Systems S definition

Systems S. = A[P] A[K] s[T ] S | S (→u,→a)S 0 CO2 features CCS-style processes, equipped with branching ∑ (not to be confused with the choice op- erator used in contracts), parallel composition , restrictions of session and participant variables, and named process invocation. The prefixes are for internal action (τ), contract advertisement (tell ), session creation upon contractual agreement (fuse), and execution of contractual actions (do). A latent contract of the form u A says c represents the promise of participant A to fulfil c by executing do-actions on a session variable u. CO2 systems may be parallel compositions of processes A[P] (where A is the partici- pant executing P), latent contracts A[K] (where A is the participant to which the contracts in K have been advertised), and established sessions s[T ] (where s is a session name, and T is a system of stipulated con- tracts as in Section 2). We assume well-formed systems where each participant A has at most one process A[P]. Note that CO2 process and system productions allow to delimit both session names/variables (→u) and participant variables (→a), but not participant names, which are considered public. We give the main reduction rules for the semantics of CO2 (where + and are standard associative and commutative operators):

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Systems S. = A[P] A[K] s[T ] S | S (˙u,˙a)S 0 CO2 features CCS-style processes, equipped with branching ∑ (not to be confused with the choice op- erator used in contracts), parallel composition , restrictions of session and participant variables, and named process invocation. The prefixes are for internal action (τ), contract advertisement (tell ), session creation upon contractual agreement (fuse), and execution of contractual actions (do). A latent contract of the form u A says c represents the promise of participant A to fulfil c by executing do-actions on a session variable u. CO2 systems may be parallel compositions of processes A[P] (where A is the partici- pant executing P), latent contracts A[K] (where A is the participant to which the contracts in K have been advertised), and established sessions s[T ] (where s is a session name, and T is a system of stipulated contracts as in Section 2). Note that CO2 process and system productions allow to delimit both session names/variables (˙u) and participant variables (˙a), but not participant names, which are considered public. We give the main reduction rules for the semantics of CO2 (where + and are standard associative and commutative operators): π K dσ T ˙u = dom(σ) ˙a = dom(π) ran(σ) = {s} s fresh [CO2 -FUSE] (˙u,˙a) .AΣfuse . P + Pj | QΣ | A[K] | SΣ →− (s)(A[P | Q] σπ | s[T | Q(T )] | Sσπ) T A=B:e T j s[T ] | AΣdos e . P + Pj | QΣ →− sΣT jΣ | A[P | Q] π [CO2 -TELL] allows a participant A to advertise a contract c to B; as a result, a new latent contract is created, recording the fact that it was promised by A. [CO2 -FUSE] establishes a new session: the latent contracts held in A[K] are combined, and their participant variables substituted, in order to find an agreement, i.e., a T which satisfies the relation K dσ T (see Definition 3.2 below). Provided an agreement is found, fresh session variable s and participants names are shared among the parties, via substitutions σ and π; within the session, the involved contracts become stipulated (as opposed to “latent”, before the agreement). Rule [CO2 -DO] allows A to perform an input/output action e towards B on session s, provided that T permits it. The omitted CO2 rules are standard, and they are listed in the online appendix [14]: they cover internal actions, parametric processes, parallel composition, and delimitations. When needed, we label CO system transitions: S A: p Sj means that S reduces to Sj through a prefix p fired by participant A.

Examples of Systems S in a sentence

• Israel On file with the Administrative Agent On file with the Administrative Agent Excluded Cadence Design Systems (Japan) B.V. Netherlands On file with the Administrative Agent On file with the Administrative Agent Excluded Cadence Design Systems (S) Pte Ltd.

• Member of the Supervisory Board and advisor to the Chairman of the Board of Directors of Vignal Systems S.

• Benchmark and Stratus’ affiliated company, Stratus Technologies International S.à r.▇., (formerly Computer Systems S.

• Korea On file with the Administrative Agent On file with the Administrative Agent Excluded Subsidiary Cadence Design Systems (S) Pte Ltd.

• Pi P | P (→u,→a)P X (→u,→α) 0 Latent contracts K ::= ↓u A says c K | K Systems S ::= A[P] A[K] s[T ] S | S (→u,→a)S 0 CO2 features CCS-style processes, equipped with branching ∑ (not to be confused with the choice op- erator used in contracts), parallel composition , restrictions of session and participant variables, and named process invocation.

• Benchmark and Stratus’ affiliated company, Stratus Technologies International S.à ▇.▇., (formerly Computer Systems S.