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

10.4 A System of Basic Transformations 313
¡ that is weak enough to tackle most of the practical cases. The search for
NoComChange¡
such a predicate is still going on.
As an example of an application of 6, consider a specification (A ¢ B ¢ C ¢ D)§ e© a¥ e© b
, e© c¥ e© d ¥ Sys p ¥ Sys . If the transformation condition is satisfied, this specification
can be transformed into (A ¢ B)§ e© a¥ e© b¥ e© c¥ e© d ¢ (C ¢ D)§ e© a¥ e© b¥ e© c¥ e© d ¥ Sys p ¥
. The application of two more transformation steps yields specification Sys e© a¥ e© (A§
e© c¥ e© d ¢ B§ e© a¥ e© b¥ e© c¥ e© d ¢ C§ e© a¥ e© b¥ e© c¥ e© d ¢ D)§ e© a¥ e© b¥ e© c¥ e© d ¥ Sys b¥ p Sys . The
¥
modification of the specification is visualised by the following Instance Structure Diagrams:
A B
C D
a
e d
¢
b e
Transformation
7
e BSpec
L¥ envs¥ Sys p ¥ Sys
c
e
e
¡
A B
C D
e BSpec ¥ envs¥ p Sys ¥ Sys
¢
¡
if ChSort(BSpece ¥ Sysp ) L ¤ ¨
§ =
According to 7 one may drop or introduce a hiding of non-involved channels. For
example, consider a specification BSpec¥ Sysp Sys B§ ¥ d© ¢ a¥ b© c , where BSpec A with
channel sort £
a¥ b¥ c¥ d¦ . This specification is transformation equivalent to £
g¦ ¥ ¥ e¥
(BSpec
f Sysp ¥ Sys . The Instance Structure Diagrams are
c
A B
a
b
c
d
a
¢
¡
c
A B
K¥ envs¥
Transformation 8
e BSpec L Sysp
¡ ¥ (L Sys
¦ K)¥ envs¥ Sys
¢
e BSpec p ¥ Sys ¨
According to 8 two successive channels hidings may be reduced to a single one. For
instance, BSpec £ £
¥ a¦ b¥ e¦ Sysp Sys ¥ (where BSpec is as defined in the example of 7)
and (BSpec £
¥ a¥ b¥ e¦ Sysp Sys ¥ are transformation equivalent.
a
a
d
d
c
b
e
a
b
b
c
c
d
a