Event Model Decomposition

Introduction

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 $A$ into sub-models $A_1, ..., A_n$, which can be refined separately and more confortably than the whole.

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 $C$ in a way that guarantees that $C$ refines $A$. An event-based decomposition of a model is detailed in 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.

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.

Terminology

• Event model decomposition: The decomposition of a model, as defined in the modelling language, in sub_models.

As illustrated in the figure below, a model can contain contexts, machines, or both. The events are contained in the machines, as well as the variables on which they act, the invariants constraining these variables, and optionnally the variants. The notion of model decomposition is then an extrapolation for the notion of machine decomposition.

• Shared variable: A variable of a given model which is accessed (read/written) by several distinct events.
• External event: An event of a sub-model simulating the way the read (but not written) variables of a sub-model are handled in the initial model.

Bibliography

• J.R. Abrial, Mathematical Models for Refinement and Decomposition, in The Event-B Book, February 2007.
• J.R. Abrial, Event Model Decomposition, Version 1.3, April 2009.
• M. Butler, Decomposition Structures for Event-B, in Integrated Formal Methods iFM2009, Springer, LNCS 5423, 2009 (lien externe).