Tasking Event-B Overview

Tasking Event-B

Tasking Event-B can be viewed as an extension of the existing Event-B language. We use the existing approaches of refinement and decomposition to structure a project that is suitable for a Tasking Development. During the modelling phase parameters are introduced to facilitate decomposition. As a result of the decomposition process, parameters become part of the interface that enables event synchronization. We make use of this interface and add information (see #Implementing Events) to facilitate code generation. The tasking extension consists of the constructs in the following table.

Construct	Options
Machine Type	DeclaredTask, AutoTask, SharedMachine, Environ
Control	Sequence, Loop, Branch, EventSynch, Output
Task Type	Periodic(n), Triggered, Repeating, OneShot
Priority	-
Event Type	Branch, Loop, ProcedureDef, ProcedureSynch, Actuating, Sensing
Parameter Type	ActualIn, ActualOut, FormalIn, FormalOut
Addressed Variable	Address, Base

Tasking Developments

A Tasking Development is modelling component that is generated programmatically, at the direction of the user. The Tasking Development consists of a number of machines (and perhaps associated contexts). We make use of the Event-B EMF extension mechanism , which allows addition of new constructs to a model. The machines in the Tasking Development are extended with the constructs shown in the table, and may be viewed as keywords in a textual representation of the language. With extensions added, a Tasking Development can be translated to a common language model for mapping to implementation source code. There is also a translator that constructs new machines/contexts modelling the implementation, and these should refine/extend the existing elements of the Event-B project.

Tasking Machines

The following constructs relate only to Tasking Machines, and provide implementation details. Timing of periodic tasks is not modelled formally. Tasking Machines are related to the concept of an Ada task. These can be implemented in Ada using tasks, in C using the pthread library C, or in Java using threads.

• Tasking Machines may be characterised by the following types:
  • AutoTasks - Singleton Tasks.
  • Declared tasks - (Not currently used) A task template relating to an Ada tasktype declaration.
  • TaskType - Defines the scheduling, cycle and lifetime of a task. i.e. one-shot periodic or triggered. The period of a task is specified in milliseconds.
  • Priority - An integer value is supplied, the task with the highest value priority takes precedence when being scheduled. For the demonstrator tool the default priority is 5.

Auto Tasks are tasks that will be declared and defined in the Main procedure of the implementation. The effect of this is that the Auto Tasks are created when the program first loads, and then activated (made ready to run) before the Main procedure body runs.

Shared Machines

A Shared Machine corresponds to the concept of a protected resource, such as a monitor. They may be implemented in Ada as a Protected Object, in C using mutex locking, or in Java as a monitor.

• Applied to the Shared Machine we have:
  • A SharedMachine keyword that identifies a machine as a Shared Machine.

The Environ Machine

An Environ machine is a model of the environment. It can be used to generate code for use in a simulation, or discarded (from the IL1 model) in the case that a simulated environment is not required.

• Applied to the Environ Machine we have:
  • An Environ Machine keyword that identifies a machine as an Environ Machine.

Implementation Specifics

At the stage where we are considering how to implement the Event-B development we need to think about controlling the flow of execution, and how events should be implemented. The following section describes the constructs that we have introduced to facilitate this.

Control Constructs

Each Tasking Machine has a task body which contains the flow control (algorithmic constructs).

• We have the following constructs available in the Tasking Machine body:
  • Sequence - for imposing an order on events.
  • Branch - choice between a number of mutually exclusive events.
  • Loop - event repetition while it's guard remains true.
  • EventWrapper - a wrapper for the Event-B element (soon to be redundant).
  • Synch Events - synchronizes two events.
  • Text Output - writes textual output to the screen.

Synchronization corresponds to:

• a subroutine call from task to shared machine, or,
• sensing or actuating of environment variables.

In the case of a subroutine call the subroutine is an atomic (with respect to an external viewer) update to state. The updates in the protected resource are implemented by a procedure call to a protected object, and tasks do no share state. The synchronization construct also provides the means to specify parameter passing, both in and out of the task.

In the case of a sensing or actuating event, the updates of the action correspond to reads of monitored variables, and writes to controlled variables of the environment.

Event wrappers:

• The event synchronization construct is contained in an event wrapper. The wrapper may also contain a single event (we re-use the synchronization construct, but do not use it for synchronizing). The event may belong to the Tasking Machine, a Shared Machine that is visible to the task, or the Environ machine. Single events in a wrapper correspond to a subroutine call in an implementation.

When Editing the EMF model the constructs have the following names:

Construct	EMF name
Sequence	Seq
Branch	Branch
Loop	Do
Text Output	Output
EventWrapper	EventWrapper
SynchEvents	SynchEvents

The abstract syntax is:

TaskBody ::=

Seq

> Branch

Do

EventWrapper

Output

Seq ::= TaskBody TaskBody

Branch ::= Body [SubBranch] Else

SubBranch ::= Body [SubBranch]

Else ::= EventWrapper

Body ::= EventWrapper

Do ::= Body [Finally]

Finally ::= EventWrapper

Output ::= Text Variable

EventWrapper ::= SynchEvents

SynchEvents ::= Local Remote

Local ::= Event

Remote ::= Event

Implementing Events

An event's role in the implementation is identified using the following extensions which are added to the event. Events used in task bodies are 'references' that make use of existing event definitions from the abstract development. The events are extended. to assist with translation, with a keyword indicating their role in the implementation.

• Event implementation.
  • Branch - In essence a task's event is split in the implementation; guards are mapped to branch conditions and actions are mapped to the branch body. If the branch refers to a Shared Machine event (procedureDef) then this is mapped to a simple procedure call.
  • Loop - The task's event guard maps to the loop condition and actions to to loop body. If the loop refers to a Shared Machine event then it is mapped to a simple procedure call.
  • ProcedureSynch - This usually indicates to the translator that the event maps to a subroutine, but an event in a task may not require a subroutine implementation if its role is simply to provide parameters for a procedure call.
  • ProcedureDef - Identifies an event that maps to a (potentially blocking) subroutine definition. Event guards are implemented as a conditional wait; in Ada this is an entry barrier, and in C may use a pthread condition variable .
  • Sensing - Identifies an event that maps to a read from the environment. If the environment is simulated without address variables then the sensing event is similar to a ProcedureSynch event, in that it has an update action that models assignment of a return value from a subroutine call. The event parameters act like the actualIn parameters of a ProcedureSynch event. On the other hand, if the event has addressed variables associated with its event parameters, then they map to direct reads from memory mapped variables in the generated code.
  • Actuating - Identifies an event that maps to a write to the environment. If the environment is simulated without address variables then the actuating event has no update action, the parameters act like actualOut parameters of a ProcedureSynch event. If a sensing event has addressed variables associated with its parameters then they map to direct writes to memory mapped variables in the generated code.

Sensing (and actuating) can be viewed as a kind of synchronisation. Synchronisation between tasks and shared objects are represented as subroutine calls. The sensing/actuating synchronisations only occur between tasks and the environment. In implementable code, when an subroutine is defined, its formal parameters are replaced by actual parameter values at run-time. To assist the code generator we extend the Event-B parameters. We identify formal and actual parameters in the implementation, and add the following keywords to the event parameters, as follows:

• Event parameter types - Note: formal parameters are place-holders in a subroutine; they are replaced by the actual parameters at call time.
  • FormalIn or FormalOut - event parameters are extended with the ParameterType construct. Extension with formal parameters indicates a mapping to formal parameters in the implementation.
  • ActualIn or ActualOut - Extension with an actual parameter indicates a mapping to an actual parameter in the implementation.

Addressed Variables

When sensing monitored variables, or actuating controlled variables in the environment, we may wish to use explicit memory addresses for use in the final implementation, or perhaps in the environment simulation too. We can link a task's event parameters, and an Environ machines variables, with specific addresses and use these in the generated code.