Structured Types

Modelling Structured Types

The Event-B mathematical language currently does not support a syntax for the direct definition of structured types such as records or class structures. Nevertheless it is possible to model structured types using projection functions to represent the fields/attributes. For example, suppose we wish to model a record structure C with fields 'e' and 'f' (with type E and F respectively). Let us use the following syntax for this (not part of Event-B):

$\begin{array}{lcl} \textbf{RECORD}~~~~ C &::& e\in E\\ && f \in F \end{array}$

We can model this structure in Event-B by introducing (in a context) a set $C$ and two functions $e$ and $f$ as constants as follows:

$\begin{array}{l} \textbf{SETS}~~ C\\ \textbf{CONSTANTS}~~ e,~ f\\ \textbf{AXIOMS}\\ ~~~~\begin{array}{l} e \in C \tfun E\\ f \in C \tfun F\\ \end{array} \end{array}$

Now, given an element $c\in C$ representing a record, we write $e(c)$ for the 'e' component of structure