imported>Pascal |
imported>Tommy |
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| | {{TOCright}} | | {{TOCright}} |
| | + | Return to [[Rodin Plug-ins]] |
| | | | |
| − | == Introduction ==
| + | [[Image:RodinEditor_basicView1.png|400px|left|a basic view of the Rodin Editor on a context]] |
| − | One of the most important feature of the Event-B approach is the ability to introduce new events during refinement steps, but a consequence is an increasing complexity of the refinement process when having to deal with many events and many state variables.
| |
| | | | |
| − | The main idea of the decomposition is to cut a model <math>A</math> into sub-models <math>A_1, ..., A_n</math>, which can be refined separately and more confortably than the whole. | + | The Rodin Editor is an editor, based on the same principles as the historical structured Event-B Editor. This latter editor shown its weakness while editing large models. Moreover, it was impossible to show some information, which are needed when one edits an Event-B model (such as the inherited elements which were formerly displayed only in the pretty print view). This is to solve all these issues that the Rodin Editor was created. |
| | | | |
| − | The constraint that shall be satisfied by the decomposition is that these refined models might - the recomposition will never be performed in practice - be recomposed into a whole model <math>C</math> in a way that guarantees that <math>C</math> refines <math>A</math>. An event-based decomposition of a model is detailed in [[#ancre_1|Event Model Decomposition]]: the events of a model are partitioned to form the events of the sub-models. In parallel, the variables on which these events act are distributed among the sub-models.
| + | This editor aims to be clean, in order to read easily models, but new comers may find it less easy to use. Please read the '''Principles''' section to get the necessary background to understand how this editor works. Furthermore, the text base of this editor aims to bring with it all the navigation and edition ease provided by text editor. |
| | + | <br style="clear: both" /> |
| | | | |
| − | The purpose is here to precisely describe what is required at the Rodin platform level to integrate this event model decomposition, and to explain why. The details of how it could be implemented are out of scope. | + | Please have a look also at the [[Rodin Editor User Guide]]. |
| | + | === Current version === |
| | + | The current version for <b>Rodin 2.3</b> is 0.5.1 released on Monday 3 October 2011. This version is similar to v.0.5.0 but made compatible with Rodin 2.3<br> |
| | + | The current version for <b>Rodin 2.2.x</b> is 0.5.0 released on Wednesday 13 July 2011. This version is not compatible with Rodin 2.3<br> |
| | + | ''<span style="color:#FF4500">IMPORTANT : we identified a source of concurrency in the current version (0.5.0 & 0.5.1) of the plug-in.</span>''<br> |
| | + | <span style="color:#FF4500">'''To avoid any trouble, please do not generate files while having some Rodin Editor open, and edit only one model per project at once.'''</span> |
| | | | |
| − | Other [[#ancre_2|decomposition structures for Event-B]] are not considered here.
| + | === Principles === |
| | + | '''The component contents are displayed as text.''' Once you component opened with the Rodin Editor, its contents are printed as text inside the Rodin Editor. However, as said, the Rodin Editor is not a text editor, and even if the component you edit is streamlined to basic text, what you edit is stored in an underlying database. That's the reason why you can not type text at any place at any moment. (i.e. there is no parsing of text file: what you see is a text component based form editor). |
| | | | |
| − | == Terminology ==
| + | '''There are two types of edition possible.''' Because Rodin manipulates Event-B elements and their attributes, the Rodin Editor provides two ways to modify Event-B models: |
| | + | * you can navigate through the model contents and do things on the Event-B elements (e.g. add/remove/move/etc.) with the right-click actions or the keyboard shortcuts, depending on where is your cursor, or what you selected, |
| | + | * you can edit the Event-B element's attributes by entering the "edition" mode provided by the overlay editor. This is detailed here-after. |
| | | | |
| − | * Event model decomposition: The decomposition of a model, as defined in [[Machines_and_Contexts_(Modelling_Language)|the modelling language]], in sub-models.
| + | '''An overlay editor displays over the text to edit element's attributes''' The basic idea is: ''"when I want to edit some contents, I should open the overlay editor that will allow me to modify its value"''. |
| − | A model can contain contexts, machines, or both. The notion of model decomposition covers on the one hand the machine decomposition, and on the other hand the context decomposition, both being interdependent.
| |
| − | [[Image:Models.png]]
| |
| − | * Sub-machine: A machine built from a non-decomposed machine during the event model decomposition.
| |
| − | * Sub-context: A context built from a non-decomposed context during the event model decomposition.
| |
| − | * ''Shared'' variable: A variable of a given machine which is accessed by events distributed in distinct sub-machines (by opposition to ''private'' variable).
| |
| − | * ''Private'' variable: A variable of a given machine which is only accessed by events of the same sub-machine (by opposition to ''shared'' variable).
| |
| − | * ''External'' event: An event of a sub-machine which is built from an event of the non-decomposed machine, and which simulates the way the ''shared'' variables (between this sub-machine and another sub-machine) are handled in the non-decomposed machine (by opposition to ''internal'' event).
| |
| − | * ''Internal'' event: An event copied from the non-decomposed machine to a sub-machine, according to the end-user specified distribution (by opposition to ''external'' event).
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| | | | |
| − | Note that a variable is said to be ''accessed'' when it is read or written. More precisely, such an access may be performed by a predicate (invariant, guard, witness) or in an assignment (action).
| + | '''Everything happens where I click, or where my text caret is.''' The caret position, also set when the user left-clicks in the editor, is the base for component modifications: |
| | + | * if you click an editable attribute, the overlay editor opens on it and you are able to modify the attribute. The same action is possible if you press "Backspace" if the caret is on an editable attribute, |
| | + | * if you click on non editable places of the editor, you just move the text caret to the pointed position. |
| | | | |
| − | == Architecture ==
| + | '''Implicit elements are displayed in grayed colors.''' The elements that are implicit at the current level of edition are not editable, and displayed in grayed colors. (See the figure below) |
| − | <font color="red">TODO</font>
| + | [[Image:RodinEditor_basicView4.png|400px|center]] |
| | | | |
| − | == Low-level Specification == | + | === A basic overview === |
| − | The low-level specification details through several steps how the event model decomposition shall be performed, and in which order. It establishes a distinction between the steps performed on the end-user's initiative, and the computed ones. It links when possible to the already implemented features of the Rodin platform which can be used at some steps. | + | The Rodin Editor might not be the 'preferred' editor that Rodin uses to open your Event-B models.<br> |
| | + | Thus, to open a component (e.g. a machine, a context, etc.), '''right-click''' on it and select '''Open with''' > '''Rodin Editor'''.<br> |
| | + | The context component is then opened with the Rodin Editor.<br> |
| | | | |
| − | === Decomposition of a machine in sub-machines ===
| + | [[Image:RodinEditor_basicView2.png|600px]] |
| − | The purpose of this paragraph is to specify how to decompose a machine in sub-machines.
| |
| | | | |
| − | <font color="red">What about the <math>EXTENDS</math> clause and the hierarchy of machines? Is it necessary to flatten this hierarchy?</font> | + | On the figure above, you see the context component.<br> |
| | + | * The user is editing the axiom ''axm8'' and we see that the text is black and the background is grayed. This is the actually the overlay editor, that is open to edit the predicate contained by the axiom ''axm8''. |
| | + | * There are buttons in the left ruler to fold some elements. |
| | + | * The comments are preceeded by the character ' › ' to indicate where to click for edition. |
| | + | * The other attributes are inlined as grayed text. |
| | + | ** Note that : some attributes have type boolean, thus change value on click, and some attributes are choice attributes thus display a list of clickable values (see the image below) on click. |
| | | | |
| − | ==== About the variables ====
| + | [[Image:RodinEditor_basicView3.png|center]] |
| − | Some variables are needed by several sub-machines of the decomposition. As a consequence, these variables shall be replicated in the sub-machines. Beyond that, since it is not possible to ensure that such a variable will be refined in the same way in each sub-machine, they shall be given a special status (''shared'' variable), with the limitation that they cannot be refined.
| |
| | | | |
| − | We will specify in this section how to introduce the notion of ''shared'' variable in the Rodin platform, and how to check the associated rules.
| + | For more details, please go to the [[Rodin_Editor_User_Guide| Rodin Editor User Guide]]. |
| | | | |
| − | ===== Defining a variable as shared =====
| + | [[Category:Plugin]] |
| − | The following DTD excerpt describes the structure of a variable in the Rodin database:
| + | [[Category:User documentation]] |
| − | | |
| − | <pre>
| |
| − | <!ENTITY % NameAttDecl "name CDATA #REQUIRED">
| |
| − | <!ENTITY % CommentAttDecl "org.eventb.core.comment CDATA #IMPLIED">
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| − | <!ENTITY % IdentAttDecl "org.eventb.core.identifier CDATA #REQUIRED">
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| − | | |
| − | <!ELEMENT %variable; EMPTY>
| |
| − | <!ATTLIST %variable;
| |
| − | %NameAttDecl;
| |
| − | %CommentAttDecl;
| |
| − | %IdentAttDecl;
| |
| − | >
| |
| − | </pre>
| |
| − | | |
| − | A first possibility to tag a variable as ''shared'' would be to add a <tt>shared</tt> specific attribute, which would be set to <tt>true</tt> if and only if the variable is ''shared'':
| |
| − | | |
| − | <pre>
| |
| − | <ENTITY % shared "org.eventb.core.shared CDATA #REQUIRED">
| |
| − | | |
| − | <!ELEMENT %variable; EMPTY>
| |
| − | <!ATTLIST %variable;
| |
| − | ...
| |
| − | %shared; (false|true) #REQUIRED
| |
| − | >
| |
| − | </pre>
| |
| − | | |
| − | Another possibility would be to define a more generic attribute, which could take different values, according to the nature of the variable:
| |
| − | | |
| − | <pre>
| |
| − | <ENTITY % nature "org.eventb.core.nature CDATA #REQUIRED">
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| − | | |
| − | <!ATTLIST %variable;
| |
| − | ...
| |
| − | %nature; (0|1) #REQUIRED
| |
| − | >
| |
| − | | |
| − | <!-- The nature attribute encodes the kind of variable:
| |
| − | 0: private variable
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| − | 1: shared variable
| |
| − | -->
| |
| − | </pre>
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| − | | |
| − | The second option, which has the main advantage to be more evolutive, is retained here.
| |
| − | | |
| − | ===== Ensuring that a shared variable is not data-refined =====
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| − | A shared variable shall always be present in the state space of any refinement of the component.
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| − | The verification shall be added to those already performed by the static checker.
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| − | | |
| − | ===== <font id="var_partition">Partitionning the variables in the sub-machines of the decomposition</font> =====
| |
| − | It is assumed in this section that the events have been previously partitionned among sub-machines.
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| − | | |
| − | The following cases have to be taken into consideration when dealing with the variable distribution:
| |
| − | * If <math>v</math> is a variable that is only accessed by events of a given sub-machine <math>m</math>, then <math>v</math> is a ''private'' variable of <math>m</math>, and it shall be deplaced to <math>m</math>.
| |
| − | * If <math>v</math> is a variable that is accessed by events of distinct sub-machines <math>m_1, ..., m_n</math>, then <math>v</math> is a ''shared'' variable, and it shall be duplicated in all sub-machines.
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| − | | |
| − | If all the variables are ''shared'' at the conclusion of the partition, the end user shall be notified (it certainly means that the decomposition was not judicious).
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| − | | |
| − | ==== About the events ====
| |
| − | It shall be possible to simulate the way the ''shared'' variables are handled in the non-decomposed machine. This is precisely the purpose of the so-called ''external'' events.
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| − | | |
| − | We will examine in this section how to define such events in the Rodin platform, how to construct them, and how to enforce the rules that apply (in particular, these events cannot be refined).
| |
| − | | |
| − | ===== Identifying an event as external =====
| |
| − | An attribute is already defined, which is introduced below, to precise the nature of an event. A first solution would be to add another masked value (''eg.'' 4) to encode the ''external'' status.
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| − | | |
| − | <pre>
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| − | <!ENTITY % convergence "org.eventb.core.convergence">
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| − | | |
| − | <!ATTLIST %event;
| |
| − | ...
| |
| − | %convergence; (0|1|2) #REQUIRED
| |
| − | ...
| |
| − | >
| |
| − | <!--
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| − | The convergence attribute specifies which PO should be generated
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| − | for the combination event / variant:
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| − | 0: ordinary event, no PO
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| − | 1: convergent event, PO to show event decreases variant
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| − | 2: anticipated event, PO to show event doesn't increase variant
| |
| − | -->
| |
| − | </pre>
| |
| − | | |
| − | Another solution would be to add a distinct <tt>external</tt> attribute, which would be set to <tt>true</tt> if and only if the event is ''external'':
| |
| − | | |
| − | <pre>
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| − | <ENTITY % external "org.eventb.core.external CDATA #REQUIRED">
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| − | | |
| − | <!ATTLIST %event;
| |
| − | ...
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| − | %external; (false|true) #REQUIRED
| |
| − | >
| |
| − | </pre>
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| − | | |
| − | This solution is preferred because the notion of ''external'' event is totally orthogonal to the notion of convergence.
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| − | | |
| − | ===== <font id="build_external">Constructing an external event</font> =====
| |
| − | An ''external'' event shall be built for each event of the non-decomposed machine modifying ''shared'' variables.
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| − | | |
| − | As explained in [[Actions_(Modelling_Language)|the modelling language]], a non-deterministic action expressed as a variable identifier, followed by <math>\bcmin</math>, followed by a set expression, can always be translated to a non-deterministic action made of a list of distinct variable identifiers, followed by <math>\bcmsuch</math>, followed by a before-after predicate.
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| − | | |
| − | In the same manner, a deterministic action can always be translated to a non-deterministic action, as shown in the following example. Let's consider a machine with variables <math>x</math>, and <math>y</math>. Here is an action:
| |
| − | <center>
| |
| − | {{SimpleHeader}}
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| − | |<math>x \bcmeq y</math> is the same as <math>x \bcmsuch\ x' = y</math>
| |
| − | |}
| |
| − | </center>
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| − | | |
| − | As a consequence, we will first focus on the construction of an external event from an event of a sub-machine <math>m</math> whose action relies on <math>\bcmsuch</math>, and then derivate the construction from an event of <math>m</math> whose action relies on <math>\bcmeq</math> or <math>\bcmin</math>.
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| − | <br>
| |
| − | <math>e</math> is an event of <math>m</math>, <math>v_i</math> are ''private'' variables of <math>m</math>, <math>s_i</math> are ''shared'' variables between <math>m</math> and the destination sub-machine (''i.e.'' the sub-machine where the ''external'' event will be dispatched), <math>P,~P_i,~Q_i</math> are before-after predicates of <math>m</math>, and <math>G</math> is a predicate of <math>m</math>.
| |
| − | | |
| − | '''Generic construction for <math>\bcmsuch</math>'''
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| − | | |
| − | e
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| − | '''WHERE''' <math>G(v_1,...,v_n,s_1,...,s_m)</math>
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| − | '''THEN'''
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| − | <math>v_1,...,v_n,s_1,...,s_m \bcmsuch P(v1,...,v_n,s_1,...,s_m, v_1',...,v_n',s_1',...,s_m')</math>
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| − | | |
| − | The first step of the construction is to replace the ''private'' variables by parameters. Note that this step is purely fictive, because assigning an event parameter is not allowed!
| |
| − | | |
| − | e
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| − | '''ANY''' <math>x_1,...,x_n</math>
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| − | '''WHERE''' <math>G(x_1,...,x_n,s_1,...,s_m)</math>
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| − | '''THEN'''
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| − | <math>v_1,...,v_n,s_1,...,s_m \bcmsuch P(x1,...,x_n,s_1,...,s_m, x_1',...,x_n',s_1',...,s_m')</math>
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| − | | |
| − | The second step consists of adding guards to define the types of the parameters, if necessary. More precisely, a theorem shall be added for each parameter for which typing is required. The .bcm file associated to the non-decomposed machine shall be parsed in order to retrieve the typing information.
| |
| − | <font color="red">TODO: Some precisions and examples should be added here</font>.
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| − | | |
| − | The third and last step of the construction is to introduce an existantial quantifier to resolve the invalid assigment. <math>external\_e</math> is the newly built external event.
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| − | | |
| − | external_e
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| − | '''ANY''' <math>x_1,...,x_n</math>
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| − | '''WHERE''' <math>G(x_1,...,x_n,s_1,...,s_m)</math>
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| − | '''THEN'''
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| − | <math>s_1,...,s_m \bcmsuch \exists y_1,...y_n.P(x1,...,x_n,s_1,...,s_m, y_1,...,y_n,s_1',...,s_m')</math>
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| − | | |
| − | '''Derived construction for <math>\bcmsuch</math>'''
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| − | | |
| − | e
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| − | '''WHERE''' <math>G(v_1,...,v_n,s_1,...,s_m)</math>
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| − | '''THEN'''
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| − | <math>v_1 \bcmsuch P_1(v_1,...,v_n,s_1,...,s_m,v_1')</math>
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| − | ...
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| − | <math>v_n \bcmsuch P_n(v_1,...,v_n,s_1,...,s_m,v_n')</math>
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| − | <math>s_1 \bcmsuch P_{n+1}(v_1,...,v_n,s_1,...,s_m,s_1')</math>
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| − | ...
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| − | <math>s_m \bcmsuch P_{n+m}(v_1,...,v_n,s_1,...,s_m,s_m')</math>
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| − | | |
| − | It may alternatively be represented with a single predicate, which is an intersection of the P_1,...,P_{n+m} predicates:
| |
| − | | |
| − | e
| |
| − | '''WHERE''' <math>G(v_1,...,v_n,s_1,...,s_m)</math>
| |
| − | '''THEN'''
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| − | <math>v_1,...,v_n,s_1,...,s_m \bcmsuch P_1(v1,...,v_n,s_1,...,s_m,v_1') \land ... \land P_n(v_1,...,v_n,s_1,...,s_m,v_n') \land P_{n+1}(v_1,...,v_n,s_1,...,s_m,s_1') \land ... \land P_{n+m}(v_1,...,v_n,s_1,...,s_m,s_m') </math>
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| − |
| |
| − | It is then possible to build the external event, by following the same steps of construction than for the generic case:
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| − | | |
| − | external_e
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| − | '''ANY''' <math>x_1,...,x_n</math>
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| − | '''WHERE''' <math>G(x_1,...,x_n,s_1,...,s_m)</math>
| |
| − | '''THEN'''
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| − | <math>s_1,...,s_m \bcmsuch \exists y_1,...y_n.(P_1(x1,...,x_n,s_1,...,s_m,y_1) \land ... \land P_n(x_1,...,x_n,s_1,...,s_m,y_n) \land P_{n+1}(x_1,...,x_n,s_1,...,s_m,s_1') \land ... \land P_{n+m}(x_1,...,x_n,s_1,...s_m,s_m'))</math>
| |
| − | | |
| − | Or, after applying some simplification rules:
| |
| − | | |
| − | external_e
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| − | '''ANY''' <math>x_1,...,x_n</math>
| |
| − | '''WHERE''' <math>G(x_1,...,x_n,s_1,...,s_m)</math>
| |
| − | '''THEN'''
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| − | <math>s_1 \bcmsuch \exists y_1.(P_1(x1,...,x_n,s_1,...,s_m,y_1)) \land ... \land \exists y_n.(P_n(x_1,...,x_n,s_1,...,s_m,y_n)) \land P_{n+1}(x_1,...,x_n,s_1,...,s_m,s_1')</math>
| |
| − | ...
| |
| − | <math>s_m \bcmsuch \exists y_1.(P_1(x1,...,x_n,s_1,...,s_m,y_1)) \land ... \land \exists y_n.(P_n(x_1,...,x_n,s_1,...,s_m,y_n)) \land P_{n+m}(x_1,...,x_n,s_1,...s_m,s_m')</math>
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| − | | |
| − | '''Construction for <math>\bcmeq</math>'''<br>
| |
| − | Additional simplification rules apply:
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| − | If <math>P_i(x_1,...,x_n,s_1,...,s_m,y_i)</math> is equal to <math>y_i = Q_i(x_1,...,x_n,s_1,...,s_m)</math>, then <math>\exists y_i.P_i(x1,...,x_n,s_1,...,s_m,y_i)</math> is always true and shall be deleted.
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| − | | |
| − | If <math>P_i(x_1,...,x_n,s_1,...,s_m,s_i')</math> is equal to <math>s_i' = Q_i(x_1,...,x_n,s_1,...,s_m)</math>, and if there is no private variable (''i.e.'' there is no existantial quantifier on the right-hand side of the assigments), then <math>s_i \bcmsuch P_{n+i}(x_1,...,x_n,s_1,...s_m,s_i')</math> shall be rewritten as <math>s_i \bcmeq Q_i(x_1,...,x_n,s_1,...,s_m)</math>.
| |
| − | <br>
| |
| − | Proof obligations generated for deterministic actions are indeed more suitable than those generated for non-deterministic actions.
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| − | | |
| − | '''Construction for <math>\bcmin</math>'''<br>
| |
| − | Additional simplication rules apply:
| |
| − | If <math>P_i(x_1,...,x_n,s_1,...,s_m,s_i')</math> is equal to <math>s_i' \in Q_i(x_1,...,x_n,s_1,...,s_m)</math>, and if there is no private variable (''i.e.'' there is no existantial quantifier on the right-hand side of the assigments), then <math>s_i \bcmsuch P_{n+i}(x_1,...,x_n,s_1,...s_m,s_i')</math> shall be rewritten as <math>s_i \bcmin Q_i(x_1,...,x_n,s_1,...,s_m)</math>.
| |
| − | <br>
| |
| − | For a given set <math>S</math>, proving that <math>\exists x.x \in S</math> (proof obligation generated from <math>x \bcmsuch x' \in S</math>) is indeed not as "simple" as proving that <math>S \neq \emptyset</math> (proof obligation generated from <math>x \bcmin S</math>).
| |
| − | | |
| − | ===== Partitionning the events in the sub-machines of the decomposition =====
| |
| − | Let's first assume that the variables have been previously partitionned among sub-machines. The case where <math>e</math> is an event that accesses a ''private'' variable <math>v1</math> associated to a sub-machine <math>m1</math> and a ''private'' variable <math>v2</math> associated to a sub-machine <math>m2</math> cannot be successfully handled. As a consequence, the following sequence shall be followed:
| |
| − | * The events shall be first partitionned, as indicated by the end-user. More precisely, machines shall be created, according to this partition. At this step, the machines shall only contain the specified events. In particular, the <math>SEES</math> and <math>EXTENDS</math> clauses shall be empty.
| |
| − | * The Rodin platform shall then be able to distribute the variables, according to the event partition (see [[#var_partition|Variable partition]]).
| |
| − | * The Rodin platform shall be able to distribute the invariants, according to the variable partition (see [[#inv_partition|Invariant partition]]).
| |
| − | * If <math>e</math> is an event that modifies a ''shared'' variable <math>s</math> (''i.e.'' <math>s</math> is listed among the free identifiers on the left-hand side of an assignment), then an ''external'' event that modifies <math>s</math> shall be built from <math>e</math> in each sub-machine where <math>s</math> is accessed.
| |
| − | | |
| − | ''N.B.'' : Note that the construction of an ''external'' event depends on the ''source'' sub-machine (''i.e.'' the sub-machine containing the ''internal'' event <math>e</math> from which the ''external'' event is to be built) and on the ''destination'' sub-machine (''i.e.'' the sub-machine where the ''external'' event is to be built).
| |
| − | <br>
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| − | Building an ''external'' event from a given event <math>e</math> modifying a ''shared'' variable <math>s</math> and duplicating it in each sub-machine where <math>s</math> is accessed does not indeed entirely fit the requirements, as illustrated below: the sub-machine <math>M3</math> does not know the ''shared'' variable <math>s2</math> and the sub-machine <math>M1</math> does not know the ''shared'' variable <math>s4</math>.
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| − | | |
| − | <center>
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| − | [[Image:External_events.png]]
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| − | </center>
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| − | | |
| − | ===== <font id="convergence">Propagating the convergence status</font> =====
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| − | A sub-machine can be seen as a new abstract machine. As a consequence, the convergence status of a given event shall be propagated in the sub-machines as described below:
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| − | * An event tagged as ordinary in the non-decomposed machine shall remain ordinary in the sub-machine.
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| − | * An event tagged as convergent in the non-decomposed machine shall become ordinary in the sub-machine.
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| − | * An event tagged as anticipated in the non-decomposed machine shall remain anticipated in the sub-machine.
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| − | * An ''external'' event shall always be declared as ordinary.
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| − | | |
| − | See [[Events_(Modelling_Language)|the modelling language]] for precisions on the convergence status.
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| − | | |
| − | ===== Propagating the inheritance status =====
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| − | An event (''external'' or not) of a sub-machine shall always be declared as non-extended.
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| − | | |
| − | ===== Ensuring that an external event cannot be refined =====
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| − | The verification shall be performed by the static checker.
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| − | | |
| − | ===== Decomposing the initialization event =====
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| − | An initialization event shall be built in each sub-machine from the initialization event of the non-decomposed machine, and according the distribution of the variables among these sub-machines. The construction is detailed below. <math>initialization</math> is the initial event and <math>e</math> the built event, <math>x_i</math> are variables (''private'' or ''shared'') of the sub-machine containing <math>e</math>, <math>y_i</math> are variables of other sub-machines, P is a before-after predicate and G is a predicate.
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| − | | |
| − | initialization
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| − | '''WHERE''' <math>G(x_1,...,x_n,y_1,...,y_m)</math>
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| − | '''THEN'''
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| − | <math>x_1,...,x_n,y_1,...,y_m \bcmsuch P(x1,...,x_n,y_1,...,y_m,x_1',...,x_n',y_1',...,y_m')</math>
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| − | | |
| − | Only the variables of the considered sub-machine shall appear in the built initialization event; other variables shall become bound:
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| − | | |
| − | e
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| − | '''WHERE''' <math>G(x_1,...,x_n)</math>
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| − | '''THEN'''
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| − | <math>x_1,...,x_n \bcmsuch \exists z_1,...,z_m.P(x1,...,x_n,y_1,...,y_m,x_1',...,x_n',y_1,...,y_m')</math>
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| − | | |
| − | The derivated cases and simplification rules introduced during [[#build_external|the construction of the external events]] apply here as well.
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| − | | |
| − | ==== <font id="inv_partition">About the invariants</font> ====
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| − | We will see in this section how to distribute the invariants among the sub-machines, once the variables have been partitionned.
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| − | | |
| − | * Case 1: If <math>i</math> is an invariant only involving ''private'' variables, then it shall be copied in the sub-machines containing these variables.
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| − | * Case 2: If <math>i</math> is an invariant only involving ''shared'' variables, then it shall be copied in the sub-machines containing these variables.
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| − | * Case 3: If <math>i</math> is an invariant involving ''private'' variables and ''shared'' variables, then it shall not be copied.
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| − | | |
| − | <font color="red">If an invariant involving a ''private'' variable and a ''shared'' variable is used for typing and is not copied, a problem will be detected by the static checker.</font>
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| − | | |
| − | ==== About the variants ====
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| − | As mentionned [[#convergence|before]], there is no convergent event in sub-machines. As a consequence, there is no need to take the variants into consideration when performing the decomposition.
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| − | | |
| − | === Decomposition of a context in sub-contexts ===
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| − | The purpose of this paragraph is to specify how to decompose the contexts, according to the decomposition of the machines, and to establish how to link the sub-contexts to the sub-machines.
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| − | | |
| − | The hierarchy of contexts shall be first accumulated in a single context. More precisely, a new context shall be built (virtually or not), which contains all the carrier sets, constants and axioms of the hierarchy. This context is assumed to be the non-decomposed context from which the sub-contexts shall be built.
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| − | <br>Note that it may be necessary to rename some axioms when flattening the hierarchy.
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| − | | |
| − | <center>
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| − | [[Image:Flattening_contexts.png]]
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| − | </center>
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| − | | |
| − | Then, an empty context shall be built for each sub-machine <math>m</math>, which shall be linked to <math>m</math> through its <math>SEES</math> clause. Note that at the conclusion of the context decomposition, the sub-contexts that may be empty shall not be kept, and a <math>SEES</math> clause shall not be added to the associated sub-machines.
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| − | | |
| − | ==== About the carrier sets ====
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| − | A carrier set shall be visible from any sub-machine that references it, through a predicate (invariant or guard) or an assignment (action). In other terms, a carrier set of a non-decomposed context shall be copied in a sub-context if and only if this set appears in a predicate or assignment of the associated sub-machine.
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| − | | |
| − | ==== About the constants ====
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| − | Similarly, a constant of a non-decomposed context shall be copied in a sub-context if and only if it appears in a predicate or an assignment of the associated sub-machine.
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| − | | |
| − | ==== About the axioms ====
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| − | We will see in this section how to distribute the axioms among the sub-contexts, once the carrier sets and constants have been copied.
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| − | | |
| − | <font color="red">TODO</font>
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| − | | |
| − | == High-level Specification ==
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| − | The high-level specification details how the event model decomposition shall be integrated into the Rodin platform as a new feature, by linking to existing architecture.
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| − | | |
| − | === Definition of the decomposition ===
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| − | <font color="red">
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| − | It is necessary to first give a definition of the event model decomposition in the Rodin platform. Is it an Event-B project decomposition? Or, is it a decomposition performed from some well-identified machines and contexts of a given Event-B project?
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| − | </font>
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| − | | |
| − | === Configuration of the decomposition ===
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| − | The end-user shall be asked to parametrize the decomposition.
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| − | | |
| − | * Identifying the event model to be decomposed
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| − | * Identifying the sub-components to be created
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| − | * Specifying how to perform the decomposition (event partition)
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| − | * Asking for invariants and theorems that can be "forgotten" during the decomposition (because they are not required any longer by user)
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| − | | |
| − | === Execution of the decomposition ===
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| − | * Generating the sub-machines
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| − | * Generating the sub-contexts
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| − | * Actions, menus, buttons
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| − | * New project?
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| − | | |
| − | === Generation of the proof obligations ===
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| − | <font color="red">TODO</font>
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| − | * Generating the useful proof obligations
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| − | * Not "propagating" useless proof obligations
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| − | | |
| − | == Mathematical Approach ==
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| − | The purpose of this section is to mathematically formalize the Event-B decomposition previously specified, and by the way to remove the possible remaining ambiguity.
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| − | | |
| − | Let's define <math>\mathit{MACHINE}</math> as the set of all machine handles, <math>\mathit{EVENT}</math> the set of all events, and <math>\mathit{VAR}</math> the set of all variables.
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| − | | |
| − | * The distribution of the events of the non-decomposed machine among the different sub-machines (according to the end-user configuration) can be represented as with a partial function:
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| − | <math>\mathit{partition}\in\mathit{EVENT}\pfun\mathit{MACHINE}</math>
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| − | <br>For a given sub-machine <math>m</math>, <math>partition^{-1}[\{m\}]</math> is then the set of ''internal'' events of <math>m</math>.
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| − | * The access of a variable by a given event (according to the static-checker) can be expressed as:
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| − | <math>\mathit{access}\in\mathit{EVENT}\rel\mathit{VAR}</math>
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| − | <br>For a given sub-machine <math>m</math>, <math>(access;partition^{-1})[\{m\}]</math> is then the set of variables accessed by the events contained in <math>m</math>.
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| − | * The association of a variable with the events modifying this variable (according to the static-checker) can be specified as:
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| − | <math>\mathit{modify}\in\mathit{VAR}\rel\mathit{EVENT}</math>
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| − | <br>For a given sub-machine <math>m</math> and a variable <math>v \in (access;partition^{-1})[\{m\}]</math>, <math>modify[\{v\}]</math> is then the set of the events modifying <math>v</math>.
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| − | * The construction of the ''external'' events for a sub-machine can be represented with a relation:
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| − | <math>\mathit{extern}\in\mathit{MACHINE}\rel\mathit{EVENT}</math>
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| − | <br>It is computed as follows: <math>extern = (modify;access;partition^{-1}) \setminus partition^{-1}</math>
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| − | <br>Thus, the ''external'' events of a given sub-machine <math>m</math> are events modifying the variables accessed by the ''internal'' events of <math>m</math>, but they are not ''internal'' events of <math>m</math>.
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| − | | |
| − | === Example ===
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| − | The following example is taken from the [[#ancre_1|Event Model Decomposition]].
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| − | | |
| − | <center>
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| − | [[Image:Decomposition.png]]
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| − | </center>
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| − | | |
| − | A non-decomposed machine has been decomposed in two sub-machines <math>M1</math> and <math>M2</math>, as illustrated by the figure.
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| − | <br>According to the terminology, <math>in\_a</math> and <math>a\_2\_b</math> are ''internal'' events of <math>M1</math>, and <math>b\_2\_c</math> and <math>out\_c</math> are ''internal'' events of <math>M2</math>. Concerning the variables, <math>a</math> and <math>m</math> are ''private'' variables of <math>M1</math>, <math>c</math> and <math>p</math> are ''private'' variables of <math>M2</math>, and <math>b</math>, <math>r</math> and <math>s</math> are ''shared'' variables.
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| − | <br>The variables accessed by the ''internal'' events of <math>M1</math> are <math>a</math>, <math>m</math>, <math>b</math>, <math>r</math> and <math>s</math>. The events modifying these variables are <math>in\_a</math>, <math>a\_2\_b</math>, which both are ''internal'' events of <math>M1</math>, and <math>b\_2\_c</math>, which is an ''internal'' event of <math>M2</math>. Thus, according to the definition given before, <math>b\_2\_c</math> is an ''external'' event for <math>M1</math>. In the same manner, <math>a\_2\_b</math> is an ''external'' event for <math>M2</math>.
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| − | | |
| − | ''N.B.'': Note that the expression "is an ''external'' event for" is an extrapolation, and shall be literally interpreted as "should lead to the construction of an ''external'' event in".
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| − | | |
| − | == Bibliography ==
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| − | | |
| − | * J.R. Abrial, Mathematical Models for Refinement and Decomposition, in ''The Event-B Book'', to be published in 2009 ([http://www.event-b.org/abook.html lien externe]).
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| − | * J.R. Abrial, <font id="ancre_1">''Event Model Decomposition''</font>, Version 1.3, April 2009.
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| − | * M. Butler, <font id="ancre_2">Decomposition Structures for Event-B</font>, in ''Integrated Formal Methods iFM2009'', Springer, LNCS 5423, 2009 ([http://eprints.ecs.soton.ac.uk/16965/1/butler.pdf lien externe]).
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| − | [[Category:Design]] | |
| − | [[Category:Work in progress]] | |
