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

274 Process Part of POOSL
execution at the place of the m(p1£ ¡ ¡ ¡£ pm) , after the output parameters are bound to variables
p1 ¥¡ ¡ ¡ ¥ pm and the local method variables have been popped from the stack. Statement
S p£ e
1
interrupted Sp2
¥ Sp£ e
2 denotes that Sp£ e
1
is the portion of S p
2
was interrupted (in the past) by Sp2
. Statement Sp£ e
2
that remains to be executed before the execution control is returned
to S p£ e
1 . denotes successful process termination. The three extended statements are
introduced to facilitate our semantics.
Now that we have defined the set Conf p of configurations, we will show how the set Act
of atomic actions looks like. We will distinguish the following three kinds of actions:
(1) The internal action, also known as the silent action, which is denoted as ¡ . This
action reflects an internal computation which cannot be observed by the system
environment.
(2) Send actions of the form ch!m§ data indicating that the system can send message m,
together with data data, on channel ch.
(3) Receive actions of the form ch?m§ data indicating that the system is willing to receive
message m with data data from channel ch.
When two processes exchange a message, a deepCopy of every message parameter is
passed from the sending process to the receiving one. The data part of the above send and
receive actions therefore consists of a list of deepCopies, one for each message parameter.
Every deepCopy will be represented by a minimal Sys-structure (see Paragraph 8.6), and
every data by a list of such structures.
¡ For each n we will let Strucn Sys£ min denote the set of lists of minimal Sys-structures
consisting of n elements. The set of all lists of minimal Sys-structures will be denoted
by Sys£ Struc min and will range data¥¡ ¡ ¡ over .
The set Act of actions can now be defined as
£
¡
¦
Act ¢¦
where , the set of all communication actions, is
£
£
data ch?m§ ¥ ¡ ¡ Sys£ ¦ ¡ ¦
¡ ch Chan m MName and data Struc min
data ch!m§ ¥ ¡ ¡ ¡ ¡ Sys£ ch Chan m MName and data Struc min ¦
¡ a¥¡ l¥¡ ¡ ¡ ¡ Elements of will be denoted as , and elements of Act as .
We now define what we mean by functions abstract action sort (AASort) and channel
sort (ChSort). Both functions are defined on a number of constructs. In general the
AASort of a construct is the set of all associated abstract communication actions. ChSort
calculates the set of associated channels. For process configurations both functions
have a particular meaning. The AASort of a process configuration is the set of abstract
communication actions corresponding to those communication actions that can ever