state machine is turned into a graph
    • the machine is flattened : all outgoing transitions from a compound state are replaced by the equivalent set of transitions whose origin state is an atomic substate... well, except for the outgoing INIT transition, which remains identical
      • [A < B < C, A < B < D], and A -ev-> B, is replaced by C -ev-> B, D -ev-> B
    • a transition to a history state will be translated in a transition to any possible history target, with an attached guard which only allows the transition if the history state is indeed the attached control state
  • the graph is searched starting with the initial state with the view to generate all possible paths of the state machine, starting from the initial state
    • if the graph is A -> B, B-> C, B -> D, then the graph search generates [A,B,C] and [A,B,D]
  • At any point, the state of the search is the array of test cases already generated, and the test case in process, starting from an initial state with empty test cases
  • a test case is generated iteratively as follows :
    • the machine starts in the initial state.
    • the test case is initially empty
    • the graph search produces a candidate edge (transition)
    • if the edge is not traversable (isTraversableEdge) then the search branch is abandoned, no input case is generated, the search backtracks and continues with investigating another path sequence
    • otherwise, the input generator generates an input exercising that transition or signals there is no such input
      • if no satisfying input can be generated, the search branch is abandoned, no input case is generated, the search backtracks and continues with investigating another path sequence
        • for instance, for the previous graph, if [A,B,C] fails to generate a case, then [A,B,D] is tried next
      • if an input trigerring the transition is generated, it is added to the test case in progress, together with the corresponding outputs of the machine, and the resulting control state
    • the candidate transition may result in a cascade of transitions, due to special transitions (eventless, automatic transitions (for instance entering a compound state, transition involving history states). The test case is adjusted accordingly.
    • if the goal is reached (isGoalReached) with the updated test case, then that test case is considered finalized and added to the current list of generated test case. the search backtracks and continues with investigating another path sequence
  • in summary, there are two reductions processes and two accumulators involved:
    • the PathTraversalState, which gathers the path sequence and associated data (input sequence, output sequence, control state sequence)
    • the GraphTraversalState, which gathers the generated test cases
  • when the search finished, the array of generated test cases is returned

Contracts

Type contracts apply.

/**
 * @typedef {Array<GenTransitionFromState>} Generators An array of transitions associated to an input generator for
 * the sut
 */
/**
 * @typedef {{from: ControlState, event: Event, guards: Array<GenSpecs>}} GenTransitionFromState Transition for the
 * specified state is contingent to some guards being passed. Those guards are defined as an array. The `from` and
 * `event` properties are not used by the program, we kept them here to assist writing the input generator by having
 * the transition it refers to at hand.
 */
/**
 * @typedef {{predicate: Predicate, gen: InputGenerator, to: ControlState}} GenSpecs Specifies a generator `gen`
 * which will be responsible for computing event data for events which pass the predicate, triggering a transition to
 * `to` control state. The `predicate` and `to` properties are not used by the program, we kept them here to
 * assist writing the input generator by having the transition it refers to at hand.
 */
/**
 * @typedef {function (ExtendedState) : {input: EventData, hasGeneratedInput: Boolean}} InputGenerator generator which
 * knows how to generate event data for an event to trigger the related transition, taking into account the extended
 * state of the machine under test. In the event, it is not possible to generate the targeted transition of the
 * state machine, the generator sets the returned property `hasGeneratedInput` to `false`.
 */
/**
 * @typedef {{inputSequence: InputSequence, outputSequence:OutputSequence, controlStateSequence:ControlStateSequence}} TestCase
 */
/**
 * @typedef {Array<LabelledEvent>} InputSequence
 */
/**
 * @typedef {Array<MachineOutput>} OutputSequence
 */
/**
 * @typedef {Array<ControlState>} ControlStateSequence
 */
/**
 * @typedef {function (Edge, Graph, PathTraversalState, GraphTraversalState) : Boolean} SearchPredicate Computes a
 * boolean in function of the current visited edge, the current search path, and the previously accumulated results.
 * In addition the graph ADT is available for querying graph entities (vertices, edges, etc).
 */
/**
 * @typedef {{ isGoalReached : SearchPredicate, isTraversableEdge : SearchPredicate}} SearchStrategy
 */
/**
 * @typedef {{strategy : SearchStrategy, updateState, ...}} GenSettings Must contain settings for the associated
 * state machine under test (the `...` part), and the search strategy for the associated graph. Most often, it will
 * be enough to reuse premade search strategy : ALL_TRANSITIONS,  ALL_n_TRANSITIONS, etc.
 */

Implementation example

We are going to reuse here a former example :

state machine under test

We remind here the machine definition:

  const states = { [OUTER]: { [INNER]: { [INNER_S]: '', [INNER_T]: '' }, [OUTER_A]: '', [OUTER_B]: '' }, [Z]: '' };
  const hs = makeHistoryStates(states);
  const fsmDef = {
    states,
    events: [EVENT1, EVENT2, EVENT3, EVENT4, EVENT5],
    initialExtendedState: { history: DEEP, counter: 0 },
    transitions: [
      { from: INIT_STATE, event: INIT_EVENT, to: OUTER, action: ACTION_IDENTITY },
      { from: OUTER, event: INIT_EVENT, to: OUTER_A, action: ACTION_IDENTITY },
      { from: OUTER_A, event: EVENT1, to: INNER, action: ACTION_IDENTITY },
      { from: INNER, event: INIT_EVENT, to: INNER_S, action: ACTION_IDENTITY },
      { from: INNER_S, event: EVENT3, to: INNER_T, action: ACTION_IDENTITY },
      { from: INNER_T, event: EVENT3, to: INNER_S, action: ACTION_IDENTITY },
      { from: INNER, event: EVENT2, to: OUTER_B, action: ACTION_IDENTITY },
      { from: OUTER, event: EVENT5, to: Z, action: ACTION_IDENTITY },
      {
        from: Z, event: EVENT4, guards: [
          {
            predicate: function isDeep(x, e) {return x.history === DEEP},
            to: hs.deep(OUTER),
            action: incCounter
          },
          {
            predicate: function isShallow(x, e) {return x.history !== DEEP},
            to: hs.shallow(OUTER),
            action: incCounter
          }
        ]
      },
    ],
  };

We are seeking to generate test cases which end with the machine in the state OUTER_B.

We are configuring our input generators by copy pasting the state machine under test and adding the generators definition for each control state ;

  const genFsmDef = {
    transitions: [
      {
        from: INIT_STATE, event: INIT_EVENT, to: OUTER,
        gen: function genINITtoOUTER(extS) {return { input: extS, hasGeneratedInput: true }}
      },
      { from: OUTER, event: INIT_EVENT, to: OUTER_A },
      {
        from: OUTER_A, event: EVENT1, to: INNER,
        gen: function genOUTER_AtoINNER(extS) {return { input: null, hasGeneratedInput: true }}
      },
      { from: INNER, event: INIT_EVENT, to: INNER_S },
      {
        from: INNER_S, event: EVENT3, to: INNER_T,
        gen: function genINNER_StoINNER_T(extS) {return { input: null, hasGeneratedInput: true }}
      },
      {
        from: INNER_T, event: EVENT3, to: INNER_S,
        gen: function genINNER_TtoINNER_S(extS) {return { input: null, hasGeneratedInput: true }}
      },
      {
        from: INNER, event: EVENT2, to: OUTER_B,
        gen: function genINNERtoOUTER_B(extS) {return { input: null, hasGeneratedInput: true }}
      },
      {
        from: OUTER, event: EVENT5, to: Z,
        gen: function genOUTERtoZ(extS) {return { input: null, hasGeneratedInput: true }}
      },
      {
        from: Z, event: EVENT4, guards: [
          {
            predicate: function isDeep(x, e) {return x.history === DEEP},
            to: hs.deep(OUTER),
            gen: function genZtoOUTER_DEEP_H(extS) {return { input: DEEP, hasGeneratedInput: extS.history === DEEP }},
          },
          {
            predicate: function isShallow(x, e) {return x.history !== DEEP},
            to: hs.shallow(OUTER),
            gen: function genZtoOUTER_SHALLOW_H(extS) {
              return {
                input: SHALLOW,
                hasGeneratedInput: extS.history !== DEEP
              }
            },
          }
        ]
      },
    ],
  };

Note that :

  • some events carry no event data (EVENT_1 for instance). The generator hence sets null as generated event data.
  • some events have no guards. The corresponding generators hence always have hasGeneratedInput = true, as those events are always triggering a transition when they occur
  • some events have guards. The corresponding generator will set hasGeneratedInput to false when the guard cannot be satisfied. A guard is a function of the extended state extS and the event data. The generator is passed the event data. According to the guard at end, the generator must resolve the equation find extS so that for all eventData, guard(extS, eventData) = false. For those extS, the hasGeneratedInput will be set to false : no matter the event, the guard can never be satisfied. For the rest of the cases, the generator will pick an EventData which satisfies the guard, if any.

We then define our extended state update method, our search strategy (All-transitions coverage) :

  const generators = genFsmDef.transitions;
  const settings = { updateState: applyJSONpatch, strategy: ALL_TRANSITIONS({ targetVertex: 
  OUTER_B }) };
  const results = generateTestSequences(fsmDef, generators, settings);

We then get the results back :

Test case inputs

[
    [
      { "init": { "counter": 0, "history": "deep" } },
      { "event1": null }, { "event3": null }, { "event3": null }, { "event2": null }
    ],
    [
      { "init": { "counter": 0, "history": "deep" } },
      { "event1": null }, { "event3": null }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }
    ],
    [
      { "init": { "counter": 0, "history": "deep" } },
      { "event1": null }, { "event3": null }, { "event2": null }
    ],
    [
      { "init": { "counter": 0, "history": "deep" } },
      { "event1": null }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event2": null }
    ],
    [
      { "init": { "counter": 0, "history": "deep" } },
      { "event1": null }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }
    ],
    [
      { "init": { "counter": 0, "history": "deep" } },
      { "event1": null }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event1": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event3": null }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event3": null }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event3": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }],
    [{
      "init": { "counter": 0, "history": "deep" }
    }, { "event5": null }, { "event4": "deep" }, { "event1": null }, { "event5": null }, { "event4": "deep" }, { "event2": null }]
]

Test case outputs

[
    [null, null, null, null, null],
    [null, null, null, null, null, 0, null],
    [null, null, null, null],
    [null, null, null, null, 0, null, null],
    [null, null, null, null, 0, null, null, 1, null],
    [null, null, null, null, 0, null],
    [null, null, null],
    [null, null, null, 0, null, null, null],
    [null, null, null, 0, null, null],
    [null, null, null, 0, null, null, 1, null, null],
    [null, null, null, 0, null, null, 1, null],
    [null, null, null, 0, null],
    [null, null, 0, null, null, null, null],
    [null, null, 0, null, null, null, null, 1, null],
    [null, null, 0, null, null, null],
    [null, null, 0, null, null, null, 1, null, null],
    [null, null, 0, null, null, null, 1, null, null, 2, null],
    [null, null, 0, null, null, null, 1, null],
    [null, null, 0, null, null],
    [null, null, 0, null, null, 1, null, null, null],
    [null, null, 0, null, null, 1, null, null],
    [null, null, 0, null, null, 1, null, null, 2, null, null],
    [null, null, 0, null, null, 1, null, null, 2, null],
    [null, null, 0, null, null, 1, null]
  ]

Note that :

  • to every input passed to the machine, there is an array of data produced as output. That array is concatenated to constitute the output sequence.
  • Here because that array of data only has one item, we can easily relate input from a given input sequence to the matching output of the corresponding output sequence : they have the same index! That would however not be the case in general.

The corresponding sequence of control states is as follows :

[
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "inner_t", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "inner_t", "inner_s", "z", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "inner_t", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "inner_t", "z", "inner_t", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "inner_t", "z", "inner_t", "inner_s", "z", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "inner_t", "z", "inner_t", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "z", "inner_s", "inner_t", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "z", "inner_s", "inner_t", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "z", "inner_s", "inner_t", "z", "inner_t", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "z", "inner_s", "inner_t", "z", "inner_t", "outer_b"],
    ["nok", "OUTER", "outer_a", "INNER", "inner_s", "z", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "inner_t", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "inner_t", "inner_s", "z", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "inner_t", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "inner_t", "z", "inner_t", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "inner_t", "z", "inner_t", "inner_s", "z", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "inner_t", "z", "inner_t", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "z", "inner_s", "inner_t", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "z", "inner_s", "inner_t", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "z", "inner_s", "inner_t", "z", "inner_t", "inner_s", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "z", "inner_s", "inner_t", "z", "inner_t", "outer_b"],
    ["nok", "OUTER", "outer_a", "z", "outer_a", "INNER", "inner_s", "z", "inner_s", "outer_b"]
]

Note that:

  • we have exercised all possible transitions in our state machine.
  • The somewhat tricky part here is to understand that, for instance, the transition INNER -EVENT2-> OUTER.B in fact is a factorisation of 2 transitions : INNER.S -EVENT2-> OUTER.B, INNER.T-EVENT2-> OUTER.B!
  • An even trickier part is to realize that transitions to history states are factorizations for transitions to any of the relevant substates of the nesting compound state. Hence z -EVENT4-> H is factorization for z -EVENT4-> OUTER.A, z -EVENT4-> OUTER.B, z -EVENT4-> INNER, and z -EVENT4-> H* is factorization for z -EVENT4-> OUTER.A, z -EVENT4-> OUTER.B, z -EVENT4-> INNER.S , z -EVENT4-> INNER.T!
  • we had 5 non-trivial control states, 8 non-trivial transitions, and we ended up with 24 input sequences to test all paths on which no transitions is repeated (loop-free paths)!

There are ample tests which can serve as example in the test directory.

Possible API extensions

Because of the API design choices, it is possible to realize the possible extensions without modifying the state chart library (open/closed principle):

  • entry and exit actions
  • logging/tracing/monitoring
    • achieved through decorating both guards and action factories
  • contract checking (preconditions, postconditions and probably invariants - to be investigated) for both states and transitions
    • can be done by inserting in first position extra guards which either fail or throw, and decorating exising guards
  • starting with a specific control state and extended state
    • can be achieved by modifying the INIT transition (by contract there is exactly one such transition) and the initial_extended_state; and leaving everything else intact

Note that these extensions more often than not would perform effects (logs, ...), meaning that the order of application becomes significant in general. The practical consequences of this are to be investigated further at a later point.

Equipped with a history of inputs and the corresponding history of outputs, it is also possible to do property-based testing (for instance checking that a pattern in a sequence of outputs occurs only when a pattern occurs in the matching sequence of inputs).

These extensions are useful to check/test the design of the automata, i.e. checking that the automata which acts as modelization of requirements indeed satisfies the requirements. When sufficient confidence is acquired, those extensions can be safely removed.

Tests

Automated tests are close to completion. Contracts are so far not enforced. To run the current automated tests, type in a terminal : npm run test

Visualization tools

We have included two helpers for visualization of the state transducer :

  • conversion to plantUML : toPlantUml :: FSM_Def -> PlantUml.
    • the resulting chain of characters can be pasted in plantText or plantUML previewer to get an automated graph representation. Both will produce the exact same visual representation.
  • conversion to online visualizer format (dagre layout engine) : for instructions, cf. github directory : toDagreVisualizerFormat :: FSM_Def -> JSON

visualization example

Automated visualization works well with simple graphs, but seems to encounter trouble to generate optimally satisfying complex graphs. The Dagre layout seems to be a relatively good option. The yed orthogonal layout also seems to give pretty good results.

References

Roadmap v0.9

Roadmap v0.10

  • support for live, interactive debugging
  • document entry actions
  • turn the test generation into an iterator(ES5 generator) : this allows it to be composed with transducers and manipulate the test cases one by one as soon as they are produced. Will be useful for both example-based and property-based testing. When the generators runs through thousands of test cases, we often have to wait a long time before seeing any result, which is pretty damageable when a failure is located toward the ends of the generated input sequences.
    • by doing so we have integration with transducer and IxJS for free
  • add other searches that DFS, BFS (add probability to transitions, exclude some transitions, etc.). HINT : store.pickOne can be used to select the next transition
    • pick a random transition
    • pick next transition according to ranking (probability-based, prefix-based or else)
  • showcase property-baesd testing with the iterator (no need to have jsverify, just predicates)
  • !write proper state machine tracer
  • !show example of integration with react (same demo example?)
  • write a minimal all-transitions coverage test case generator
  • add exit actions
  • document exit actions
  • include initial history state as a part of initial extended state (this allows to recreate a state machine from its full state : control state, extended state, history state), which opens the way to serialization/de-serialization )

Footnotes

  1. In fact, computability theory links the feasability of a computation to the existence of a machine whose run produces the desired results. Some formalizations of the matching computing machine however can be useless in practice, which is why we use the term advantageously to indicate those computations where a formalization of the computing machine brings desired benefits. ↩

  2. Our rationale is as follows : ↩

  3. David Harel, Statecharts.History.CACM : Speaking in the strict mathematical sense of power of expression, hierarchy and orthogonality are but helpful abbreviations and can be eliminated ↩

  4. David Harel, Statecharts.History.CACM : <<I definitely do not recommend having a single statechart for an entire system. (...) concurrency occurs on a higher level.)>> ↩

  5. There are however semantics which allow such transitions, thus possibilitating event bubbling. ↩