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Ivan LaneseComputer Science Department

University of BolognaItaly

Behavioural Theory for SSCC

Joint work with Luis Cruz-Filipe, Francisco Martins, Antonio Ravara and Vasco Vasconcelos

Univerisities of Lisbon, Portugal

Roadmap

SSCC

Behavioural theory

Program transformations

Conclusions

Roadmap

SSCC

Behavioural theory

Program transformations

Conclusions

Stream-based Service Centred Calculus

SSCC is a calculus for modelling services based on sessions and streams

One of the Sensoria core calculi– Follows the same thread of SCC and CaSPiS

SSCC provides operators for– Defining and invoking services

– Describing conversations (sessions) between services

– Orchestrating complex service systems

SSCC syntax

P ::= P jQ(ºa)P0recX :PX

9>>>>=

>>>>;

Standard operators

a ) Pa ( P

¾

Services

v:P(x)P

¾Conversations

streamP asf inQfeedv:Pf (x):P

9=

;Orchestration

SSCC services

Services are defined by their name a and their protocol P Service definition and service invocation are symmetric Invocations and definitions interact creating two session

endpoints executing their respective protocols

Sessions are not available when programming– Only runtime construct

a ) P ja ( Q ! (ºr)(r B P jr C Q)

SSCC conversations

Sessions can exchange information via input and output

We can imagine to extend conversations with all the typical session constructs (e.g., choice)

(ºr)(r B v:P jr C (x)Q) ! (ºr)(r B P jr C Q[v=x])

Orchestrating SSCC services

We propose the stream construct– Induces a clear style of programming– Good tradeoff between expressive power and structured

communication P and Q are concurrently executing f is a communication stream (i.e., a queue) from P to Q P can feed values inside f (feed v.P’)

– Non blocking – Values stored in the nearest stream

Q can read values from f (f(x).Q’)– Blocking– Reads from stream f

streamP asf inQ

A stream at work

streamfeedv:P asf = hi inf (x):Q! streamP asf = hvi inf (x):Q

! streamP asf = hi inQ[v=x]

Orchestrating 3 services

Invoke services a and b and use their results to invoke c

stream(a ( (x)feedx)j(b( (y)feedy)

asf = hi inf (z):f (w):c ( z:w:(t)feedt

Useful macros

Direct communications

b* v:P ,streamb( v:feed ² asf inf (z):P

b+(x)P ,streamb) (z):feedzasf inf (x):P

Roadmap

SSCC

Behavioural theory

Program transformations

Conclusions

Why a behavioural theory?

To understand the relationships between the different operators

To be able to reason axiomatically on systems To be able to prove the correctness of program

transformations and optimizations

Which behavioural theory?

We consider the classic bisimilarity approach– Processes should be able to mimik each other labelled

transitions

We have labels for session communications, service invocations, feeds, reads from stream, internal actions…

We choose full (substitution-closed) bisimilarity– Strong bisimilarity ~f for more basic transformations

– Weak bisimilarity ≈f allows optimizations» Abstracts away internal actions

≈≡'

A compositionality result

Strong and weak full bisimilarity are congruences– Capture the corresponding contextual equivalences

– Axioms can be applied to subterms

– Transformations can be applied to arbitrarily complex systems

The congruence result does not hold for strong/weak plain bisimilarity

We will present some useful axioms– We are not interested in a complete axiomatization

Structural congruence is a bisimulation

stream(º a)P asf =~v inQ ´ (º a)(streamP asf =~v inQ)if a =2 fn(Q) [ Set(~v)

streamP asf =~v in(º a)Q ´ (º a)(streamP asf =~v inQ)if a =2 fn(P ) [ Set(~v)

r ./ (º a)P ´ (º a)(r ./ P )

Standard rules for parallel composition, restriction and recursion

Additional scope extension rules

Session axioms

Different sessions are independent

Terminated sessions can be garbage collected(º r)D[[r . 0;r / 0]]» f D[[0;0]] if D does not bind r

r ./ (s ./ Qj P)» f s ./ Qj r ./ P if s 6= r

Stream axioms (1)

Stream = parallel composition + communication

Terminated streams can be garbage collected

streamP asf inQ» f P jQif f =2 fn(Q) and P does not contain feed

stream0asf inP » f P if f does not occur in P

streamP asf in(Q jQ0) » f(streamP asf inQ) jQ0 if f =2 fn(Q0)

Stream axioms (2)

Uncatched feeds are τ steps

Different streams are independent

streamP asf instreamP 0asg inQ» fstreamP 0asg instreamP asf inQ if f 6= g

streamP asf in0¼f P f feedv:Q ! Qg

Sessions vs streams

Feeds are unaffected by sessions

Session outputs are unaffected by streams

More in general

r ./ (feedvj P )» f feedvj r ./ P

streamvj P asf inQ» f vj streamP asf inQ

r ./ (Q j P ) » f Q j r ./ Pif Q contains no session input/ outputstreamR jP asf inQ» f R j streamP asf inQ

if R contains no feeds

Roadmap

SSCC

Behavioural theory

Program transformations

Conclusions

Object-oriented interaction pattern

UML sequence diagrams show the exchange of messages among components of a complex system…

…but have no session information

Session-oriented interaction pattern

There are two sessions:– r between A and B

– s between B and C

There are local communications in B

The session-oriented pattern in SSCC

The pattern can be implemented in SSCC

Communications between different sessions in B

exploit auxiliary services

SC, (ºb;c) ( A j B j C)A , b( w:(y)P B , (º b1;b2) ( B1 j B2 )

C , c ) (x)v:SB1 , b) (x)b1 * x:b2 +(y)y:Q

B2 , c ( b1 +(x)x:(y)b2 * y:R:

Optimization: using a subsession

The subsession pattern in SSCC

Now the SSCC implementation is:

A and C are as before

Two auxiliary communications have been eliminated

Two are still used

E , b) (x)(º b1)(c ( x:(y)b1 * y:R j b1 +(y)y:Q)

SC0 , (º b;c) ( A j E j C )

Is the program transformation correct?

The two diagrams can be proved full weak bisimilar

The proof exploits:

– Standard coinductive techniques

– Congruence

– Some axioms (session independence, garbage collection)

Since full weak bisimilarity is a congruence the

optimization can be applied in any context

Introducing streams

We can use a stream to avoid the remaining auxiliary communications

Correctness proof similar to the previous one

SC0 , (º b;c) ( A j G j C )G , b) (x)

streamc( x:(y)feedy:R as f in f (y):y:Q

Breaking sessions

Current technologies does not provide sessions– Only request and request/response primitives

– Correspond to sessions with fixed protocol

Useful to break sessions in smaller pieces– A long session may correspond to a sequence of

request/responses

– Next request/response name sent as continuation

Arbitrary sessions can not be broken preserving the semantics– Correct for all sequential sessions

– Sequentiality can be proved using a type system

Roadmap

SSCC

Behavioural theory

Program transformations

Conclusions

Conclusions

SSCC can model session-based communication patterns Behavioural theory allows to work axiomatically on

patterns Complex program transformations can be specified and

proved correct

Future work

On program transformations– Develop a methodology to drive the application of

transformations

– Apply to other case studies

On SSCC– Further understanding its behavioral theory

– Add kill and compensation primitives

On types– Type systems for deadlock freedom

– Type systems for termination

End of talk

streamivan ( question:(x):feedx asfin f (x):think