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

246 Data Part of POOSL
which have to be satisfied and which cannot be described in BNF. In this section we will
informally 2 describe the context conditions with respect to a system Sys of data classes.
The conditions are the following:
(1) All class names in Sys are different.
(2) All instance variable names in a class definition are different.
(3) All method names of a class are different.
(4) All parameter and local variable names in a method definition are different.
(5) Every variable used in a method body is either an instance variable of the corresponding
class, a method parameter, or a local method variable.
(6) The class referred to by any new expression is contained in Sys.
8.5 A Computational Semantics
8.5.1 Informal Explanation
A computational semantics is a special kind of operational semantics and is specified by
a transition system together with a semantic function. A transition system is an ordered
pair £ Conf where Conf is a set of configurations ¥ 3 £ and where denotes a transition
relation, i.e. a binary relation on Conf. In general, a configuration is of the form S¥ I
representing that some statement S is to be executed in the context of information I.
(£ Transition relation ) describes how this execution takes place. The intuitive meaning
of transition
£ S¡ ¥ I¡ is that statement S with information I leads to statement S¡
S¥ I
I¡ with information in a single computation step (also called transition step).
The transition relation is defined by a collection of inference rules (see also Subsection
7.4.5). An inference rule is of the general form
S1 ¥ I1 £
I¡ S¡1 ¥¡ ¡ ¡ ¥ 1 ¥
£ S¡ ¥ I¡ I S¥
Sn ¥ In £
S¡n ¥ I¡ n
if condition
A rule has zero or more premises and one conclusion. A rule tells us how we can deduce
a new transition (the conclusion) from the old ones (the premises). A rule may have a
condition which has to be fulfilled whenever the rule is to be applied.
Rules without premises are called axioms. An axiom tells us what is considered to be a
basic transition. Usually, the solid line is omitted when a rule is an axiom. So, an axiom
has the general form
I £ S¥
2Context conditions can also be described in a formal way. See for instance the ’static semantics’ of
CRL [GP95].
3Configurations are also called execution states, see Paragraph 6.6.3.6.
S¡ ¥ I¡ if condition