Specification of Reactive Hardware/Software Systems - Electronic ...

234 Introduction to the Semantics of POOSL
in advance, which means that it establishes a predefined correctness relation between the
involved specifications. A formal proof of correctness can only be made if the semantics
of specifications and the semantics of correctness relations are made precise.
The correctness of transformations is often based on equivalent externally observable
behaviour. Since denotational semantics typically emphasise describing systems in terms
of their external behaviour, they are often considered a good basis for the support of
transformations. However, as languages become more complicated, the creation of an
appropriate denotational semantics becomes more and more difficult. This especially
applies to parallel (object-oriented) languages. On the other hand, operational semantics,
and in particular structural operational semantics, have proven to be very fruitful.
By defining correctness relations directly on top of an operational semantics, much of
the need for denotational semantics has been side-stepped [Hen90].
Tool Support
Simulator tools, compiler tools (providing prototype implementations) and verification
tools are of great use
to be able to validate formal specifications against informal requirements;
to analyse the (dynamic) behaviour of specifications;
to implement specifications;
to formally verify specifications.
Since an operational semantics describes how specifications are executed rather than
just what the results of the execution should be, tool implementers can greatly benefit
from such a semantic description. A nice demonstration of this is given in [vE89] where
a set of simulator functions for Hippo (a LOTOS simulator) is systematically derived
from the operational semantics of LOTOS. Currently a simulator for POOSL is under
development. Our experience is that the formal semantics (described in the following
chapters) is of great value for the construction of the simulator. It was possible to create
an almost one-to-one mapping from the elements of the operational semantics to the
elements of the implementation of the simulator.
7.4 Mathematical Preliminaries
In this section we will introduce the basic mathematics that is assumed to be known in
Chapters 8, 9 and 10.
7.4.1 Sets
Sets and their Definitions
A set or collection is a finite or infinite union of mathematical objects 3 . These objects
3 This is only an informal and naive explanation. A precise definition would be beyond the scope of
this thesis.