Nested Commits for Mobile Calculi: Extending Join

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Nested Commits for Mobile Calculi Extending Join

• Roberto Bruni, Hernán Melgratti and Ugo Montanari

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Motivation

• To develop a process description language with
  primitives for agreements or negotiations
• Multiway (several parties can start separately
  but commit on reached agreement)
• Non-perfect compensations (certain actions cannot
  be undone)
• Programmable abort / compensation
• Different levels of abstraction

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Committed Join (cJoin)

• Join primitives for negotiations
• Syntax

P,Q 0 x?y? def D in P PQ D,E
J?P D?E J,K x?y? JK
Processes
Definitions
Patterns
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Committed Join (cJoin)

• Join primitives for negotiations
• Syntax

Messages
M,N 0 x?y? MN P,Q 0 x?y? def D
in P PQ D,E J?P D?E J,K x?y?
JK
Processes
Definitions
Patterns
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Committed Join (cJoin)

• Join primitives for negotiations
• Syntax

Messages
M,N 0 x?y? MN P,Q M def D in P
PQ D,E J?P D?E J,K x?y? JK
Processes
Definitions
Patterns
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Committed Join (cJoin)

• Join primitives for negotiations
• Syntax

Messages
Programmable abort
M,N 0 x?y? MN P,Q M def D in P
PQ abort PQ D,E J?P D?E J?P J,K
x?y? JK
Processes
Definitions
Patterns
Merge definition
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Committed Join (cJoin)

• Operational Semantics (CHAM Style)

0 ?
PQ ? P,Q
D?E ? D,E
def D in P ? D?dn(D) , P?dn(D) range(?) fresh
J? P, J? ? J? P, P?




heating and cooling
reaction
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Committed Join (cJoin)

• Operational Semantics (CHAM Style)

0 ?
PQ ? P,Q
D?E ? D,E
def D in P ? D?dn(D) , P?dn(D) range(?) fresh
J? P, J? ? J? P, P?
PQ ? P , ?? Q?



Contract P evolves in isolation
Compensation Q is kept frozen
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Committed Join (cJoin)

• Operational Semantics (CHAM Style)

0 ?
PQ ? P,Q
D?E ? D,E
def D in P ? D?dn(D) , P?dn(D) range(?) fresh
J? P, J? ? J? P, P?
PQ ? P , ?? Q?
Mdef D in 0 ,?? Q? ? M


Global Resources
Commit
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Committed Join (cJoin)

• Operational Semantics (CHAM Style)

0 ?
PQ ? P,Q
D?E ? D,E
def D in P ? D?dn(D) , P?dn(D) range(?) fresh
J? P, J? ? J? P, P?
PQ ? P , ?? Q?
Mdef D in 0 ,?? Q? ? M
abort P ,?? Q? ? Q

Compensation on Abort
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Committed Join (cJoin)

• Operational Semantics (CHAM Style)

0 ?
PQ ? P,Q
D?E ? D,E
def D in P ? D?dn(D) , P?dn(D) range(?) fresh
J? P, J? ? J? P, P?
PQ ? P , ?? Q?
Mdef D in 0 ,?? Q? ? M
abort P ,?? Q? ? Q
J1Jn?P, ?i Ji?, Si,?? Qi? ? J1Jn?P, ?iSi, P?, ? ?iQi?
Merge n ongoing contracts
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Committed Join Features

• Commit means termination

M def D in 0 ,?? Q? ? M
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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit

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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation

abort P ,?? Q? ? Q
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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)

• ,J1J2 ?P, J1t P1 Q1, J2t P2 Q2 ?
• ,J1J2 ?P, Pt P1 P2 Q1 Q2

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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)
• Multi-level nesting

P1 Q1 P2Q2 Q
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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)
• Multi-level nesting

P1 Q1 P2Q2 Q ? M1 P2Q2
Q
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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)
• Multi-level nesting

P1 Q1 P2Q2 Q ? M1 P2Q2
Q ? M1 M2 Q
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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)
• Multi-level nesting

P1 Q1 P2Q2 Q ? M1 P2Q2
Q ? M1 M2 Q ? M1 M2
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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)
• Multi-level nesting

P1 Q1 P2Q2 Q ? abort P1
Q1 P2Q2 Q

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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)
• Multi-level nesting

P1 Q1 P2Q2 Q ? abort P1
Q1 P2Q2 Q
? Q1 P2Q2 Q

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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)
• Multi-level nesting

P1 Q1 P2Q2 Q ? abort P1
Q1 P2Q2 Q
? Q1 P2Q2 Q
? abort Q1 P2Q2
Q
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Committed Join Features

• Commit means termination
• Global resources produced inside a negotiation
  are available at commit
• Explicit abort and compensation
• Cooperation between contracts are given by
  merging definitions (multiway contracts)
• Multi-level nesting

P1 Q1 P2Q2 Q ? abort P1
Q1 P2Q2 Q
? Q1 P2Q2 Q
? abort Q1 P2Q2
Q ? Q
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Example I Hotel Booking
H ? def WaitBooking? ? ? def
request?o? ? o?? price?? ? price??
confirm?v? ? BookedRoom?v? ?
price?? ? abort in offeringRoom
?request,confirm? Q ? BookedRoom?v?
? in WaitBooking? ?
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Example I Hotel Booking
H ? def WaitBooking? ? ? def
request?o? ? o?? price?? ? price??
confirm?v? ? BookedRoom?v? ?
price?? ? abort in offeringRoom
?request,confirm? Q ? BookedRoom?v?
? in WaitBooking? ? C ? def
BookingHotel? ? ? def hotelMsg ?r,c? ? def
offer?? ? c?visa? HotelFound
? offer?? ? abort in r?offer?
in searchRoom ?hotelMsg? Q in
BookingHotel? ?
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Example I Hotel Booking
H ? def WaitBooking? ? ? def
request?o? ? o?? price?? ? price??
confirm?v? ? BookedRoom?v? ?
price?? ? abort in offeringRoom
?request,confirm? Q ? BookedRoom?v?
? in WaitBooking? ? C ? def
BookingHotel? ? ? def hotelMsg ?r,c? ? def
offer?? ? c?visa? HotelFound? ?
? offer?? ? abort in
r?offer? in searchRoom ?hotelMsg? Q
in BookingHotel? ? HB ? def
searchRoom?hm? offeringRoom ?r,c? ? hm?r,c?
in H C
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Example I Hotel Booking
, WaitBooking? ? , BookingHotel ? ? ? ? ,
, offeringRoom?request,confirm? Q , ,
searchRoom?hotelMsg? Q ? , ,
hotelMsg?request,confirm? Q Q ? , ,
request?offer? Q Q ? , , offer??,
price?? Q Q ? , , confirm?visa?,
HotelFound , price?? Q Q ? , ,
BookedRoom?visa?, HotelFound ? ? Q Q ?
, BookedRoom?visa?, HotelFound? ?
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Example I Trip Booking I
H as before F ? def WaitBooking ? ? ? def
request?o? ? o?? price??
? price?? confirm?v? ? BookedFlight?v?
? price?? ? abort in
offeringFlight ?request,confirm? Q ?
BookedFlight?v? ? in WaitBooking ? ?

local name, different from homonym name in H
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Example I Trip Booking II
both needed to commit
C ? def hotelOK?fc? flightOK?hc? ? fc? ? hc?
? ? BookingHotel? ?? def hotelMsg?r,c?
? def offer?? ? c?visa? hotelOK?flightConf?
? offer?? ? abort ?
flightConf ? HotelFound? ? in
r?offer? in searchRoom ?hotelMsg? Q
? BookingFlight? ??def flightlMsg?r,c? ? def
offer?? ? c?visa? flightOK?hotelConf?
? offer?? ? abort ? hotelConf ?
FlightFound? ? in r?offer? in
searchFlight ?flightMsg? Q in
BookingHotel BookingFlight
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Example I Trip Booking II
both needed to commit
C ? def hotelOK?fc? flightOK?hc? ? fc? ? hc?
? ? BookingHotel? ?? def hotelMsg?r,c?
? def offer?? ? c?visa? hotelOK?flightConf?
? offer?? ? abort ?
flightConf ? HotelFound? ? in
r?offer? in searchRoom ?hotelMsg? Q
? BookingFlight? ??def flightlMsg?r,c? ? def
offer?? ? c?visa? flightOK?hotelConf?
? offer?? ? abort ? hotelConf ?
FlightFound? ? in r?offer? in
searchFlight ?flightMsg? Q in
BookingHotel BookingFlight TB ? def
searchRoom?hm? offeringRoom ?r,c? ? hm?r,c?
? searchFlight?fm? offeringFlight ?r,c?
? fm?r,c? in H F C
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Zero-safe nets

• Synchronization mechanism for transitions
• Places are divided in
• Stable Ordinary places
• Zero-safe Idealized resources, invisible to
  external observers

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Zero-safe nets

• Synchronization mechanism for transitions
• Places are divided in
• Stable Ordinary places
• Zero-safe Idealized resources, invisible to
  external observers

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Zero-safe nets

• Synchronization mechanism for transitions
• Places are divided in
• Stable Ordinary places
• Zero-safe Idealized resources, invisible to
  external observers

send
receive
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Zero-safe nets

• Synchronization mechanism for transitions
• Places are divided in
• Stable Ordinary places
• Zero-safe Idealized resources, invisible to
  external observers

send
receive
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Zero-safe nets

• Synchronization mechanism for transitions
• Places are divided in
• Stable Ordinary places
• Zero-safe Idealized resources, invisible to
  external observers

send
receive
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Zero-safe nets

• Synchronization mechanism for transitions
• Places are divided in
• Stable Ordinary places
• Zero-safe Idealized resources, invisible to
  external observers

send
receive
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Zero-safe nets Encoding

• Given a ZS net N(T,S)
• Places ports
• Transitions firing rules
• Tokens messages
• Encoding of a marking S
• E E? ?
• S1S2 S1 S2

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Zero-safe nets Encoding

• Encoding of (basic) transitions

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Zero-safe nets Encoding

• Encoding of (basic) transitions

E? ? ? def z? ? ? 0 in e?z? E? ?
e1?z? ? e2?z?
e?z? ? e1?z? e2?z?
e1?z1? e2?z2? ? e?z1?
e?z? ? E? ?
e?z? ? 0
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Zero-safe nets Encoding

• cJoin process for a ZS net
• Let N(T,S) be a ZS net,
• PN def T in S
• Theorem
• Let N(T,S) be a ZS net. (S,?) ? (S,?)
• iff def T in S ? def T in
  S

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Serializability

• A serializable transaction admits an abstract
  representation as a single transition
• cJoin negotiations may interact with other
  negotiations (not serializable in the previous
  sense)
• But all cooperating negotiations can be viewed as
  a single transition
• Moreover, we would like this property to hold at
  every level of nesting

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Serializability Shallowness

• Shallow processes any computation increases the
  height of nesting structure in at most 1
• P is shallow if every definition D in P satisfies

D J ? P, where nest(P ) 0,
or P R Q and nest( R Q ) 0
D J ? P, and nest(P ) 0
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Serializability

• Serializability as big step reduction relation
  (?) between shallow processes
• Theorem S ?cJ S iff S ? S

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Final Remarks

• cJoin models multi-way transactions by describing
  interacting agents but not their global structure
• Compensations do not undo precommitted
  activities.
• Can such compensations be encoded in cJoin?
• Are cJoin primitives implementable?
• We plan to use the D2PC protocol
• The subcalculus of flat processes can be
  implemented