Clear semantics make it easier to verify and validate automated plans and to implement a lightweight executive that conforms to the semantics of execution. This chapter elaborates the Plexil Reference by describing detailed semantics for various aspects of PLEXIL and its execution. The formal semantics presented here are based entirely on Core PLEXIL.
Recall that Core PLEXIL is a subset of PLEXIL into which all other constructs are translated for execution. Core PLEXIL consists essentially of 5 different types of nodes, which are structures containing a variety of data, a set of possible execution states and outcomes, and rules specifying the exact execution of these nodes and transitions between their states. A formal semantic framework of Core PLEXIL, together with operational, small-step semantics for its execution, is presented in detail in References 1. Much of the information given here is a distillation of these papers.
The execution of a PLEXIL plan is described formally using five relations that constitute a small-step semantics for the language.
- The atomic relation describes the state transition of an individual node.
- The micro relation is the synchronous execution of the atomic relation (i.e. transitions for all active nodes in a plan).
- The quiescence relation is the "run until completion" of the micro relation.
- The macro relation describes how PLEXIL reacts to events in the external world.
- The execution relation is the N-step iteration of the macro relation.
A PLEXIL plan executes in discrete steps within each of these relations. The following sections describe some of these steps in more detail. See References 1 for a thorough description.
The execution semantics of an individual PLEXIL node is specified in terms of node states and transitions between node states that are triggered by condition changes.
Each node must be in one and only one of the following states at any given time.
The set of condition changes that trigger node state transitions are as follows.
The first set are user-specified conditions:
- SkipCondition T : The skip condition changes from unknown or false to true.
- StartCondition T : The start condition changes from unknown or false to true.
- InvariantCondition F : Invariant condition changes from true or unknown to false.
- ExitCondition T : Exit condition changes to true
- EndCondition T : End condition changes to true
- RepeatCondition T/F : the repeat condition changes from unknown to either true or false.
The conditions below are internally generated and not directly accessible to users:
- Ancestor_invariant_condition F : The invariant condition of any ancestor changes to false.
- Ancestor_exit_condition T : The exit condition of any ancestor changes to true
- Ancestor_end_condition T : The end condition of any ancestor changes to true
- All_children_waiting_or_finished T : This is true when all child nodes are in either in node state waiting or finished and no other states.
- Command_abort_complete T : When the abort for a command action is completed.
- Parent_waiting T : The parent of the node transitions to node state waiting.
- Parent_finished T : The parent of the node transitions to node state finished.
- Parent_executing T : The parent of the node transitions to node state executing.
The Node State Transition Diagrams document all the PLEXIL node transitions.
At the beginning of plan execution, all the nodes in a plan are initialized to state Inactive. An Inactive node does not affect the external system at all.
From Inactive, root nodes transition directly to state Waiting. Interior and leaf nodes transition to state Waiting when their parent enters state Executing. A node remains in state Waiting until either its skip condition or start condition is met.
If the start condition becomes True, and the precondition is not False, the node enters state Executing. The default start condition is True, which implies that the node may execute immediately upon activation. In state Executing, a node or its children perform the specified actions.
Upon completion of the action (e.g. command sent or assignment finished), leaf nodes transition to state Iteration_Ended, from which they can transition either to state Waiting if the repeat condition is True, or to state Finished.
List and library call nodes proceed similarly from state Executing to state Iteration_Ended when their end conditions are satisfied. The default end condition for these nodes is all children being in state Finished. From Iteration_Ended list and library call nodes transition to state Finishing. Only when all children of a node are in either state Waiting or state Finished can the parent node transition to Finished.
If an ancestor node repeats, the node may transition from Finished to Inactive. Otherwise the node remains in Finished and cannot be reactivated.
Execution in the Presence of Failures
Execution failure can be invoked in several ways:
- If a precondition is False when the start condition is True, the node bypasses the Executing state.
- If an invariant condition becomes False while the node is in state Executing, execution is aborted.
- If a postcondition is False when the end condition is True, the node has already completed execution.
In each of these cases, the node's outcome is set to Failed.
The exit condition behaves similarly to the invariant condition, but with a reversed logical sense and a distinct outcome value. If an exit condition becomes True while the node is in state Executing, execution is aborted with an outcome of Interrupted.
When a failure or interruption occurs, the next state transition and execution action depends on the node type. Empty nodes transition directly to either state Iteration_Ended or state Finished (see below for the distinction).
All other node types go through the Failing state on the way to Iteration_Ended or Finished:
- Assignment nodes retract the assignment and enter state Failing, then transition immediately to Iteration_Ended or Finished.
- Command nodes abort the command and enter state Failing, to wait for acknowledgement of the abort. Upon receipt they then transition to Iteration_Ended or Finished.
- Update nodes enter state Failing and wait for acknowledgement of the update, at which point they transition to Iteration_Ended or Finished.
- List and library call nodes cause the sub-tree below them to abort in a deterministic manner. Only in the case of a failure or interruption does a parent node abort a child node.
All nodes transition to state Iteration_Ended if the failure or interruption was local, or to state Finished if the parent failed or was interrupted. The cause of a node's failure can be determined from the Failure Type field of the node.
Node Termination and Outcome
There are three main causes for node termination: completion of execution, external events, and faults. The default completion of a node depends on the type of node. Assignment and Command nodes end when the assignment is complete or a command handle is returned, respectively. A List node ends when all its child nodes have finished. External events or cascading effects of external events may satisfy the explicit end condition of a node. When the end condition of a list node is satisfied and some of its child nodes are still executing, the children will terminate cleanly, in the sense they are not aborted but rather continue executing and finish according to the node transition rules. As one technique to aid in clean termination, a plan can allow the running of “clean-up” nodes to ensure safe termination of processes. The semantics of clean termination of a list node with running children are :
- Only currently executing and just-activated child nodes continue to run
- Pending child nodes whose start conditions are not satisfied do not run
- Parent node waits for active child nodes to finish executing
Faults can also drive node termination. A node fails if its invariant condition is violated or its pre- or post-conditions are not satisfied. When a node fails it aborts its child nodes without clean-up. When a node fails no more events are processed by the sub-tree rooted at that node. All clean-up actions must be handled by sibling nodes.
Outcome is a node attribute that provides additional information about the result of node execution. During execution, the outcome of a node records the current execution status. A node may have any one of the following outcomes:
The node outcome is initialized to Unknown. The outcome is set to Skipped if the node did not run, and to Success if the current iteration completed successfully. The outcome is set to Failure if a failure happened, and to Interrupted if the node or any of its ancestors' exit conditions became true. Outcomes provide information only for the current iteration; they are reset for repeating nodes.
When a node fails, the failureType is assigned one of the following values:
- Precondition failed
- Postcondition failed
- Invariant condition failed
- Parent failed
Note that all conditions are checked once upon transition to a state in which they apply. Only the condition changes listed above cause node state transitions, e.g. a start condition changing to true causes node state transitions, but the start condition changing to false does not cause any node state transitions. Once a condition is enabled it stays enabled until it is explicitly reset. The conditions are only reset for repeating nodes.
The complete set of node state transitions that govern the semantics of the execution of a single node are provided in the Node State Transition Diagrams. In certain states, e.g. state Waiting, all node types have the same semantics. In other cases, such as state Executing, the semantics depend on the node type (list, command, assignment…). For efficiency we represent ancestor end conditions. These are easily computed from the immediate parent and child nodes. In principle, a node only needs to know about its single immediate parent and all child nodes.
The default value of each node condition for each node type is given in the following tables. All node types share common defaults for most of the conditions:
End condition defaults vary by node type:
|Node Type||Empty||List, Library Call||Command||Assignment||Update|
|End Condition||True||all children finished||True||True||update acknowledged|
For any node condition that is not explicitly specified, the default value from the tables above is used. When a condition is given explicitly, it replaces the default value in all but the following cases:
- The actual End Condition of Command nodes is the disjunction of the given expression and the command handle value being either COMMAND_FAILED or COMMAND_REJECTED. This is to allow commands rejected by the resource arbitrator and failed commands to terminate.
- The actual End Condition of Update nodes is the conjunction of the given expression and the update acknowledgement.
Micro Steps, Macro Steps, And the Quiescence Cycle
Execution of a PLEXIL plan occurs in three classes of steps: micro steps, macro steps, and quiescence steps.
A quiescence step or quiescence cycle begins when the executive is notified of an external event. This could be the addition of a new plan, a timer expiration, a command or update acknowledgement, or other external change of state. The executive reads the current external state and begins a macro step. The quiescence cycle ends when no nodes are eligible to transition and all side effects (e.g. variable assignments, external actions) have been performed, i.e. when the executive is quiescent.
A macro step consists of zero or more successive micro steps. The current state of the plan and the external world are examined to see if some node(s) are eligible for transition. A macro step ends when either no further node state transitions are possible without additional input, one or more Assignment nodes are executed, or one or more commands and/or updates needs to be sent. At the end of every macro step, any external actions are executed. Then if more transitions are possible due to node condition changes resulting from the assignments or external actions, another macro step is begun.
Micro steps correspond to transitions that modify only the local data in the executive, i.e. node states, outcomes, failure types, and the values of the timepoint variables. A micro step is defined as the synchronous parallel execution of one or more transitions, as defined by the Node State Transition Diagrams. All eligible transitions are performed in lockstep, pseudo-simultaneously. If additional transitions are possible at the end of a micro step, another micro step is started immediately.
PLEXIL does not make any assumption about the duration of execution of a micro step. An assumption that is commonly made for synchronous languages is that a step (in our case, a micro step) takes zero time. Or, alternatively, that the external world changes (and therefore the occurrence of external events happens) less frequently than the execution of steps. This assumption is not mandatory in PLEXIL. If a micro step takes more than zero time, this means that the execution of a macro step also takes more than zero time. Since the external world may keep changing in the meantime, it is possible that some micro steps within the macro step use stale data. A similar situation occurs if an event is processed much later than it was produced. In this case, it is possible that the current status of the external variables associated with the event might have changed.
NOTE: If more than one node is eligible for execution in a given quiescence cycle, the actual order of execution is unspecified. In any context where the exact node execution order really matters, it should be encoded explicitly in the plan.
Semantics of Lookups
Lookups simply read external state values. In other words, looking up these states should not have any side effects. (An implementation of the executive or external interface may choose to cache state values without violating this requirement.) It is legal, and occasionally useful, for a lookup to return UNKNOWN.
There are two types of lookups in PLEXIL: immediate (LookupNow) and continuous (LookupOnChange).
LookupNow is executed during the quiescence cycle. The executive blocks until a value is returned by the external interface.
LookupOnChange returns a value immediately as in the case of LookupNow, and also causes an internal PLEXIL event to be generated when the value has changed (i.e, the previous value is different from the current value by more than the specified tolerance, if any). If no tolerance is specified, any change in the external value provokes the internal PLEXIL event.
Any LookupNow which is active for more than one quiescence cycle, e.g. in an invariant or end condition, may have its value updated in subsequent cycles, particularly (but not exclusively) if there is also a LookupOnChange for the same state.
StartCondition: LookupOnChange(“Rover battery level”) > 10.0 && powerTrackingNode.state == EXECUTING
In this example, an asynchronous event is triggered whenever the rover battery level changes. The state of the node powerTrackingNode is maintained internally and it triggers an event when it changes. The start condition is checked whenever such events occur.
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