~q O P E R A T I O N A L
SEMANTICS F O R CSP
(Extended Abstract)
Gordon Plotkin
The p r e s e n t work is intended to illustrate
semannics of p r o g r a m m i n g
CSP, of communicating
languages.
sequential
a method of giving the operational
As an example a v a r i a n t of Hoare's
processes
is considered
[Hoa].
At the same time
some attempt is made to develop an approach to language analysis
guiding principle
of simplicity of the abstract
syntax.
language,
following a
This idea is independent
of the semantic m e t h o d used and can just as well be combined with other approaches,
such as that of d e n o t a t i o n a l
The o p e r a t i o n a l
<F,T,+>,
of
semantics.
semantics
employs the well-known
where F (ranged over b y y) is a set of configurations
final
configurations
configuration
and ÷ c F x F is the t r a n s i t i o n
new is the specification
induction on the abstract
!o
<C0~>
<C0~g>
÷
<C0;Cl~>
Dijkstra~s
principle
relation.
and define the transition
relation by structural
<Co';Cl,g'>
g'
÷ <Cl,a'>
of simplicity we try to minim~se
CSP
[Dij].
Applying our
the number of syntactic categories
way and take guarded commands
that for example if b is a Boolean e x p r e s s i o n
another a p p l i c a t i o n
What is
For this we follow the
syntax by means of such rules as:
guarded command language underlies
in a non-artificial
further any
÷ <C0~'C~>
<C0;Cl,g> +
2.
A typical
(no c o m m a n d left to be executed).
of the transition
m o d e r n emphasis on structure
systemsn
and T c F is the set
relation.
could be <c~0>, where c is a c o m m a n d and ~ is a store;
store u could be a final configuration
Sequence
idea of transition
as 5eing themselves
commands
and c is a c o m m a n d so is b + c.
we do not wish to a l l o w n-ary syntactic constructions
so
As
(for
every n) as implied by this syntax for conditions:
__if b I + C 1 ~
Rather we regard this~
[
[
~ b n + Cn --fi
for each n, as a composite
the above binary guarding
and a unary conditional
..o
construction,
if c fi.
c::= a I skip
abort
(= derived)
The syntax for commands
I c;e
I if c fi
construction
b + c, a Dinary choice c o n s t r u c t i o n
I b => c I fail
I do c o d
is then
I c ~ c 1
from
c Q c
251
where a r a n g e s over p r i m i t i v e actions and h => c is a strong g u a r d i n g construction,
useful for concurrency, w h i c h does not a l l o w a n y interruption by any p r o c e s s
b e t w e e n the t e s t i n g of b and the first action of c.
The above w e a k g u a r d i n g can
be d e r i v e d from the strong one by:
b ÷ c =
def
b => nil; c
This can be e x p r e s s e d b y the rules:
Guarding
i.
<c, ~> ÷
y
<b => c,o> + 7
(if b is true in ~)
2.
<b => c,a> ÷ failure
(if b is false in o)
w h e r e failure is a n e w c o n f i g u r a t i o n standing for failure.
are s p e c i f i e d a l o n g similar lines
The other constructs
(and another n e w configuration,
abortion,
is
needed).
The advantage of the strong g u a r d i n g is that it allows the r e s o l u t i o n of
c o m p l e x g u a r d e d commands in CSP c o n t a i n i n g input commands,
into h =>
such as b~ A ? x ÷ c,
(A ? x; c) and that in turn avoids the r e d u n d a n c y of input commands
a p p e a r i n g in two places in the syntax.
The most complex construct in CSP is the p a r a l l e l c o m m a n d
[Pl::c11[---llPn::Cn]
where, of course, the c. can p e r f e c t l y well c o n t a i n further p a r a l l e l commands.
l
We v i e w this as a b l o c k (with II r e p l a c i n g ~) and r e g a r d the p r o c e s s identifiers,
Pi' as analogous to label identifiers;
then the scope of the Pi can he taken,
f o l l o w i n g the U s u a l rules, as the whole of the block.
With this idea we can
analyse the p a r a l l e l conlmand into a binary p a r a l l e l construction,
cIle and a u n a r y
labelling c o n s t r u c t i o n P::c and a b i n a r y d e c l a r a t i o n c o n s t r u c t i o n p r o c e s s P~c as
follows
p r o c e s s PI~...; p r o c e s s Pn ~
begin
P1::cl
ii---[I ~ ::c
n
n
end
(where
begin
...
end
are
just
a pair
of
brackets).
And we have a simple syntax
for CSP
C: := (guarded c o m m a n d construction)
c II e I P::c
I process P; c
I P?r
I Q.'w I
252
where
r ranges
o~er
a n d we have o m i t t e d
processes.
a set o f input o p e r a t i o n s
certain
details
and w over a set of o u t p u t o p e r a t i o n s
relating
We h a v e a l s o o m i t t e d v a r i a b l e
to n o n - i n t e r f e r e n c e
declarations,
between parallel
process
arrays or g u a r d e d
c o m m a n d s w i t h ranges.
For the o p e r a t i o n a l
transition
and ÷c
systems,
semantics
<r,T,M,+>
w i t h their
intuitive
for the g u a r d e d
- an i n t e r n a l
idea of l a b e l l e d
(= c o m m u n i c a t i o n s )
are t h e same as before,
F o r C S P the a p p r o p r i a t e
but
messages
are:
a c t i o n of a p r o c e s s
P ? v
- P sends v to an u n k n o w n
Q I v
- an u n k n o w n
P,Q
commands
for the messages.
meanings
P,Q ? v - Q r e c e i v e s
the w e l l - k n o w n
w h e r e n o w M is a set of m e s s a g e s
F × M x F.. The r u l e s
w i t h an m above the a r r o w s
we e m p l o y
agent
agent
sends a value v to Q
v from P
I v - P sends v to Q.
Here are some t y p i c a l
Output
<Q
rules
Q:v
~ w,0>-=---9~
Labelling
<c~0>
P?v
(where v is the v a l u e
)<ca j,>
transmitted
b y w given store
~)
(if P # Q)
< Q : : c , ~ > "-p'Q?V 2 < Q : : c ' , ~ ' >
p~
Communication
<C0'G> p,Q?v
~<c0,
<%1 lh,o>
This t r e a t m e n t
w o u l d require
omits
cQnsideration
a little
the c o n f i g u r a t i o n s ,
additional
of Hoare's
this k i n d of o p e r a t i o n a l
s p e c i f y one step of e x e c u t i o n s
are m a n y choices
choice
semantics
in general
and does not in g e n e r a l
which
these are i n t e n d e d
to
to b e the
and the usual d e n o t a t i o n a l
semantics.
and do not say h o w to p u t these t o g e t h e r
for two such b e h a v i o u r s
and we r e m a i n n e u t r a l
semantics
specify
convention,
F i n a l l y we note a g r e a t d i f f e r e n c e
or w h a t it means
denotational
)<cl, O >
(One adds a t h i r d c o m p o n e n t
labels;
processes.)
between
o t h e r h a n d any normal
termination
complication.
We o n l y
to m a k e up g l o b a l b e h a v i o u r s
.,Q.v
~ ><e0'IIh',°'>
n a m e l y a set of p r o c e s s
set of labels of all t e r m i n a t e d
There
~><Cl,0 ~
between
both automatically
all the d e t a i l s
to be equal.
them.
On the
reflects
of the e x e c u t i o n
such a
sequences.
References
[Dij]
Dijkstra,
[Hoa]
Hoare~ C.A.R~ (1978)
No. 8, 666-677.
E.W.
(1976)
A Discipline
Communicating
of Programming.
Sequential
Prentice-Hall.
Processes~
CACM,
vol.
21,