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

9.5 A Computational Interleaving Semantics 273
(5)
(6)
(7)
second part ensures that BSpec e is built from the same instances, in the same
way, as BSpec p § § E1© P1 ¥¡ ¡ ¡ ¥ Er © Pr . Intuitively this means that the latter behaviour
specification is a ’decent’ descendant of the former one. BSpec p § § E1© P1 ¥¡ ¡ ¡ ¥ Er© Pr
denotes the syntactic substitution of each Pi by Ei in BSpec p . The precise definition
is given later in this subsection. Function Reset calculates, given an (extended)
behaviour specification, the corresponding initial specification. Reset is defined
later in this subsection.
e
¥ envs1¥ BSpec1 Sysp ¡ Conf ¥ Sys p e
BSpec ¥ 2 ¥ envs2 ¥
Sysp ¡ Conf ¥ Sys p
e
¢ BSpec1 BSpec e 2 ¥ envs1 envs2 Sys ¥ p ¡ Conf ¥ Sys p
¥ ¥ envs¥ ¡ Sys
L¥ envs¥
e p
BSpec Sys
p
Conf
e
BSpec Sys p Sys ¥ ¡ Conf p
¥ ¥ envs¥ Sys ¡
envs¥ ¥ Sys ¥ ¡ §
e p
BSpec Sys
p
Conf
e p
BSpec f Sys
p
Conf
Sys p and Sys are assumed to satisfy context conditions (1’) ¡ ¡ (15’) of Section 9.4.
We can now see why a system specification
¥ Sys BSpec¥ p Sys contains the empty-list
¥
part. This seemingly superfluous list allows us to consider a system specification as a
special kind of configuration, thereby simplifying our theory. By induction it is easy
to show that indeed ¥ SSpecifications Conf p . Note that the difference between a system
specification and a configuration is that system specifications can only describe systems
in their initial states, i.e. before initialisation has taken place. Configurations, on the
other hand, are also able to describe systems during execution or simulation.
As explained before, S p£ e denotes an extended process statement that still has to be executed
by some process object. S p£ e , an element of set Stat p£ e , is defined as
S p£ e :: S
ch!m(E1 ¥¡ ¡ ¡ ¥ En) ¡
ch?m(p1¥¡ ¡ ¡ ¥ pm ¡ E) ¡
m(E1 ¥¡ ¡ ¡ ¥ En)(p1¥¡ ¡ ¡ ¥ pm)
¡
S ¡ p£ e
; Sp
1
S ¡ p
1
2
or Sp
2
§ E S ¡ p
if E then S ¡ p
1 else S p
2 fi
do E then S ¡ p od
S ¡ p£ e
1 abort S p
¡
2
S p£ e
1 interrupt S p
2
¡ m(p1£ ¡ ¡£ pm) Sp£ e ¡
S ¡ p£ e
1 interrupted S p
2 ¥ Sp£ e
2
¡¡
Here, m(p1£ ¡ ¡ ¡£ pm) S p£ e indicates that the method body of method m is being executed
and that after successful termination of this execution the process has to resume its