Concurrent Constraint Programming

Origin. Vijay Saraswat's Carnegie Mellon dissertation (1989), published as Concurrent Constraint Programming (MIT Press, 1993). Saraswat and Rinard, "Concurrent constraint programming" (POPL 1990). Saraswat, Rinard, and Panangaden, "The semantic foundations of concurrent constraint programming" (POPL 1991). Subsumes and generalizes concurrent logic programming and constraint logic programming.

Models. Computation as the growth of information. Agents share one store — a constraint on the program's variables — and interact only through it: tell adds a constraint, ask blocks until the store entails one. Entailment is the synchronization primitive; there are no channels and no messages, a process waits on what is known. The store grows monotonically, and without choice the result of a finite computation is independent of scheduling. The contrast with CLP is exact: CLP computes with constraints inside SLD resolution, the solver guarding derivations during backtracking search, while ccp makes the store itself the medium of communication between concurrent agents — ask and tell generalize unification, which over the Herbrand constraint system is a tell of an equation, with the input matching of the concurrent logic languages as the corresponding ask.

Formalism.

Constraint system: Partial information in the style of Scott's information systems (Saraswat–Rinard–Panangaden 1991). Standard presentation: a complete algebraic lattice (Con, ⊑, ⊔, true, false). ⊑ is the information order — d entails c when c ⊑ d; ⊔ joins information; true is least, false greatest. Entailment is required decidable, since every ask tests it.

Hiding: An operation ∃x on constraints for each variable x: ∃x c ⊑ c ∃x(c ⊔ ∃x d) = ∃x c ⊔ ∃x d ∃x ∃y c = ∃y ∃x c The laws of cylindrification — the existential quantifier as an operator on constraints, from Cylindric Algebras.

Agents: P ::= tell(c) | ask(c) → P | P ∥ Q | P + Q | ∃x P | p(x̄) The determinate calculus omits +.

Reduction (configurations ⟨P, d⟩): ⟨tell(c), d⟩ → ⟨0, d ⊔ c⟩ — tell adds, unconditionally. ⟨ask(c) → P, d⟩ → ⟨P, d⟩ if c ⊑ d — ask fires on entailment, blocks otherwise. The store never shrinks: monotone growth is the invariant the semantics is built on.

Closure operators (Saraswat–Rinard–Panangaden 1991): A determinate process denotes a closure operator on the constraint lattice: monotone, increasing, idempotent. A closure operator is determined by its fixed points — the resting points, the stores the process cannot extend. Parallel composition is intersection: the resting points of P ∥ Q are those common to P and Q.

Timed ccp (Saraswat–Jagadeesan–Gupta, "Foundations of timed concurrent constraint programming", LICS 1994): tcc: determinate ccp run in time units, after the synchronous languages. Each unit runs a process from the environment's stimulus to its resting point; the residue moves to the next unit. The store does not persist across units, so state can change between instants while each instant stays monotone. Pre-emption constructs in the style of Esterel (do P watching c); deterministic, since each unit is. ntcc (Palamidessi–Valencia 2001) adds guarded choice and unbounded delay for nondeterministic, asynchronous timed behavior.

Linear ccp (Fages–Ruet–Soliman, LICS 1998; "Linear concurrent constraint programming: operational and phase semantics", Information and Computation 165, 2001): Constraints drawn from linear logic: ask can consume what tell deposited — the one extension in which the store does not merely grow. Linear logic's phase semantics supplies the logical characterization of the observables.

Bisimilarity (Aristizábal–Bonchi–Palamidessi–Pino–Valencia, FOSSACS 2011): Labeled transitions whose label is the minimal constraint the environment must add for the step to fire. Saturated barbed bisimilarity; bisimulations closed under adding arbitrary constraints to the store. Partition refinement adapted to ccp (Aristizábal–Bonchi–Pino–Valencia 2012): the first algorithm deciding ccp program equivalence, for finite transition systems.

Symbols.

Metatheory. The POPL 1991 paper supplies the semantics the model is known for: determinate processes are closure operators on the constraint lattice, so a process is characterized by its set of resting points, parallel composition becomes intersection of those sets, and the resulting denotational semantics is fully abstract for the natural observables. Determinacy itself — the result of a finite computation is the same under every scheduling — fails the moment guarded choice is added; de Boer and Palamidessi ("A fully abstract model for concurrent constraint programming", TAPSOFT 1991) constructed the fully abstract model for the nondeterministic language, where a single closure operator no longer suffices. The behavioral theory arrived twenty years later: Aristizábal, Bonchi, Palamidessi, Pino, and Valencia (FOSSACS 2011) derived a labeled semantics whose labels are minimal environment contributions, defined saturated barbed bisimilarity, and proved its weak form fully abstract with respect to the standard observational equivalence of the 1991 semantics; the partition-refinement adaptation of 2012 made the equivalence automatically checkable on finite transition systems. In the extensions, tcc is deterministic because each time unit is a determinate ccp computation, and linear ccp's observables are characterized by the phase semantics of linear logic.

Applies to. Concurrent constraint languages over Herbrand, finite-domain, and arithmetic constraint systems. Timed and reactive programming through tcc and ntcc. Automated checking of process equivalence. The linear-logic reading of state change, through LCC. Any concurrency model in which synchronization is entailment rather than message passing.

Limitations. Monotone growth gives the determinacy theorem and the closure-operator semantics and at the same time forbids change: a plain ccp store cannot retract, overwrite, or forget, and the two extensions that restore change each give up part of the plain theory — tcc confines change to instant boundaries and keeps determinism by excluding unbounded nondeterminism within a unit, while LCC gives up the monotone store on which the closure-operator semantics rests. Every operational step tests entailment, so the model's cost is the constraint system's: entailment must be decidable for the semantics to be effective at all, and its complexity is outside the calculus. The store is global — locality exists only through cylindrification, and there is nothing of location, failure, or distribution, so the model describes shared-knowledge concurrency rather than distributed systems. And partition refinement decides the strong equivalence on finite transition systems only, with the weak equivalence handled by later reductions.

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