Difference between pages "Tasking Event-B Tutorial" and "Theory Plug-in"

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For more information contact Andy Edmunds - University of Southampton - mailto:ae2@ecs.soton.ac.uk
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Return to [[Rodin Plug-ins]]
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=== Tasking Event-B Tutorial Overview ===
 
  
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<span style="color: RED">'''Caution''': This Page is under Construction - some parts are incomplete</span>
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See also [[Theory Release History]]
  
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This tutorial follows on from the abstract development described [http://wiki.event-b.org/index.php/Development_of_a_Heating_Controller_System here].
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The Theory plug-in provides capabilities to extend the Event-B language and the proving infrastructure in a familiar fashion to Rodin users. This page provides useful information about the plug-in and its capabilities.
  
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This code generation tutorial extends the Heating Controller tutorial example, and makes use of example projects from the download site. The code generation stage produces implementable Ada code, and also an Event-B model. It is a model of the implementation, and contains flow control variables that model the flow of execution through the task body. The Ada code is produced from an intermediate model that is not visible to the user. The Common Language model (CLM), is generated from the Tasking Event-B by a translation tool. Ada (and other implementations) may be generated from the CLM. An overview of Tasking Event-B can be found [http://wiki.event-b.org/index.php/Tasking_Event-B_Overview here].
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===Motivation===
 +
Up to Rodin v2.0, the mathematical language used in Event-B has been fixed. As such, it was not possible to define reusable polymorphic operators. A workaround was to define any required operators as set constructs in contexts. Originally, contexts were supposed to provide a parametrization of machines. The aforementioned limitations of the Event-B language lead to users to use contexts for purposes for which they were not intentionally devised. Examples of operators that can be useful to users include the sequence operator (which was present in classical B mathematical language) and the bag operator.
  
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In the example so far, the Heating Controller has been refined to the point where we wish to add implementation constructs. The Event-B language is not expressive enough to fully describe the implementation. Tasking Event-B facilitates this final step to implementation, by extending Event-B with the necessary constructs. Event-B machines modelling tasks, shared objects and the environment are identified, and extended with the appropriate implementation details.
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In Rodin v2.0, support for customised syntactic symbols was introduced. The Theory plug-in, as a result, evolved from being just a component to define rewrite rules to a versatile platform to define and validate proof and language extensions.
  
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The example/tutorial projects are are available in the [http://deploy-eprints.ecs.soton.ac.uk/304/ e-prints archive], or on [https://codegenerationd.svn.sourceforge.net/svnroot/codegenerationd/Examples/Heating_ControllerTutorial_v0.2.0/ SVN].
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The latest Theory plug-in is released for Rodin v2.8.
  
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{| border="1"
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===Overview===
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|Heating_ControllerTutorial2_Completed
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The Theory plug-in is a Rodin extension that provides the facility to define '''''mathematical extensions''''' as well as '''''prover extensions'''''.
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|An example project with an environment simulation. The environment variables are monitored and controlled using subroutine calls. The project contains a complete Tasking Development with generated Event-B and Ada code.
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Mathematical extensions are new operator definitions and new datatype definitions and axiomatic definitions. Operator definitions can be expression operators (e.g., ''card'') and predicate operators (e.g., ''finite''). Datatypes extensions can be used to define enumerated datatypes (e.g., ''DIRECTION'') as well as inductive datatypes (e.g., ''Tree''). Axiomatic definitions can be used to define new data types like "REAL".
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|-
 
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|Heating_ControllerTutorial2_Partial1
 
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|A project with the final decomposition completed, ready to begin Tasking Event-B Development.  
 
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|-
 
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|Heating_ControllerTutorial2_Partial2
 
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|A partially completed tasking specification for the continuation of the tutorial.
 
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|-
 
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|TheoriesForCG
 
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|Contains the mathematical language translations; encoded as rules in a theory plug-in rule-base.
 
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|}
 
  
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== Using the Tasking Extension ==
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The placeholder for mathematical and prover extensions is a Theory construct which looks similar to contexts and machines. A theory can include datatypes definitions, operator definitions, axiomatic definitions, inference and rewrite rules as well as polymorphic theorems. The [http://wiki.event-b.org/images/Theory_Plugin.pdf user manual] provides a guide to developing and using theories.
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The steps needed to generate code from an Event-B model, in this tutorial, are as follows,
 
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* Step 1 - [[Tasking Event-B_Tutorial#Adding the Implementation Level Refinement|Adding the Implementation Level Refinement]]
 
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* Step 2 - [[Tasking Event-B_Tutorial#Pre-processing|Pre-processing]]
 
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* Step 3 - [[Tasking Event-B_Tutorial#Providing the Annotations for Implementations|Add Tasking annotations]].
 
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* Step 4 - [[Tasking Event-B_Tutorial#Invoking the Translation|Invoke translators]].
 
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=== Download and Copy the Theories ===
 
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The translations of the Event-B mathematical language to the target language constructs are specified as rules in the theory plug-in. Two rule files are included for the example, and are available in the [https://codegenerationd.svn.sourceforge.net/svnroot/codegenerationd/Examples/Heating_ControllerTutorial_v0.2.0/ SVN]. The files can be downloaded and copied into an Event-B project called ''MathExtensions''. The theory must then be deployed. Right-Click on the theory file and select deploy to do this. The non-Event-B project, the original download may now be deleted.
 
  
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=== Adding the Implementation Level Refinement ===
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=== Installation & Update ===
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The final decomposition generates the machines that are required for code generation. However, it is not possible to edit the machines since they are machine generated, and therefore this is prohibited. In order to be able to modify the models we will refine the generated machines. This is where we begin with the ''Heating_ControllerTutorial2_Partial1'' project. To refine the machines we can use the automatic refinement feature, but this presents us with two problems that are dealt with in the pre-processing step. It is also at this stage that any remaining non-deterministic constructs should be removed by replacing them with deterministic constructs.
 
  
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TIP: Non-deterministic constructs cause strange characters to appear in the source code. If you see strange characters in the generated code, check for non-deterministic constructs in the implementation level machines.
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The installation or update for the Theory plug-in is available under the main Rodin Update site (http://rodin-b-sharp.sourceforge.net/updates) under the category "Modelling Extensions". Like always, after the installation, restarting Rodin is recommended.
  
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Alter_Temperature_Sensor1 in Envir1Impl: action becomes ts1 := ts1 + 1
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===User Manual===
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Alter_Temperature_Sensor2 in Envir1Impl: action becomes ts1 := ts1 + 1
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The user manual is available here: [http://wiki.event-b.org/images/Theory_Plugin.pdf Theory User Manual]. Below is the presentation of the sequence theory which its description can be found in the user manual:
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Alter_Heater_Status in Envir1Impl: action becomes hss := FALSE
 
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INITIALISATION in Heater_Monitor_TaskImpl: becomes shs := FALSE
 
  
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We also need to add a typing flag to an invariant. We need to add it in only one place, and this is where an invariant is used type a variable, in the Heating Controller machine. The flag is used to guide the translator to the typing invariant. This is because there is more than one invariant involving that particular variable. They may also be added to guards where parameters are typed in guards, and the parameters are referred to in more than one guard.
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[[image:SeqTheory.png|center|thumb|1500px|'''Theory of Sequence''']]
  
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* Go to the ''Heater_Monitor_TaskImpl typing_shs'' invariant.
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===Standard Library===
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* Add the typing flag, by right-clicking on the invariant and selecting typing from the menu.
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In this section, you find a set of standard theories and some models using some of these theories.  
  
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=== Pre-processing ===
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The standard library of the theories is available to download:
 +
[https://sourceforge.net/projects/rodin-b-sharp/files/Theory_StdLib/StandardTheory0.1.zip/download here] for Rodin2.8 and
 +
[https://sourceforge.net/projects/rodin-b-sharp/files/Theory_StdLib/StandardTheory0.2.zip/download here] for Rodin3.1.
 +
This library includes:
 +
* BasicTheory project: including theories of BinaryTree, BoolOps, List, PEANO, SUMandPRODUCT and Seq.
 +
* RelationOrderTheory project: including theories of Connectivity, FixPoint, Relation, Well_Fondation, closure, complement and galois.
 +
* RealTheory project: including theory of Real.
  
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The pre-processing step should be a temporary, the solutions can be incorporated into the tool to automatically perform the changes that are required.
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Also it includes three simple Event-B models that use some of the theories:
 +
* Data project: using SUMandPRODUCT theory
 +
* Queue project: using Seq theory
 +
* SimpleNetwork project: using closure theory
  
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* The Code Generator requires a flattened version of each machine; all of the Event-B elements should be available in the implementation level machine.
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In order to keep the POs discharged, you need to install "Atelier B provers" as well.
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* Composed machines are not currently able to be refined, so anything that requires synchronization of events requires some manual updates.
 
  
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===== 'Flattening' the Implementation Machines =====
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===Capabilities===
 +
The Theory plug-in has the following capabilities:
  
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The temporary solution for flattening:
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* Theory Definition:
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* Make events ''not extended''.
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** Definition of datatypes: datatypes are defined by supplying the types on which they are polymorphic, a set of constructors one of which has to be a base constructor. Each constructor may or may not have destructors.
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* Copy missing invariants.
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** Definition of operators: operators can be defined as predicate or expression operators. An expression operator is an operator that "returns" an expression, an example existing operator is ''card''. A predicate operator is one that "returns" a predicate, an example existing predicate operator is ''finite''.
 +
** Definition of axiomatic definitions: axiomatic definitions are defined by supplying the types, a set of operators, and a set of axioms.
 +
** Definition of rewrite rules: rewrite rules are one-directional equalities that can be applied from left to right. The Theory plug-in can be used to define rewrite rules.
 +
** Definition of inference rules: inference rules can be used to infer new hypotheses, split a goal into sub-goals or discharge sequents.
 +
** Definition of polymorphic theorems: theorems can be defined and validated once, and can then be imported into sequents of proof obligations if a suitable type instantiation is available.
 +
** Validation of extensions: where appropriate, proof obligations are generated to ensure soundness of extensions. This includes, proof obligations for validity of inference and rewrite rules, as well as proof obligations to validate operator properties such as associativity and commutativity.
 +
*Theory Deployment: this step signifies that a theory is ready for use. Theories can be deployed after they have been optionally validated by the user. It is strongly advisable to discharge all proof obligations before deployment.
 +
Once a theory has been deployed to its designated project, all its extensions (mathematical and prover extensions) can be used in models.
  
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I found the Event-B Machine Editor's synthesis view useful for this. Invariants can be copy-pasted into the implementation machine from the abstraction. (A dummy invariant can be added and selected for pasting)
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===Insider Look===
 +
The Theory plug-in partially satisfies the requirements outlined in the following document:
 +
* [http://deploy-eprints.ecs.soton.ac.uk/80/ Abrial, Jean-Raymond and Butler, Michael and Schmalz, Matthias and Hallerstede, Stefan and Voisin, Laurent. Mathematical Extensions Proposal]
  
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===== Providing the correct Composed Machine =====
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A more accurate description of the implemented functionalities of the plug-in can be found in the following document:
 +
* [http://deploy-eprints.ecs.soton.ac.uk/251/ Michael Butler, Issam Maamria. Mathematical Extensions Summary]
  
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The composed machine problem is sub-divided into two sub-problems. Firstly composed machines cannot be refined, and secondly when a machine is further decomposed there is no link between the first composed machine and the newly generated composed machine. So one or both of these problems may occur, depending on the number of decompositions.
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The following two papers describe rewriting and well-definedness issues that has to be accounted for:
  
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We must manually add the information to the composed machines to address these two problems.
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* [http://eprints.ecs.soton.ac.uk/18269/ Issam Maamria, Michael Butler, Andrew Edmunds, and Abdolbaghi Rezazadeh. On an Extensible Rule-based Prover for Event-B, ABZ'2010.]
 +
* [http://eprints.ecs.soton.ac.uk/21221/ Issam Maamria, Michael Butler. Rewriting and Well-Definedness within a Proof System.]
  
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The temporary solution for composed machines:
 
−
* Modify the lowest level decomposed machine, HCtrl_M1_cmp, to ''include'' the implementation level machines (task names ending in *Impl). To do this,
 
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* open the composed machine editor. Open the INCLUDES edit feature.
 
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* Select the second drop-down box and find the *Impl version of each machine.
 
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* Save the composed machine.
 
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* Now add missing synchronizations to the composed machine. Add the ''Envir1Impl'' to the includes of HCtrl_M1_cmp.
 
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* Each composed event in the task, that synchronizes with the Environ machine, must have the remote event synchronization added manually. This can only be done by inspection of each composed event. We need to update Sense_Temperatures, Display_Current_Temperature, Actuate_OverHeat_Alram, Actuate_Heat_Source, Sense_Heater_Status, Actuate_NoHeat_Alarm, Sense_PressIncrease_Target_Temperature, Sense_PressDecrease_Target_Temperature, Display_Target_Temperature. One by one, expand the events in the composed events section of the composed machine editor; add a new event in the combines events section, select ''Envir1Impl'' and add the synchronizing event from the list-box to the right.
 
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=== Adding Tasking Event-B ===
 
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Each Machine should be completed as follows.
 
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==== The Temp_Ctrl_Task1Impl Machine ====
 
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Continuing with the tutorial project ''Heating_ControllerTutorial2_Partial2'', we need to make changes to the following machines. During the tutorial we will cut and paste from the ''completed'' model when specifying the task bodies to save typing.
 
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have already identified the ''Temp_Ctrl_Task1Impl'' as an ''Auto Task'' Tasking Machine, by adding the ''Auto Task'' extension. ''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. We have set the task type to ''Periodic'', and set a period of 250 milliseconds. We have provided a screenshot of the completed ''Temp_Ctrl_Task1Impl'' [http://wiki.event-b.org/images/Temp_Ctrl_Task1Impl.pdf here], it can be read in conjunction with the tutorial.
 
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The next step is to construct the task body using the TaskBody Editor, with control constructs such as sequence, branch, loop and output. These constructs are discussed in the [http://wiki.event-b.org/index.php/Tasking_Event-B_Overview overview] of Tasking Event-B. We will now complete the sequence that has been partially defined in the task body.
 
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?????????????????????????????
 
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By relating the sensing events in this way we describe a simulation of the interaction between the task and environment. The details of the interaction are embodied in the events themselves; and this is implemented in the simulation code by reading the values of the environment variables.
 
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Next we look at the sensing event ''TCSense_Temperatures'' event in ''Temp_Ctrl_Task1Impl''. 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.
 
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−
*'''Add The Sensed Event Extension'''.
 
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** Right-click on the ''TCSense_Temperatures'' Event node.
 
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** Select ''New Child/Implementation'' from the menu.
 
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** Go to the Implementation properties view and set the ''Implementation Type'' property to ''Sensing''.
 
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==== The Shared Machine ====
 
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The next step is to identify the ''Shared_Object1Impl'' machine as a ''Shared Machine''. A screenshot of the [http://wiki.event-b.org/images/Shared_Object1Impl.pdf Shared_Object1Impl] shared machine can be read in conjunction with the text.
 
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* Optionally collapse open branches of the EMF editor to remove clutter. 
 
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* Right-click on the ''Shared_Object'' Machine node in the Rose Editor.
 
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* Select ''New Child/Shared Machine'' from the menu.
 
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==== The Environ Machine ====
 
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In the prepared machine we have identified the ''Envir1Impl'' as an ''Environ Machine'', by adding the ''Environ Machine'' extension. ''Envir1Impl'' models a task that simulates the environment, and can be used to generate simulation code. For deployment in a non-simulated environment the environ machine's generated code can be ignored; we provide details of non-simulated code using addressed variables later. As before, a screenshot is available [http://wiki.event-b.org/images/Envir1Impl_2.pdf here]. In the prepared Environment Machine we have already set task type to ''Periodic'' extension, and set a period of 100 milliseconds.
 
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We will now complete the sequence that has been partially defined in the task body. The following specification models simulation of a temperature change; the temperature value is represented by a monitored variable in the environment. The generated code simulates the temperature change in the environment by changing the monitored value. 
 
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*'''Model Temperature Change in the environment'''.
 
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??????
 
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* Output to the screen during the simulation can be specified as follows:
 
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??????
 
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The generated code will print the text, and the value of the variable, to the screen.
 
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The final step is to complete the ''ENSense_Temperatures'' event. The event is a sensing event, sensing is a kind of synchronisation, it synchronises with the ''TCSense_Temperatures'' event in the ''Temp_Ctrl_Task1'' tasking machine. We add formal parameters annotations corresponding to the actual parameters that we have already defined in the task.
 
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*'''Add The Sensed Event Extension'''.
 
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** Right-click on the ''ENSense_Temperatures'' Event node.
 
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** Select ''New Child/Implementation'' from the menu.
 
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** Go to the Implementation properties view and set the ''Implementation Type'' property to ''Sensing''.
 
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We have identified the event as a sensing event. Now we add the parameter direction:
 
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=== A Summary of Steps ===
 
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For a Tasking Machine definition:
 
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# Add the Tasking Machine type (Auto etc).
 
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# Set the task type (Periodic etc.).
 
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# Set the task priority.
 
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# Specify the task body.
 
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# For sensing/actuating events, add the Event Type.
 
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For a Shared Machine definition:
 
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# Add the ''SharedMachine'' Machine type.
 
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For an Environ Machine definition:
 
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# Make the type an Environ Machine type.
 
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# Set the task type Periodic; a shorter period than the shortest task period is best for simulation.
 
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# Set the task priority.
 
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# Specify the task body, it will contain a simulation of changes in the environment.
 
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# For each sensing/actuating event, add the Event Type.
 
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== Invoking the Translators ==
 
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* To generate Ada code,
 
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** Right-Click on the composed machine, or any tasking machine in the development, select ''Code Generation/Translate Event-B to Ada''.
 
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** Open the generated ''code'' directory in the project to view the source files. A refresh will be necessary to make the code visible. The .gpr file has been provided for AdaCore GPS users.
 
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* To create the Event-B model of the implementation,
 
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** Right-Click on the composed machine, or any tasking machine in the development, select ''Code Generation/Translate Tasking Event-B to Event-B''.
 
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** The Event-B model should be updated with the flow control variables. Users are not able to manually edit the generated elements. The additions can be removed using the menu option ''Code Generation/Remove Generated Event-B''
 
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−
== Generated Code ==
 
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The Ada Code generated by the translator is available at the following links:
 
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−
for simulation of environment without addressed variables, [http://wiki.event-b.org/images/Code_Heating_ControllerTutorial_Completed.pdf Heating_ControllerTutorial_Completed]
 
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−
for simulation of environment with addressed variables, [http://wiki.event-b.org/images/Code_Heating_Controller5AddressedSim_Completed.pdf Heating_Controller5AddressedSim_Completed]
 
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Removal of the environment task from the ''Heating_Controller5AddressedSim_Completed'' should be deployable.
 
  
 +
[[Category:Plugin]]
 
[[Category:User documentation]]
 
[[Category:User documentation]]
 +
[[Category:Proof]]
 +
[[Category:Theory Plug-in]]

Latest revision as of 14:53, 14 June 2021

Return to Rodin Plug-ins

See also Theory Release History

The Theory plug-in provides capabilities to extend the Event-B language and the proving infrastructure in a familiar fashion to Rodin users. This page provides useful information about the plug-in and its capabilities.

Motivation

Up to Rodin v2.0, the mathematical language used in Event-B has been fixed. As such, it was not possible to define reusable polymorphic operators. A workaround was to define any required operators as set constructs in contexts. Originally, contexts were supposed to provide a parametrization of machines. The aforementioned limitations of the Event-B language lead to users to use contexts for purposes for which they were not intentionally devised. Examples of operators that can be useful to users include the sequence operator (which was present in classical B mathematical language) and the bag operator.

In Rodin v2.0, support for customised syntactic symbols was introduced. The Theory plug-in, as a result, evolved from being just a component to define rewrite rules to a versatile platform to define and validate proof and language extensions.

The latest Theory plug-in is released for Rodin v2.8.

Overview

The Theory plug-in is a Rodin extension that provides the facility to define mathematical extensions as well as prover extensions. Mathematical extensions are new operator definitions and new datatype definitions and axiomatic definitions. Operator definitions can be expression operators (e.g., card) and predicate operators (e.g., finite). Datatypes extensions can be used to define enumerated datatypes (e.g., DIRECTION) as well as inductive datatypes (e.g., Tree). Axiomatic definitions can be used to define new data types like "REAL".

The placeholder for mathematical and prover extensions is a Theory construct which looks similar to contexts and machines. A theory can include datatypes definitions, operator definitions, axiomatic definitions, inference and rewrite rules as well as polymorphic theorems. The user manual provides a guide to developing and using theories.

Installation & Update

The installation or update for the Theory plug-in is available under the main Rodin Update site (http://rodin-b-sharp.sourceforge.net/updates) under the category "Modelling Extensions". Like always, after the installation, restarting Rodin is recommended.

User Manual

The user manual is available here: Theory User Manual. Below is the presentation of the sequence theory which its description can be found in the user manual:

Theory of Sequence

Standard Library

In this section, you find a set of standard theories and some models using some of these theories.

The standard library of the theories is available to download: 

here for Rodin2.8 and
here for Rodin3.1.

This library includes:

  • BasicTheory project: including theories of BinaryTree, BoolOps, List, PEANO, SUMandPRODUCT and Seq.
  • RelationOrderTheory project: including theories of Connectivity, FixPoint, Relation, Well_Fondation, closure, complement and galois.
  • RealTheory project: including theory of Real.

Also it includes three simple Event-B models that use some of the theories:

  • Data project: using SUMandPRODUCT theory
  • Queue project: using Seq theory
  • SimpleNetwork project: using closure theory

In order to keep the POs discharged, you need to install "Atelier B provers" as well.

Capabilities

The Theory plug-in has the following capabilities:

  • Theory Definition:
    • Definition of datatypes: datatypes are defined by supplying the types on which they are polymorphic, a set of constructors one of which has to be a base constructor. Each constructor may or may not have destructors.
    • Definition of operators: operators can be defined as predicate or expression operators. An expression operator is an operator that "returns" an expression, an example existing operator is card. A predicate operator is one that "returns" a predicate, an example existing predicate operator is finite.
    • Definition of axiomatic definitions: axiomatic definitions are defined by supplying the types, a set of operators, and a set of axioms.
    • Definition of rewrite rules: rewrite rules are one-directional equalities that can be applied from left to right. The Theory plug-in can be used to define rewrite rules.
    • Definition of inference rules: inference rules can be used to infer new hypotheses, split a goal into sub-goals or discharge sequents.
    • Definition of polymorphic theorems: theorems can be defined and validated once, and can then be imported into sequents of proof obligations if a suitable type instantiation is available.
    • Validation of extensions: where appropriate, proof obligations are generated to ensure soundness of extensions. This includes, proof obligations for validity of inference and rewrite rules, as well as proof obligations to validate operator properties such as associativity and commutativity.
  • Theory Deployment: this step signifies that a theory is ready for use. Theories can be deployed after they have been optionally validated by the user. It is strongly advisable to discharge all proof obligations before deployment.

Once a theory has been deployed to its designated project, all its extensions (mathematical and prover extensions) can be used in models.

Insider Look

The Theory plug-in partially satisfies the requirements outlined in the following document:

A more accurate description of the implemented functionalities of the plug-in can be found in the following document:

The following two papers describe rewriting and well-definedness issues that has to be accounted for:

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