Translating Orc Features into Petri Nets and the Join Calculus

Translating Orc Features into Petri Nets and the Join Calculus

Hernán MelgrattiIMT Lucca Institute for Advance Studies

Joint Work with

Roberto Bruni and Emilio Tuosto

WS-FM 2006 Hernán Melgratti@IMTLucca-

Aims

To distill Orc primitives Orc is an orchestration language

•It is a process calculus

•It does not provide any explicit mechanism for name creation


Roadmap

Is it an Orc process an ordinary Petri net?

Place / transition Petri nets are not enough•The need of distinguishing different

evaluations of the same expression

•The need of killing executions So, we encode Orc into the Join

calculus


Orc in one slide Basic services or sites: M,M1,M2,…

•Providing functionalities Site call: M(p0,…,pn)

•Return at most one result Pipeline: f>x>g

•Sequential composition (x occurs bound in g) Symmetric Parallelism: f|g

• Independent computation Asymmetric Parallelism: g where x:f

•x occurs bound in f Recussion: E(q0,…,qn) f, and E occurs

in f


Orc by example [KCM06]

CNN and BBC are news services CNN(d)

•It may return 0 or 1 value CNN(d) | BBC(d)

•May produce 0, 1, or 2 values (CNN(d) | BBC(d)) > x > email(a,x)

•email may be called 0, 1, or 2 times email(a,x) where x:(CNN(d)| BBC(d))

•email is called at most one


Orc into Petri Nets

1-answer 0-answer

call

return

Site invocation


Orc into Petri Nets

1-answer 0-answer

call

return

Site invocation f > x > g


Orc into Petri Nets

1-answer 0-answer

call

return

Site invocation

f

g

f > x > g


Orc into Petri Nets

1-answer 0-answer

call

return

Site invocation

Actually we need coloured

tokensx

x

f

g

f > x > g


Orc into Petri Nets

1-answer 0-answer

call

return

Site invocation

f

g

f | g f > x > g


Orc into Petri Nets

1-answer 0-answer

call

return

Site invocation

f

g

f g

f > x > g f | g


Orc into Petri Nets

1-answer 0-answer

call

return

Site invocation

f

g

f g

f > x > g f | g


Orc into Petri Nets

1-answer 0-answer

call

return

Site invocation

f

g

f g

f > x > g f | g


An Orc Process as a PN

(CNN(d) | BBC(d))> x > email(a,x)



1-answer 0-answer 1-answer 0-answer

Call_CNN Call_BBC




1-answer 0-answer

Return_CNN

1-answer 0-answer

Call_CNN Call_BBC

Return_BBC




1-answer 0-answer

Return_CNN

1-answer 0-answer

Call_CNN Call_BBC

Return_BBC


1-answer 0-answer

Return_Email

Call_Email


Mapping the Asym. composition

f where x: g

f g



f where x: g

f g



f where x: g

f g



email(a,x) where x:(CNN(d)| BBC(d))



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer

Call_CNN Call_BBC1-answer 0-answer

Return_Email

Call_Email



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email

lock


But it doesn’t work

email(a,x) where x:(CNN(d)| BBC(d))f > d >



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email

f > d >

lock



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email

f > d >

lock



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email

f > d >

lock



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email

f > d >

lock



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email

f > d >

lock



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email

f > d >

lock



Return_BBC


1-answer 0-answer

Return_CNN

1-answer 0-answer


Return_Email

Call_Email

f > d >

lock

•We should kill the running computation (i.e., remove tokens from the net). •This can be done by using inhibitor or reset arcs

•In any case we sequentialise several evaluations of the same expression


Join

Join processes can be seen as dynamic and reconfigurable, coloured nets


Join

Join processes can be seen as dynamic and reconfigurable, coloured netsa

x

b

x

ax xb


Join


x

b

x

ax xb

ac

defin aa | ac

a

x

b

x

ax xb

b

def

in ab | cb

bc

a

x

b

x

ax xb

a

defin aa | cb

bc


Join


x

ax def cy yx in cc

c

y

x

cy


Join


x

ax def cy yx in cc

ab

def

c

y

x

cy

in aa | ab

a

x

ax def cy yx in cc

b

def

c

y

x

cy

in ab | cc

c yc

y

cy ay


Orc into Join

f

w

g

z

Any evaluation of g is done on a fresh

copy of the net

wv {g}zdef

v

in {f}w

{ f > x > g }z


Orc into Join

f

w

g

z

wv {g}zdef in {f}w

v

{ f | g }z

f g

z

{f}z | {g}z

f

w

v

g

v

valx

wv | tok valx def in {f}w | {g}z | tok

{ f where x: g }z{ f > x > g }z


Orc into Join

Site invocation

{ CNN(d) }z

Using the continuation style

CNN(d,k)

kv zvdef in CNN(d,k)

We can receive more

than one answer for a

call

kv | tok zvdef in CNN(d,k) | tok


We don’t get exactly the same behaviour

When x is chosen g is killed

After one x is chosen, all other value produced by g is ignored

After receiving one answer, the sender is blocked

Only one received answer is considered

CNN(d)

kv | tok zvdef in CNN(d,k) | tok

wv | tok valx def in {f}w | {g}z | tok

f where x: g


Correspondence

Theorem: Let O be an Orc Program and {O} its encoding in Join. Then, O {O} when considering the non killing asymmetric composition.


Final Remarks

The encoding highlights the fact that Orc primitives involve dynamic creation of names

Pruning of asymmetric composition is an operation not common in PC•Is it realistic in a distributed setting?

•This can be seen as equivalent to the disabling of input ports

Documents

Translating Orc Features into Petri Nets and the Join Calculus