This section presents a normative algorithm for the
interpretation of an SCXML document. Implementations are free to
implement SCXML interpreters in any way they choose, but they must
behave as if they were using the algorithm defined
here.
The fact that SCXML implements a variant of the Statechart
formalism does not as such determine a semantics for SCXML. Many
different Statechart variants have been proposed, each with its own
semantics. This section presents an informal semantics of SCXML
documents, as well as a normative algorithm for the interpretation
of SCXML documents.
Informal Semantics
The following definitions and highlevel principles and
constraint are intended to provide a background to the normative
algorithm, and to serve as a guide for the proper understanding of
it.
Preliminary definitions
- state
- An element of type <state>, <parallel>,
<final> or <scxml>.
- pseudo state
- An element of type <initial> or <history>.
- transition target
- A state, or an element of type <history>.
- atomic state
- A state of type <state> with no child states, or a state
of type <final>.
- compound state
- A state of type <state> with at least one child
state.
- start state
- A dummy state equipped with a transition which when triggered
by the Run event leads to the initial state(s). Added by the
interpreter with an id guaranteed to be unique within the
statemachine. The only role of the start state is to
simplify the algorithm.
- configuration
- The maximal consistent set of states (including parallel and
final states) that the machine is currently in. We note that if a
state s is in the configuration c, it is always the case that the
parent of s (if any) is also in c. Note, however, that
<scxml> is not a(n explicit) member of the
configuration.
- source state
- The source state of a transition is the atomic state from which
the transition departs.
- target state
- A target state of a transition is a state that the transition
is entering. Note that a transition can have zero or more target
states.
- targetless transition
- A transition having zero target states.
- eventless transition
- A transition lacking the 'event' attribute.
- external event
- An SCXML event appearing in the external event queue. Such
events are either sent by external sources or generated with the
<send> element.
- internal event
- An event appearing in the internal event queue. Such events are
either raised automatically by the platform or generated with the
<event> element.
- microstep
- A microstep involves the processing of a single transition (or,
in the case of parallel states, a single set of transitions.) A
microstep may change the the current configuration, update the
datamodel and/or generate new (internal and/or external) events.
This, by causality, may in turn enable additional transitions which
will be handled in the next microstep in the sequence, and so
on.
- macrostep
- A macrostep consists of a sequence (a chain) of microsteps, at
the end of which the state machine is in a stable state and ready
to process an external event. Each external event causes an SCXML
state machine to take exactly one macrostep. However, if the
external event does not enable any transitions, no microstep will
be taken, and the corresponding macrostep will be empty.
Principles and
Constraints
We state here some principles and constraints, on the level of
semantics, that SCXML adheres to:
- Encapsulation
- An SCXML processor is a pure event processor. The only
way to get data into an SCXML statemachine is to send external
events to it. The only way to get data out is to receive events
from it.
- Causality
- There shall be a causal justification of why events
are (or are not) returned back to the environment, which can be
traced back to the events provided by the system environment.
- Determinism
- An SCXML statemachine which does not invoke any external event
processor must always react with the same behavior (i.e. the same
sequence of output events) to a given sequence of input events
(unless, of course, the statemachine is explicitly programmed to
exhibit an non-deterministic behavior). In particular, the
availability of the <parallel> element must not introduce any
non-determinism of the kind often associated with concurrency. Note
that observable determinism does not necessarily hold for state
machines that invoke other event processors.
- Completeness
- An SCXML interpreter must always treat an SCXML document as
completely specifying the behavior of a statemachine. In
particular, SCXML is designed to use priorities (based on document
order) to resolve situations which other statemachine frameworks
would allow to remain under-specified (and thus non-deterministic,
although in a different sense from the above).
- Run to completion
- SCXML adheres to a run to completion semantics in the sense
that an external event can only be processed when the processing of
the previous external event has completed, i.e. when all microsteps
(involving all triggered transitions) have been completely
taken.
- Termination
- A microstep always terminates. A macrostep may not. A macrostep
that does not terminate may be said to consist of an infinitely
long sequence of microsteps. This is currently allowed.
Algorithm
This section presents a normative algorithm for the
interpretation of SCXML documents. Implementations are free to
implement SCXML interpreters in any way they choose, but they must
behave as if they were using the algorithm defined here.
Note that the algorithm assumes a Lisp-like semantics in which the
empty Set null is equivalent to boolean 'false' and all other
entities are equivalent to 'true'.
Datatypes
These are the abstract datatypes that are used in the
algorithm.
datatype List
function head() // Returns the head of the list
function tail() // Returns the tail of the list
function append(l) // Returns the list appended with l
function filter(f) // Returns the list of elements that satisfy the predicate f
function some(f) // Returns true if some element in the list satisfies the predicate f
function every(f) // Returns true if every element in the list satisfies the predicate f
datatype OrderedSet
procedure add(e) // Adds e to the set
procedure delete(e) // Deletes e from the set
function member(e) // Is e a member of set?
function isEmpty() // Is the set empty?
function toList() // Converts the set to a list that reflects the order in which elements were added.
function diff(set2) // Returns an OrderedSet containing all members of OrderedSet that are not in set2.
datatype Queue
procedure enqueue(e) // Puts e last in the queue
function dequeue() // Removes and returns first element in queue
function isEmpty() // Is the queue empty?
datatype BlockingQueue
procedure enqueue(e) // Puts e last in the queue
function dequeue() // Removes and returns first element in queue, blocks if queue is empty
Global
variables
The following variables are global from the point of view of the
algorithm. Their values will be set in the
procedureinterpret().
global datamodel;
global configuration;
global previousConfiguration
global statesToInvoke
global datamodel
global internalQueue;
global externalQueue;
global historyValue;
global continue
Predicates
The following binary predicates are used for determining the
order in which states are entered and exited.
entryOrder // Ancestors precede descendants, with document order being used to break ties
exitOrder // Descendants precede ancestors, with reverse document order being used to break ties
Procedures and Functions
This section defines the procedures and functions that make up
the core of the SCXML interpreter.
procedure
interpret(scxml,id)
The purpose of this procedure is to initialize the interpreter
and to start processing. It is called with a parsed representation
of an SCXML document.
In order to interpret an SCXML document, first convert initial
attributes to <initial> container children with transitions
to the state specified by the attribute (such transitions will not
contain any executable content). Then (optionally) validate the
resulting SCXML, and throw an exception if validation fails. Create
an empty configuration complete with a new populated instance of
the data model and a execute the global scripts. Create the two
queues to handle events and set the global continue variable to
true. Finally call enterState on the initial transition that is a
child of scxml and start the interpreter's event loop.
procedure interpret(doc):
expandScxmlSource(doc)
if not valid(doc): failWithError()
configuration = new OrderedSet()
previousConfiguration = new OrderedSet()
statesToInvoke = new OrderedSet()
datamodel = new Datamodel(doc)
executeGlobalScriptElements(doc)
internalQueue = new Queue()
externalQueue = new BlockingQueue()
continue = true
enterState([doc.initial.transition])
startEventLoop()
procedure
startEventLoop()
Upon entering the state machine, we take all internally enabled
transitions, namely those that either don't require an event or
that are triggered by internal events. (Internal events can only be
generated by the state machine itself.) When all such transitions
have been taken, we move to the main event loop, which is driven by
external events.
procedure procedure startEventLoop():
initialStepComplete = false ;
until initialStepComplete:
enabledTransitions = selectEventlessTransitions()
if enabledTransitions.isEmpty():
if internalQueue.isEmpty():
initialStepComplete = true
else:
internalEvent = internalQueue.dequeue()
datamodel["event"] = internalEvent
enabledTransitions = selectTransitions(internalEvent)
if not enabledTransitions.isEmpty():
microstep(enabledTransitions.toList())
mainEventLoop()
procedure
mainEventLoop()
This loop runs until we enter a top-level final state or an
external entity cancels processing. In either case 'continue' will
be set to false (see EnterStates, below, for termination by
entering a top-level final state.)
Each iteration through the loop consists of three main steps: 1)
execute any <invoke> tags for states that we entered on the
last iteration through the loop 2) Wait for an external event and
then execute any transitions that it triggers. However special
preliminary processing is applied to the event if the state has
executed any <invoke> elements. First, if this event was
generated by an invoked process, apply <finalize> processing
to it. Secondly, if any <invoke> elements have autoforwarding
set, forward the event to them. These steps apply before the
transitions are taken. 3) Take any subsequent internally enabled
transitions, namely those that don't require an event or that are
triggered by an internal event.
This event loop thus enforces run-to-completion semantics, in
which the system process an external event and then takes all the
'follow-up' transitions that the processing has enabled before
looking for another external event. For example, suppose that the
external event queue contains events ext1 and ext2 and the
machine is in state s1. If processing ext1 takes the machine to s2
and generates internal event int1, and s2 contains a
transition t triggered by int1, the system is guaranteed to take t,
no matter what transitions s2 or other states have that would be
triggered by ext2. Note that this is true even though ext2 was
already in the external event queue when int1 was generated. In
effect, the algorithm treats the processing of int1 as finishing up
the processing of ext1.
procedure procedure mainEventLoop():
while continue:
for state in statesToInvoke:
for inv in state.invoke:
invoke(inv)
statesToInvoke.clear()
previousConfiguration = configuration
externalEvent = externalQueue.dequeue() # this call blocks until an event is available
datamodel["event"] = externalEvent
for state in configuration:
for inv in state.invoke:
if inv.invokeid == externalEvent.invokeid: # event is the result of an <invoke> in this state
applyFinalize(inv, externalEvent)
if inv.autoforward:
send(inv.id, externalEvent)
enabledTransitions = selectTransitions(externalEvent)
if not enabledTransitions.isEmpty():
microstep(enabledTransitions.toList())
# now take any newly enabled null transitions and any transitions triggered by internal events
macroStepComplete = false
until macroStepComplete:
enabledTransitions = selectEventlessTransitions()
if enabledTransitions.isEmpty():
if internalQueue.isEmpty():
macroStepComplete = true
else:
internalEvent = internalQueue.dequeue()
datamodel["event"] = internalEvent
enabledTransitions = selectTransitions(internalEvent)
if not enabledTransitions.isEmpty():
microstep(enabledTransitions.toList())
# if we get here, we have reached a top-level final state or some external entity has set continue to false
exitInterpreter()
procedure
exitInterpreter()
The purpose of this procedure is to exit the current SCXML
process by exiting all active states. If the machine is in a
top-level final state, a Done event is generated. (Note that in
this case, the final state will be the only active state.) The
implementation of returnDoneEvent is platform-dependent, but if
this session is the result of an <invoke> in another SCXML
session, returnDoneEvent will cause the event
done.invoke.<id> to be placed in the external event queue of
that session, where <id> is the id generated in that session
when the <invoke> was executed.
procedure exitInterpreter():
statesToExit = configuration.toList().sort(exitOrder)
for s in statesToExit:
for content in s.onexit:
executeContent(content)
for inv in s.invoke:
cancelInvoke(inv)
configuration.delete(s)
if isFinalState(s) and isScxmlState(s.parent):
returnDoneEvent(s.donedata)
function
selectEventlessTransitions()
This function selects all transitions that are enabled in the
current configuration that do not require an event trigger. First
test if the state has been preempted by a transition that has
already been selected and that will cause the state to be exited
when it is taken. If the state has not been preempted, find a
transition with no 'event' attribute whose condition evaluates to
true. If multiple matching transitions are present,
take the first in document order. If none are present, search in
the state's ancestors in ancestry order until one is found. As soon
as such a transition is found, add it to enabledTransitions, and
proceed to the next atomic state in the configuration. If no such
transition is found in the state or its ancestors, proceed to the
next state in the configuration. When all atomic states have been
visited and transitions selected, return the set of enabled
transitions.
function selectEventlessTransitions():
enabledTransitions = new OrderedSet()
atomicStates = configuration.toList().filter(isAtomicState).sort(documentOrder)
for state in atomicStates:
if not isPreempted(state, enabledTransitions):
loop: for s in [state].append(getProperAncestors(state, null)):
for t in s.transition:
if not t.event and conditionMatch(t):
enabledTransitions.add(t)
break loop
return enabledTransitions
function
selectTransitions(event)
The purpose of the selectTransitions()procedure is to collect
the transitions that are enabled by this event in the current
configuration.
Create an empty set of enabledTransitions. For each
atomic state test if the state has been preempted by a transition
that has already been selected and that will cause the state to be
exited when it is taken. If the state has not been preempted, find
a transition whose 'event' attribute matches event and
whose condition evaluates to true. If multiple
matching transitions are present, take the first in document order.
If none are present, search in the state's ancestors in ancestry
order until one is found. As soon as such a transition is found,
add it to enabledTransitions, and proceed to the next atomic state
in the configuration. If no such transition is found in the state
or its ancestors, proceed to the next state in the configuration.
When all atomic states have been visited and transitions selected,
return the set of enabled transitions.
function selectTransitions(event):
enabledTransitions = new OrderedSet()
atomicStates = configuration.toList().filter(isAtomicState).sort(documentOrder)
for state in atomicStates:
if not isPreempted(state, enabledTransitions):
loop: for s in [state].append(getProperAncestors(state, null)):
for t in s.transition:
if t.event and nameMatch(t.event, event.name) and conditionMatch(t):
enabledTransitions.add(t)
break loop
return enabledTransitions
function
isPreempted(s transitionList)
Return true if a transition T in transitionList exits an
ancestor of state s. In this case, taking T will pull the state
machine out of s and thus we say that it preempts the selection of
a transition from s. Such preemption will occur only if s is a
descendant of a parallel region and T exits that region. If we did
not do this preemption check, we could end up in an illegal
configuration, namely one in which there were multiple active
states that were not all descendants of a common parallel
ancestor.
function isPreempted(s transitionList):
preempted = false
for t in transitionList:
if t.target:
LCA = findLCA([t.source].append(getTargetStates(t.target)))
if isDescendant(s,LCA):
preempted = true
break
return preempted
procedure
microstep(enabledTransitions)
The purpose of the microstep procedure is to
process a single set of transitions. These may have been enabled by
an external event, an internal event, or by the presence or absence
of certain values in the datamodel at the current point in time.
The processing of the enabled transitions must be done in parallel
('lock step') in the sense that their source states must first be
exited, then their actions must be executed, and finally their
target states entered.
If a single atomic state is active, then enabledTransitions will
contain only a single transition. If multiple states are active
(i.e., we are in a parallel region), then there may be multiple
transitions, one per active atomic state (though some states may
not select a transition.) In this case, the transitions are taken
in the document order of the atomic states that selected them.
procedure microstep(enabledTransitions):
exitStates(enabledTransitions)
executeTransitionContent(enabledTransitions)
enterStates(enabledTransitions)
procedure
exitStates(enabledTransitions)
Create an empty statesToExit set. For each transition t in
enabledTransitions, if t is targetless then do nothing, else let
LCA be the least common ancestor state of the source state and
target states of t. Add to the statesToExit set all states in the
configuration that are descendants of LCA. Next remove all the
states on statesToExit from the set of states that will have invoke
processing done at the start of the next macrostep. (Suppose
macrostep M1 consists of microsteps m11 and m12. We may enter state
s in m11 and exit it in m12. We will add s to statesToInvoke in
m11, and must remove it in m12. In the subsequent macrostep M2, we
will apply invoke processing to all states that were enter, and not
exited, in M1.) Then convert statesToExit to a list and sort it in
exitOrder.
For each state s in the list, if s has a deep history state h,
set the history value of h to be the list of all atomic descendants
of s that are members in the current configuration, else set its
value to be the list of all immediate children of s that are
members of the current configuration. Again for each state s in the
list, first execute any onexit handlers, then cancel any ongoing
invocations, and finally remove s from the current
configuration.
[NOTE: this function must be updated to handle transitions with
'type'="internal". It currently treats all transitions as if they
were external.]
procedure exitStates(enabledTransitions):
statesToExit = new OrderedSet()
for t in enabledTransitions:
if t.target:
LCA = findLCA([t.source].append(getTargetStates(t.target)))
for s in configuration:
if isDescendant(s,LCA):
statesToExit.add(s)
for s in statesToExit:
statesToInvoke.delete(s)
statesToExit = statesToExit.toList().sort(exitOrder)
for s in statesToExit:
for h in s.history:
if h.type == "deep":
f = lambda s0: isAtomicState(s0) and isDescendant(s0,s)
else:
f = lambda s0: s0.parent == s
historyValue[h.id] = configuration.toList().filter(f)
for s in statesToExit:
for content in s.onexit:
executeContent(content)
for inv in s.invoke:
cancelInvoke(inv)
configuration.delete(s)
procedureexecuteTransitionContent(enabledTransitions)
For each transition in the list of
enabledTransitions, execute its executable
content.
procedure executeTransitionContent(enabledTransitions):
for t in enabledTransitions:
executeContent(t)
procedure
enterStates(enabledTransitions)
Create an empty statesToEnter set, and an empty
statesForDefaultEntry set. For each transition t in
enabledTransitions, if t is targetless then do nothing, else let
LCA be the least common ancestor state of the source state and
target states of t. For each target state s, call statesToEnte.
This will add to statesToEnter s plus all states that will have to
be entered in order to enter s. (This may include s's ancestors or
parallel siblings.) If LCA is a parallel state, call statesToEnter
on each of its children.)
We now have a complete list of all the states that will be
entered as a result of taking the transitions in
enabledTransitions. Add them to statesToInvoke so that invoke
processing can be done at the start of the next macrostep. Convert
statesToEnter to a list and sort it in enterorder. For each state s
in the list, first add s to the current configuration, then execute
any onentry handlers. If s's initial state is being entered by
default, execute any executable content in the initial transition.
Finally, if s is a final state, generate relevant Done events. If
we have reached a top-level final state, set continue to false as a
signal to stop processing.
procedure enterStates(enabledTransitions):
statesToEnter = new OrderedSet()
statesForDefaultEntry = new OrderedSet()
for t in enabledTransitions:
if t.target:
LCA = findLCA([t.source].append(getTargetStates(t.target)))
for s in getTargetStates(t.target):
addStatesToEnter(s,LCA,statesToEnter,statesForDefaultEntry)
if isParallelState(LCA):
for child in getChildStates(LCA):
addStatesToEnter(child,LCA,statesToEnter,statesForDefaultEntry)
for s in statesToEnter:
statesToInvoke.add(s)
statesToEnter = statesToEnter.toList().sort(enterOrder)
for s in statesToEnter:
configuration.add(s)
for content in s.onentry:
executeContent(content)
if statesForDefaultEntry.member(s):
executeContent(s.initial.transition)
if isFinalState(s):
parent = s.parent
grandparent = parent.parent
internalQueue.enqueue(new Event("done.state." + parent.id, parent.donedata))
if isParallelState(grandparent):
if getChildStates(grandparent).every(isInFinalState):
internalQueue.enqueue(new Event("done.state." + grandparent.id, grandparent.donedata))
for s in configuration:
if isFinalState(s) and isScxmlState(s.parent):
continue = false
procedureaddStatesToEnter(s,root,statesToEnter,statesForDefaultEntry)
The purpose of this procedure is to add to statesToEnter all
states that must be entered as a result of entering state s. Note
that this procedure permanently modifies both statesToEnter and
statesForDefaultEntry.
First, If s is a history state then add either the history
values associated with sor s's default target to statesToEnter.
Else (if s is not a history state), add >s to statesToEnter.
Then, if s is a parallel state, add each of s's children to
statesToEnter. Else, if s is a compound state, add s to
statesForDefaultEntry and add its default initial state to
statesToEnter. Finally, for each ancestor anc of s, add anc to
statesToEnter and if anc is a parallel state, add any child of anc
that does not have a descendant on statesToEnter to
statesToEnter.
procedure addStatesToEnter(s,root,statesToEnter,statesForDefaultEntry):
if isHistoryState(s):
if historyValue[s.id]:
for s0 in historyValue[s.id]:
addStatesToEnter(s0,s,statesToEnter,statesForDefaultEntry)
else:
for t in s.transition:
for s0 in getTargetStates(t.target):
addStatesToEnter(s0,s,statesToEnter,statesForDefaultEntry)
else:
statesToEnter.add(s)
if isParallelState(s):
for child in getChildStates(s):
addStatesToEnter(child,s,statesToEnter,statesForDefaultEntry)
elif isCompoundState(s):
statesForDefaultEntry.add(s)
for tState in getTargetStates(s.initial):
addStatesToEnter(tState, s, statesToEnter, statesForDefaultEntry)
for anc in getProperAncestors(s,root):
statesToEnter.add(anc)
if isParallelState(anc):
for pChild in getChildStates(anc):
if not statesToEnter.toList().some(lambda s2: isDescendant(s2,pChild)):
addStatesToEnter(pChild,anc,statesToEnter,statesForDefaultEntry)
procedure
isInFinalState(s)
Return true if s is a compound <state> and one of its
children is an active <final> state (i.e. is a member of the
current configuration), or if s is a <parallel> state and
isInFinalState is true of all its children.
function isInFinalState(s):
if isCompoundState(s):
return getChildStates(s).some(lambda s: isFinalState(s) and configuration.member(s))
elif isParallelState(s):
return getChildStates(s).every(isInFinalState)
else:
return false
function
findLCA(stateList)
The Least Common Ancestor is the
element s such that s is a proper ancestor of all states on
stateList and no descendant of s has this property. Note that there
is guaranteed to be such an element since the <scxml> wrapper
element is a common ancestor of all states. Note also that since we
are speaking of proper ancestor (parent or parent of a parent,
etc.) the LCA is never a member of stateList.
function findLCA(stateList):
for anc in getProperAncestors(stateList.head(), null):
if stateList.tail().every(lambda s: isDescendant(s,anc)):
return anc
