# D23 Decomposition

# Overview

The Event-B model decomposition is a new feature in the Rodin platform.

Two methods have been identified in the DEPLOY project for model decomposition: the *shared variable* decomposition (or A-style decomposition), and the *shared event* decomposition (or B-style decomposition). They both answer to the same requirement, namely the possibility to decompose a model <math>M</math> into several independent sub-models <math>M_1, ...,M_n</math>.

Academic (ETH Zurich, University of Southampton) and industrial (Systerel) partners were involved in the specification and development of model decomposition. Systerel, which could have useful discussions with Jean-Raymond Abrial on the topic, was more especially responsible for the A-style decomposition. The University of Southampton, where Michael Butler is professor, was in charge of the B-style decomposition.

# Motivations

One of the most important feature of the Event-B approach is the possibility to introduce additional details such as new events and data during refinement steps.

Therefore, the reﬁnement process entails an increasing complexity of a model, where one has to deal with a growing number of events, state variables, and consequently proof obligations.
This is well illustrated in the *Event build-up* slide of the Wright presentation during the Rodin Workshop 2009.

The purpose of the Event-B model decomposition is precisely to give a way to address such a difficulty, by cutting a large model <math>M</math> into smaller sub-models <math>M_1, ..., M_n</math>. The sub-models can then be refined separately and more comfortably than the whole. The constraint that shall be satisfied by the decomposition is that these refined models might be recomposed into a whole model <math>MR</math> in a way that guarantees that <math>MR</math> refines <math>M</math>.

The model decomposition leads to some interesting benefits:

- Design/architectural decision. It applies in particular when it is noticed that it is not necessary to consider the whole model for a given refinement step, because only a few events and variables are involved instead.
- Complexity management. In other words, it alleviates the complexity by splitting the proof obligations over the sub-models.
- Team development. More precisely, it gives a way for several developers to share the parts of a decomposed model, and to work independently and possibly in parallel on them.

Note that the possibility of team development is among the current priorities for all industrial partners. The model decomposition is a first answer to this issue.

# Choices / Decisions

The main decision concerning the implementation of the Event-B model decomposition in the Rodin platform is to make available both decomposition styles (*shared variables* and *shared events*) through one single plug-in. These approaches are indeed complementary and the end-user may take advantage of the former or of the latter, depending on the model, e.g., the *shared variables* approach seems more suitable when modelling parallel system and the *shared events* approach seems more suitable when modelling message-passing distributed systems.

Choices, either related to the plug-in core or to the plug-in graphical user interface, have been made with the following constraints in mind:

- Planning. Some options, such as using the Graphical Modelling Framework for the decomposition visualization, or outsourcing the context decomposition, have not been explored (at least in the first instance), mainly because of time constraints (in the DEPLOY description of work, the decomposition support is planned for end of 2009).
- Easy-to-use (however not simplistic) tool. It applies on the one hand to the tool implementation (decomposition wizard, configuration file to replay the decomposition) and on the other hand to the tool documentation (the purpose of the user's guide is to provide useful information for beginners and for more advanced users, in particular through a
*Tips and Tricks*section). - Modularity and consistency. In particular, the developments have not been performed in the Event-B core. Instead the Eclipse extension mechanisms have been used to keep the plug-in independent (e.g., the static checker, the proof obligation generator and the editor have been extended).
- Performance. The decomposition tool should perform in reasonable time and memory, compared to other Rodin plug-ins.
- Recursivity. It must be possible to decompose a previously decomposed model.

Other technical decisions are justified in the specification wiki pages.

# Available Documentation

The following wiki pages have been respectively written for developers and end-users to document the Event-B model decomposition:

- Event model decomposition specification.

- Decomposition plug-in user's guide.

# Planning

The decomposition plug-in has been available since release 1.2 of the platform (initial version).

A further version allowing to edit an existing decomposition configuration is planned with release 1.3 of the platform.