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

10.4 A System of Basic Transformations 317
creation of a new cluster class. For example, suppose we are given a system
specification
¢ B(E2)¥ A(E1) Sysp Sys and assume we want to replace A(E1) ¢ B(E2) by some cluster
¥
instance Cc ¥ (E1 E2). Then, according to the condition of 13 , the class definition of Cc should be of the form
cluster class C c P1 ¥ P2
communication channels ch1 ¡ ¡ chk
message interface l a 1 ¡ ¡ la l
behaviour specification BSpec p
where BSpec p is such that BSpec p § § E1© P1 ¥ E2© P2 A b (E1) ¢ B b (E2). We can now distinguish
three cases
(1) Sys p contains a class C c P1 ¥ P2 of the above form. In this case we are done, and the
replacement can be performed.
(2) Sys p contains a class with class name C c but is not of the required form. In this
case the replacement cannot be performed, unless a class name different from C c
is chosen.
(3) Sys p does not contain a class with class name C c . In this case, the class can be added
to Sys p to obtain a new system of process classes, say Sys p ¡ . For BSpec p , behaviour
expression A(P1) ¢ B(P2) can be chosen. Channels ch1 ¡ ¡ chk and abstract actions
l a 1 ¡ ¡ la l are determined by the ChSort respectively the AASort of BSpecp . Since Sys p
and Sysp are non-conflicting, we have by 12 that ¡ ¢ B(E2)¥ A(E1) Sysp Sys
¢
¡
¥
¢ B(E2)¥ A(E1) Sysp ¥ Sys . Since Sys ¡ p then contains class C ¡ c ¥ P2 P1 which is of the
correct form, case (i) applies and thus ¢ A(E1) B(E2) can be replaced by Cc ¥ (E1 E2).
If we assume that system A(E1) ¢ B(E2)¥ Sys p ¥ Sys is represented by the left-hand side
of the following picture, then an Instance Structure Diagram of the transformation
equivalent system C c (E1 ¥ E2)¥ Sys p ¡ ¥ Sys is given by the right-hand side.
c d
A B
a
Transformation 14
(i) Cb 1 (E1
¡ ¥ Er)§ f1 ¥ ¥ Sys ¥¡ ¡ p ¥ Sys
if
b
¢
¡
¢
¡
C c
c d
A B
a
C b 2 (E1 ¥¡ ¡ ¡ ¥ Er)§ f2 ¥
b
¥ Sys p Sys ¥
(1) (a) Process class Cb
1 ¥¡ ¡ ¡ ¥ xr x1 contains a message-send statement
ch!m(E¡1
¥¡ ¡ ¡ ¥ E¡n ).