R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Parc, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are not blocking. The monotonic evolution of the store during CC computations (constraints can only be added to the store along a computation path) provides CC languages with a simple denotational semantics in which agents are identi ed to closure operators on the semi lattice of constraints [26, 13]. Such denotational semantics are used in [7] to obtain a complete calculus for partial correctness assertions where the rules of the proof system mirror the equations of the denotational semantics. Nevertheless the monotonic evolution of the store is also a severe limitation to the expressive ....

R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic nondeterminism in concurrent constraint programming. Technical report, Xerox Parc, 1991.

.... BP 105, 78153 Le Chesnay Cedex France e mail: fFrancois.Fages,Sylvain.Solimang inria.fr Contact author: Fran cois Fages, tel. 33 1 39 63 57 09 fax 33 1 39 63 54 69 with a simple denotational semantics in which agents are identi ed to closure operators on the semi lattice of constraints [26, 13]. Such denotational semantics are used in [7] to obtain a complete calculus for partial correctness assertions where the rules of the proof system mirror the equations of the denotational semantics. Nevertheless the monotonic evolution of the store is also a severe limitation to the expressive ....

R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic nondeterminism in concurrent constraint programming. Technical report, Xerox Parc, 1991.

....at different levels of abstraction, getting rid of useless details of the execution. The monotonic evolution of the store during CC computations provides CC languages with a simple denotational semantics 2 in which agents are identified to closure operators on the semi lattice of constraints [35, 15]. Such denotational semantics are used in [5] to obtain a complete calculus for partial correctness assertions where the rules of the proof system mirror the equations of the denotational semantics. In this article, we explore another route based on Girard s intuitionistic linear logic (ILL) 10] ....

....with the blind choice rule, but then: 1) the observed store has not changed, and 2) the terminal configuration is not a success. The monotonicity and extensivity properties provide CC with a denotational semantics, where the agents are seen as closure operators on the semi lattice of constraints [35, 15]. In this paper however, we shall also be concerned with a variant of CC languages where constraints are formulas in linear logic [10] and where extensivity is dropped. 2.2 Linear CC Roughly speaking, there are two reasons to consider linear constraints: on one hand, as we shall see in ....

R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Parc, 1991.

....of the execution. The monotonic evolution of the store during CC computations (constraints can only be added to the store along a computation path) provides CC languages with a simple denotational semantics in which agents are identi ed to closure operators on the semi lattice of constraints [26, 13]. Such denotational semantics are used in [6] to obtain a complete calculus for partial correctness assertions where the rules of the proof system mirror the equations of the denotational semantics. The search for a logical semantics for CC led to interesting developments that bene ted from recent ....

R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic nondeterminism in concurrent constraint programming. Technical report, Xerox Parc, 1991.

....the synchronisation free languages, such observables can be described compositionally in a simple way. 2.3. 1 Semantics of CCP The denotational semantics of the synchronisation free version of CCP has an elegant formulation in terms of a Smyth power domain construction on the constraint system C [14, 24, 30]. The basic construction of the semantics considers interpretations, that is maps from agents into some special subsets of C describing the results of the agent computation, and a xpoint operator on the set of interpretations. A semantics is obtained by iteratively applying starting ....

R. Jagadeesan, V. Saraswat, and V. Shanbhogue. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Park, 1991.

....at di erent levels of abstraction, getting rid of useless details of the execution. The monotonic evolution of the store during CC computations provides CC languages with a simple denotational semantics 2 in which agents are identi ed to closure operators on the semi lattice of constraints [35, 15]. Such denotational semantics are used in [5] to obtain a complete calculus for partial correctness assertions where the rules of the proof system mirror the equations of the denotational semantics. In this article, we explore another route based on Girard s intuitionistic linear logic (ILL) 10] ....

....with the blind choice rule, but then: 1) the observed store has not changed, and 2) the terminal con guration is not a success. The monotonicity and extensivity properties provide CC with a denotational semantics, where the agents are seen as closure operators on the semi lattice of constraints [35, 15]. In this paper however, we shall also be concerned with a variant of CC languages where constraints are formulas in linear logic [10] and where extensivity is dropped. 2.2 Linear CC Roughly speaking, there are two reasons to consider linear constraints: on one hand, as we shall see in ....

R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Parc, 1991. 31

....of ccp to be rather complicated (see [3] and [15] and therefore programs are difficult to analyze and to reason about. Various subsets of ccp, which admit a simpler semantics, have been investigated. In particular, determinate ccp [15] where no form of choice is allowed, and local choice ccp [8], where choice is allowed, but it does not depend on the external environment (i.e. the choice of the branch does not depend on the present store: the guard is checked after the branch is selected) For both these two languages a denotational semantics based on closure operators has been given; ....

....and is more similar to (the process interpretation of) Logic Programming rather than to CCS, we define the notion of confluence as independence from the selection rule. We show that also for (structurally) confluent programs it is possible to define a denotational semantics along the lines of [8], allowing us to retrieve the same class of observables. This is an extension of the results in [8] because local choice ccp programs are clearly confluent (in the same way that logic programs are) but the vice versa is not always true. One of the drawbacks of the above notion of confluence, ....

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R. Jagadeesan, V.A. Saraswat, and V. Shanbhogue. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Park, 1991.

....and completeness of the system it is convenient to deal with a more algebraically structured language. To this end we translate CLP into a sort of concurrent constraint programming language (ccp for short) which we call ffi ccp, and which is basically an extension of ccp with local choice [14]. The extension consists in allowing the presence of delay conditions in the ask construct. Such an extension enhances the expressive power, but preserves the nice properties of local ccp, in particular the denotational semantics can still be defined in a simple way by using closure operators, ....

....consists in allowing the presence of delay conditions in the ask construct. Such an extension enhances the expressive power, but preserves the nice properties of local ccp, in particular the denotational semantics can still be defined in a simple way by using closure operators, following [14]. We use the denotational semantics as a guideline for the development of a compositional proof system, where compositional means that the correctness (or specification) of a composite program can be derived directly from the correctness (or specifications) of its immediate constituents. This ....

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R. Jagadeesan, V.A. Saraswat, and V. Shanbhogue. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Park, 1991.

....namely the fixpoints of the associated closure operator. The advantage is that the semantic operators can be defined in a simple way; in particular, k is given by set intersection. In our case, the resulting construction looks very similar to the semantics of Angelic ccp as defined in [10]. 2 Given a poset (X; a function f : X X is a closure operator iff f is extensive (8x 2 X: x f(x) monotonic (8x;y 2 X: x y ) f(x) f(y) and idempotent (8x 2 X: f(f(x) f(x) Proposition 5.4 For every agent A, D U [ A] is a continuous closure operator on hP U (C) i. Since D ....

R. Jagadeesan, V.A. Saraswat, and V. Shanbhogue. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Park, 1991.

....schema can be obtained by introducing hybrid primitives to deal with ask constraints. As before, we use a program transformation (Angel) which essentially replaces don t care nondeterminism with don t know nondeterminism. Following the semantic characterization of angelic cc processes given in [14], we obtain the denotational counterpart of the transition system based suspension analysis in [2] modulo the absence of the consistency check) Simple results relate the accuracy of these different solutions when the program is suspensionfree, showing that the first approach is always better ....

....successful or suspended. 3. 2 Denotational Semantics The standard denotational semantics for concurrent constraint languages models processes as sets of reactive sequences [6] or trace operators [16] In this paragraph we consider the simpler denotational semantics modeling the angelic language [14], i.e. the language obtained by replacing the global choice operator by the local choice operator. This semantics is a suitable base for reasoning about synchronization approximation, since it separates the choice operator from the synchronization operator (while in the standard semantics their ....

[Article contains additional citation context not shown here]

R. Jagadeesan, V. Shanbhogue, and V. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, System Science Lab., Xerox PARC, 1991.

....of ccp to be rather complicated (see [3] and [16] and therefore programs are difficult to analyze and to reason about. Various subsets of ccp, which admit a simpler semantics, have been investigated. In particular, determinate ccp [16] where no form of choice is allowed, and local choice ccp [8], where choice is allowed, but it does not depend on the external environment (i.e. the choice of the branch does not depend on the present store: the guard is checked after the branch is selected) For both these two languages a denotational semantics based on closure operators has been given; ....

....and is more similar to (the process interpretation of) Logic Programming rather than to CCS, we define the notion of confluence as independence from the selection rule. We show that also for (structurally) confluent programs it is possible to define a denotational semantics along the lines of [8], allowing us to retrieve the same class of observables. This is an extension of the results in [8] because localchoice ccp programs are clearly confluent (in the same way that logic programs are) but the converse is not always true. One of the drawbacks of the above notion of confluence, ....

[Article contains additional citation context not shown here]

R. Jagadeesan, V.A. Saraswat and V. Shanbhogue, Angelic non-determinism in concurrent constraint programming, Tech. Rep., Xerox Park, 1991.

....new proof system is obtained from table 3 by replacing rule C2 by the rule C2 l given in table 6. Soundness and (relative) completeness of this calculus can be proved analogously to the previous case. Note that the semantics resulting from table 2 modified by equation D2 l is the one introduced in [18] for angelic ccp. The same semantics was used in [13] to approximate the operational semantics obtained from rules R1 R6 (i.e. with global choice) by observing the upward closure of the set of the resting points of a process P for a given input c. D2 l [ D: P i ask(c i ) A i ] e) S i (Cn ....

R. Jagadeesan, V.A. Saraswat, and V. Shanbhogue. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Park, 1991.

.... programming language Oz [6] using the programmable search engine described in [5] Although we describe our technique in the case where we have and parallelism but no or parallelism, the technique can be extended to the case where we have in addition angelic or parallelism as e.g. described in [4]. In the next section, we will give some preliminaries and define the notion of symmetries. In Section 3, we will explain the concept of symmetries in the case where we have finite domain variables with a geometric interpretation. We will then introduce the technique of symmetry exclusion in ....

R. Jagadeesan, V. Saraswat, and V. Shanbhogu. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox PARC, 1991.

....traditional in concurrent programming, like reactive systems and protocol specifications. The monotonic evolution of the store during CC computations provides CC languages with a simple denotational semantics in which agents are identified to closure operators on the semi lattice of constraints [25, 11]. Such denotational semantics are used in [4] to obtain a complete calculus for partial correctness assertions where the rules of the proof system mirror the equations of the denotational semantics. In this paper, we explore another route based on Girard s intuitionistic linear logic (ILL) 6] ....

....B; Gamma) Gamma ( y; d; Delta) x; c; A B; Gamma) Gamma ( y; d; Delta) would obviously change the suspensions of a program. It is worth noting however that the set of successes, as well as the set of accessible stores remain the same under both interpretations. Moreover as remarked in [11, 4] the difference between don t know non determinism (backtracking non determinism) and don t care nondeterminism (committed choice indeterminacy) arises in the way observations are defined, more than the way transitions are defined. For the sake of simplicity we have not explicitly treated here all ....

R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Parc, 1991.

....Note that the non deterministic agent A B, can behave either like A or like B. The operator of non deterministic choice , called blind choice, is thus different from the one step guarded choice defined by: A Gamma A 0 A B Gamma A 0 and B Gamma B 0 A B Gamma B 0 . As remarked in [12, 8] the difference between (backtracking) non determinism and (committed choice) in determinism arises in the way observations are defined, more than the way transitions are defined. However backtracking nondeterminism generally refers to the blind choice rule, which is the only choice rule ....

.... ) Gamma (y; d; Delta) then for every multi set of agents Sigma and every constraint e, x; c e; Gamma; Sigma ) Gamma (y; d e; Delta; Sigma ) These properties provide CC with a denotational semantics where the agents are seen as closure operators on the semi lattice of constraints [31, 12]. The property of monotonicity can however be dropped from CC programming, by considering linear constraint systems where constraints are formulas in linear logic [9] 2.2 Linear CC Non monotonic variants of CC have been introduced by Saraswat and Lincoln [30] then further studied in [3] As for ....

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R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Parc, 1991.

....functions from initial constraints to answer constraints (i.e. closure operators on the constraint domain) However, our language is nondeterministic, so we must take a more sophisticated approach. Fortunately the kind of choice we are dealing with is local (or angelic , in the sense of Jagadeesan et al. [1991]) and it is therefore more easy to treat than the global choice of nondeterministic ccp [Saraswat 1989; Saraswat et al. 1991] Jagadeesan et al. [1991] showed that, if one is interested only in observing the upward closure of the computed answers, then the denotational semantics of local ....

....so we must take a more sophisticated approach. Fortunately the kind of choice we are dealing with is local (or angelic , in the sense of Jagadeesan et al. [1991] and it is therefore more easy to treat than the global choice of nondeterministic ccp [Saraswat 1989; Saraswat et al. 1991] Jagadeesan et al. [1991] showed that, if one is interested only in observing the upward closure of the computed answers, then the denotational semantics of local (angelic) ccp can still be constructed, by using closure operators, in a very simple way. However, the price to pay for the simplicity of this approach, is that ....

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Jagadeesan, R., Shanbhogue, V., and Saraswat, V. 1991. Angelic non-determinism in concurrent constraint programming. Tech. rep., System Science Lab., Xerox PARC.

....considering downward closed properties, because we can base our static analysis on a confluent semantics being as precise as the c.a.c. semantics. Confluence is easily obtained by reading the CC indeterministic program as a nondeterministic program (an angelic program, using the terminology of [18]) that is by interpreting all the don t care choice operators of the program as don t know choice operators. In the nondeterministic case, when considering a choice operator we split the control and consider all the branches. In the transition system this difference is captured by replacing rule ....

....that any uco is fully determined by the set of its fixpoints. Moreover all the semantic operators on processes are naturally mapped into simple set theoretic operations over their representations, e.g. the parallel composition of two processes is obtained by intersecting their sets of fixpoints. [18] extends such a semantics to nondeterministic CC languages. When upward closed observables are considered, each (nondeterministic) process can be mapped into a linear uco over the Smyth s powerdomain of the constraint system. These functions can be coded as sets of (singleton) fixed point, ....

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R. Jagadeesan, V. Shanbhogue, and V. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, System Science Lab., Xerox PARC, 1991.

.... we shall retain here (see table 1 and section 2 for the definition of Gamma cc transitions) Computation is monotonic (the constraints in the store are not consumed) this allows to provide cc with a denotational semantics, viewing agents as closure operators on the semi lattice of constraints [31, 12]. From the logic programming tradition however, the operational aspects of cc programming should also be closely connected to proof theory, via the computation as proof search paradigm. This paradigm, first introduced for the Horn clause fragment of classical logic, has been smoothly applied to ....

....of the rule. I The non deterministic choice A B, called blind choice, can behave either like A or like B, it has both capabilities. This is in slight contrast with the one step guarded choice, defined by A Gamma A 0 A B Gamma A 0 and B Gamma B 0 A B Gamma B 0 . As remarked in [12, 7] the difference between (angelic, backtracking) non determinism and (demonic, committed choice) in determinism arises in the way observations are defined, however angelic non determinism refers generally to the blind choice rule and demonic non determinism to the one step committed choice rule. ....

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R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Parc, 1991.

....and (concurrent) higher order) constraint) logic programming languages. 1 Introduction and overview The concurrent constraint (cc) programming paradigm is based on a set of very simple ideas, arising from concurrent logic programming and constraint logic programming. The basic references are [Sar89, SR90, SRP91, JSS91]; we summarize here briefly. Imperative languages may be thought of as based on the notion of store as valuation: a state of the computation is described by a valuation which assigns a unique value to each variable of interest. In constraint based computation, this notion is replaced by that of ....

....it is necessary to introduce a form of disjunction into the programming language. We discuss the extension of the operational and denotational semantics for this construct (Section 3) Essentially, the extension can be done smoothly in the same way as was possible for the basic cc languages [JSS91]. A fully abstract model is obtained by taking the initial solution of E = P S (A (E E) for PS ( the Smyth power domain construction. The above two sections establish the semantic foundations for the propositional cc languages. In these languages, any notion of a variable on which ....

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R. Jagadeesan, V. Shanbhogue, and V. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, System Sciences Laboratory, Xerox PARC, January 1991.

....1 Introduction and overview Our objective is to develop a logical foundation for concurrent programming that transparently integrates constraint programming, functional programming and process algebras. Our starting point is the concurrent constraint (cc) programming paradigm (see, e.g. [Sar89,SR90,SRP91,JSS91]; we summarize here briefly. Imperative languages may be thought of as based on the store as valuation principle: a state of the computation is described by a valuation which assigns a unique value to each variable of interest. In constraint based computation, this notion is replaced by that of ....

R. Jagadeesan, V. Shanbhogue, and V. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, System Sciences Laboratory, Xerox PARC, January 1991.

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R. Jagadeesan, V. Shanbhogue, and V.A. Saraswat. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Parc, 1991.

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R. Jagadeesan, V.A. Saraswat, and V. Shanbhogue. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Park, 1991.

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R. Jagadeesan, V.A. Saraswat, and V. Shanbhogue. Angelic non-determinism in concurrent constraint programming. Technical report, Xerox Park, 1991.

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R. Jagadeesan, V.A. Saraswat and V. Shanbhogue, Angelic non-determinism in concurrent constraint programming, Tech. Rep., Xerox Park, 1991.

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R. Jagadeesan, V. A. Saraswat, and V. Shanbogue. Angelic non-determinism in concurrent constraint programming. Technical report, System Sciences Laboratory, Xerox PARC, 1991.

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