Tasking Event B Overview

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Tasking Event-B

The following text can be read in conjunction with the slides[1] from the Deploy Plenary Meeting - Zurich 2010.

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 development that is suitable for construction of a Tasking Development. At some point during the modelling phase parameters may have to be introduced to facilitate decomposition. This constitutes a natural part of the refinement process as it moves towards decomposition and on to the implementation level. During decomposition parameters form part of the interface that enables event synchronization. We make use of this interface and add information (see #Implementing Events) to facilitate code generation.

A Tasking Development is generated programmatically, at the direction of the user; the Tasking Development consists of a number of machines (and perhaps associated contexts). In our approach we make use of the Event-B EMF extension mechanism which allows addition of new constructs to a model. The tasking extension consists of the constructs in the following table.

Construct Options
Machine Type DeclaredTask, AutoTask, SharedMachine
Control Sequence, Loop, Branch, EventSynch
Task Type Periodic(n), Triggered, Repeating, OneShot
Priority -
Event Type Branch, Loop, ProcedureDef, ProcedureSynch
Parameter Type ActualIn, ActualOut, FormalIn, FormalOut

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.
    • Priority - An integer value is supplied, the task with the highest value priority takes precedence when being scheduled.

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.

Tasks and Events

Control Constructs

Each Tasking Machine has a task body which contains the flow control, or 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.
    • Event Synchronisation - synchronization between an event in a Tasking Machine and an event in a Shared Machine. Synchronization corresponds to an subroutine call with atomic (with respect to an external viewer) updates. 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.
    • 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, or to a Shared Machine that is visible to the task. Single events in a wrapper correspond to a subroutine call in an implementation.

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.
    • ProcedureSych - 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 .

In an implementation, 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
    • 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.