V. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....languages (LCC) is obtained simply by allowing constraint systems based on Jean Yves Girard s Linear Logic [5] LL) instead of classical logic. It greatly extends the expressive power of CC, as non monotonic evolutions of the store are possible through the consumption of constraints by ask agents [2, 10] but still enjoys a simple logical semantics in LL. These results have been used in [3, 4] to prove safety properties of LCC programs simply by exhibiting special phase models of programs. This presentation is about the implementation in CLP of a model checker based on the phase semantics of LL, ....

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

....nowadays in a wide variety of application domains, most notably for solving combinatorial search problems. One can give a simple translation of CC programs in Jean Yves Girard s Linear Logic [6] that is sound and complete for observing the entailment closed sets of successes and accessible stores [5, 4, 12]. This, among other reasons, led to a generalization of CC languages, called Linear Concurrent Constraint languages (LCC) that is used throughout the paper for the presentation of our results. The class LCC is obtained from CC simply by allowing constraint systems based on linear logic instead of ....

....LCC is obtained from CC simply by allowing constraint systems based on linear logic instead of classical logic. This is a generalization which greatly extends the expressive power of CC, as non monotonic evolutions of the store are possible through the consumption of constraints by ask agents [3, 12] but it still enjoys a simple linear logic semantics with the same soundness and completeness properties. These results have been used in [4, 5] to prove safety properties of LCC programs simply by exhibiting special phase models of programs. This paper presents, after some preliminary de ....

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

....of the store is also a severe limitation to the expressive power of CC languages. Several non monotonic extensions of CC, where constraints can be consumed and removed from the store during computations, have been thus de ned to escape from these limitations [4] For example, the language LCC [10, 25] is a variant of CC with constraint systems based on linear logic and where constraints are consumed by the ask agents. 25] gives simple embeddings in LCC of the calculus, the Linda coordination language [6] or the asynchronous pi calculus [5] which are not possible in monotonic CC. Being ....

....constraints can be consumed and removed from the store during computations, have been thus de ned to escape from these limitations [4] For example, the language LCC [10, 25] is a variant of CC with constraint systems based on linear logic and where constraints are consumed by the ask agents. [25] gives simple embeddings in LCC of the calculus, the Linda coordination language [6] or the asynchronous pi calculus [5] which are not possible in monotonic CC. Being Turing complete, CC can only encode these languages via ad hoc encodings, using streams for example [15] Another reason for ....

[Article contains additional citation context not shown here]

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

....of the store is also a severe limitation to the expressive power of CC languages. Several non monotonic extensions of CC, where constraints can be consumed and removed from the store during computations, have been thus de ned to escape from these limitations [4] For example, the language LCC [10, 25] is a variant of CC with constraint systems based on linear logic and where constraints are consumed by the ask agents. 25] gives simple embeddings in LCC of the calculus, the Linda coordination language [6] or the asynchronous pi calculus [5] which are not possible in monotonic CC. Being ....

....constraints can be consumed and removed from the store during computations, have been thus de ned to escape from these limitations [4] For example, the language LCC [10, 25] is a variant of CC with constraint systems based on linear logic and where constraints are consumed by the ask agents. [25] gives simple embeddings in LCC of the calculus, the Linda coordination language [6] or the asynchronous pi calculus [5] which are not possible in monotonic CC. Being Turing complete, CC can only encode these languages via ad hoc encodings, using streams for example [15] Another reason for ....

[Article contains additional citation context not shown here]

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

.... the Chemical Abstract Machine [9] Actors [2, 48] production systems [14] group communication of the broadcasting and multicasting kind [11] and constraint based programming [45] which have been variously interpreted in terms of a Linear Logic operational semantics based on proof search, as in [7, 5, 12, 35, 46]. This flowering of developments has been backed by theoretical contributions concerning those aspects of Linear Logic which are essential to proof search. In particular, there have been several investigations of the crucial problem of permutations of inference figures during proof construction ....

V.A. Saraswat and P. Lincoln. Higher order linear concurrent constraint programming. Technical report, Xerox Parc, Palo Alto, Ca, U.S.A., 1992.

....namely Linear CC (LCC) where the constraint system is axiomatized in linear logic. LCC is an extension of CC, somewhat similar to [3] or [33] but where constraints are consumed by ask agents without dependency maintenance or recomputation. Linear constraint systems have also been proposed in [34] in a higher order setting which will not be considered here. From an operational point of view, LCC extends CC in a fundamental way by introducing some forms of imperative programming, particularly useful for reactive systems. Standard CC programs can however be recovered by the usual translation ....

....logic into linear logic [10] Section 3 settles the basic soundness and completeness results of CC and LCC operational semantics w.r.t. intuitionistic linear logic, relying on [30] and preliminary results from [29] Results similar to those of this section are part of the folklore on CC languages [19, 34] but have not been published. Here we prove that 1) the stores of CC computations can be characterized in intuitionistic logic, and 2) both the stores and the successes of CC and LCC computations can be characterized in intuitionistic linear logic. Completeness results show that ILL can be used to ....

[Article contains additional citation context not shown here]

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

....and contraction, and by introducing a connective with these properties in order to recover classical logic. One can give a simple translation of CC programs in intuitionistic linear logic that is sound and complete for observing the entailment closed sets of successes and accessible stores [8, 7, 25]. This approach makes it possible to analyze both may properties, i.e. those properties which are true on some branch of the computation, and must properties, which are true on all branches of the computation. These results have been used in [7, 8] to prove safety properties of CC programs ....

....LCC is 2 obtained from CC simply by allowing constraint systems based on linear logic instead of classical logic. This is a generalization which greatly extends the expressive power of CC, as non monotonic evolution of the stores are possible through the consumption of constraints by ask agents [4, 25], but it does not a ect the logical completeness properties studied in this paper. Section 3 presents the new translation and the logical completeness results for the observations of the successes, of the accessible stores and of the suspensions of LCC computations. This series of results improves ....

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V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

....actions and proofs, but also proof search schemes so that proofs (i.e. actions) can be generated in a reasonable time. Our framework of linear logic programming can construct proofs from some programmer s aid of specifying control. Among other variants of linear logic programming paradigm[2] 6][12], we use our ACL framework[7] ACL framework offers two kinds of programming paradigms depending on two interpretations of non determinism in proof search, namely don t care non determinism or don t know non determinism. The former interpretation yields a concurrent programming paradigm, where ....

Saraswat, V., and P. Lincoln, "Higher-order, linear, concurrent constraint programming," 1992. draft.

....namely Linear CC (LCC) where the constraint system is axiomatized in linear logic. LCC is an extension of CC, somewhat similar to [3] or [33] but where constraints are consumed by ask agents without dependency maintenance or recomputation. Linear constraint systems have also been proposed in [34] in a higher order setting which will not be considered here. From an operational point of view, LCC extends CC in a fundamental way by introducing some forms of imperative programming, particularly useful for reactive systems. Standard CC programs can however be recovered by the usual translation ....

....logic into linear logic [10] Section 3 settles the basic soundness and completeness results of CC and LCC operational semantics w.r.t. intuitionistic linear logic, relying on [30] and preliminary results from [29] Results similar to those of this section are part of the folklore on CC languages [19, 34] but have not been published. Here we prove that 1) the stores of CC computations can be characterized in intuitionistic logic, and 2) both the stores and the successes of CC and LCC computations can be characterized in intuitionistic linear logic. Completeness results show that ILL can be used to ....

[Article contains additional citation context not shown here]

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

....take an important role at runtime as well as at the type checking phase, while they do not in HACL. It is because the purpose of computation in HACL is not to find answer substutions, and HACL is designed so that higher order unification is not required. Higher order linear cc Saraswat and Lincoln[20] proposed higher order linear cc, a kind of higher order concurrent linear logic programming. In the untyped setting, the expressive power of their system and our system are almost the same; a message x(v 1 ; vn ) in higher order ACL corresponds to x : v 1 ; vn ] in higher order ....

Saraswat, V., and P. Lincoln, "Higher-order, linear, concurrent constraint programming, " July 1992. draft.

....It can be considered a refinement of Prolog[20] rather than a reactive paradigm. They applied their language to several problems such as theorem proving and natural language parsing. Miller[18] also investigated a connection between linear logic and calculus. Linear cc Saraswat and Lincoln[21] recently investigated linear logic as a theoretical foundation and an extension of concurrent constraint programming[22] almost simultaneously with our work[15] Their work seem to have several fundamental similarities to our work, although their and our interpretations are dual each other. That ....

Saraswat, V., and P. Lincoln, "Higher-order, linear, concurrent constraint programming, " 1992. draft.

....in a process oriented setting, in [15] There, a process transition is controlled by the presence of a constraint in the constraint store or more precisely by its entailment from the constraint store. This enforces a strictly monotonous view of constraints, which has been partially relaxed in [16]. This approach does not make the distinction between two separate uses of constraints: for communication and for solving. This distinction clearly appears in our proposal, where communication is achieved by the global broadcast mechanism and solving is performed locally in each ....

Saraswat, V.A., Lincoln, P.: Higher Order Linear Concurrent Constraint Programming. Xerox Palo Alto Research Center, Palo Alto, CA, Technical Report, 1992

....Constraint Logic Programming [16, 18] There, a process transition is controlled by the presence of a constraint in the constraint store, or, more precisely, by its entailment from the constraint store. This enforces a strictly monotonous view of constraints, which has been partially relaxed in [28] (for a similar kind of relaxation, see also [17] This approach does not make the distinction between two different uses of constraints: for local problem solving and for communication (and hence for Distributed Problem Solving) By contrast, this distinction appears clearly in the CBKB model, ....

Saraswat, V. A., Lincoln, P.: Higher Order Linear Concurrent Constraint Programming. Xerox Palo Alto Research Center, Palo Alto, CA, Technical Report, 1992

....logic [Gir87] Intuitively, linear logic is a calculus of resource consumption where a linear implication consumes its premises to establish the conclusion. This naturally models state change in a logical setting. There have been various proposals to combine CC programming with linear logic (see [SL92], Pal97] We use here the linear concurrent constraint language LCC described in [FRS98a, FRS98b] and used for example in [Sch98] to express global constraint solvers where non monotonic imperative data structures have to be handled. A linear constraint system is a generalization of a classical ....

V.A. Saraswat and P. Lincoln, Higherorder linear concurrent constraint programming, Draft Xerox 1992.

....and we investigate the use of the phase semantics for proving safety properties of CC programs. Section 2 presents a natural extension of CC languages in this context, namely Linear CC (LCC) where the constraint system is axiomatized in linear logic. Linear constraint systems have been proposed in [24] in a higher order setting which will not be considered here. LCC is a non monotonic extension of CC, somewhat similar to [2] or [23] but where constraints are consumed by ask agents without dependency maintenance or recomputation. From an operational point of view, LCC extends CC in a ....

....be recovered by the usual translation of intuitionistic logic into linear logic [6] Section 3 settles the basic soundness and completeness results of LCC operational semantics w.r.t. intuitionistic linear logic. Results similar to those of this section are part of the folklore on CC languages [15, 24] but have not been published, we refer to the appendix B and [5, 20] for complete proofs. Completeness results show that ILL can be used to prove liveness properties of LCC programs, i.e. properties expressing that something good will eventually happen. Then we show in section 4 how safety ....

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

.... on the other hand, as a programming tool, constraints have mainly been introduced in the context of logic languages, particularly logic programming of the Prolog tradition [18] but not exclusively, as some versions of constraint programming stem from concurrent logic programming and Linear Logic [14, 13, 1]. In any case, other non logical frameworks have been and are being used to program with constraints. The significant point for our purpose is that the type of coordination programming we have proposed in the previous sections is not domain specific, as our coordination constructs do not make any ....

Saraswat, V.A., Lincoln, P. (1992). Higher Order Linear Concurrent Constraint Programming. Xerox Parc, Palo Alto, Ca, U.S.A., Technical Report.

....programs in linear logic. While moving to linear logic, it is very natural to move to a non monotonic version of CC at the same time, where constraints are consumed, but where monotonic CC can be easily encoded. Such variants have been introduced by Saraswat and Lincoln in a higher order setting [30], further studied in [3] where the logic of constraints is linear logic : in this version, constraints can be consumed, and the language is therefore closer to process calculi like Milner s calculus [20] In [7, 26] a first order non monotonic variant, LCC (linear CC) is defined in which both ....

....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 the monotonic CC, we define the constraint systems, the agents, the configurations and the transition system. Definition 8 (Linear constraint system) A linear constraint system is a pair (C; C ) where: C is a set of formulas (the linear constraints) ....

[Article contains additional citation context not shown here]

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Parc Xerox Technical Report, 1992.

....and prove its soundness with respect to a testing equivalence. 1 Introduction Linear logic programming, where computation is described in terms of a bottom up proof search in linear logic[5] has recently been investigated as frameworks for novel concurrent programming languages[3] 2] 6] 7] 8][12]. The general goal of this paper is to investigate several equivalence relations for processes in linear logic programming, by which establishing foundations for program transformation in linear logic programming. In this paper, we consider a subset of ACL[7] a variant of linear logic ....

....for program transformation in linear logic programming. In this paper, we consider a subset of ACL[7] a variant of linear logic programming. One of our particular interests is in an issue: What does logical equivalence of formulas mean in terms of computation In ACL (and also in linear cc[12]) each formula of linear logic is viewed as a process, hence logical equivalence is expected to imply some equivalence for processes. The first simple observation is that logical equivalence implies a weak testing equivalence[11] A logical equivalence of two formulas A and B implies that for ....

[Article contains additional citation context not shown here]

Saraswat, V., and P. Lincoln, "Higher-order, linear, concurrent constraint programming," 1992. draft.

....programs in linear logic. While moving to linear logic, it is very natural to move to a non monotonic version of cc at the same time, where constraints are consumed, but where monotonic cc can be easily encoded. Such variants have been introduced by Saraswat and Lincoln in a higher order setting [30], further studied in [5, 33] where the logic of constraints is linear logic: in this version, constraints can be consumed, and the language is therefore closer to process calculi like Milner s calculus [21] In [26] a first order non monotonic variant, lcc, is defined in which the successes ....

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Manuscript, 1992.

....It is because the purpose of computation in HACL is not to find answer substutions, and HACL is designed so that higher order unification is not required. 7 The view message as an atomic formula is possible because of the linearity in linear logic. Higher order linear cc Saraswat and Lincoln[16] proposed higher order linear cc, a kind of higher order concurrent linear logic programming. In the untyped setting, the expressive power of their system and our system are almost the same; a message x(v 1 ; v n ) in higher order ACL corresponds to x : v 1 ; v n ] in ....

Saraswat, V., and P. Lincoln, "Higher-order, linear, concurrent constraint programming, " July 1992. draft.

....namely Linear CC (LCC) where the constraint system is axiomatized in linear logic. LCC is an extension of CC, somewhat similar to [3] or [30] but where constraints are consumed by ask agents without dependency maintenance or recomputation. Linear constraint systems have also been proposed in [31] in a higher order setting which will not be considered here. From an operational point of view, LCC extends CC in a fundamental way by introducing some forms of imperative programming, particularly useful for reactive systems. Classical CC programs can however be recovered by the usual ....

....by the usual translation of intuitionistic logic into linear logic [10] Section 3 settles the basic soundness and completeness results of CC and LCC operational semantics w.r.t. intuitionistic linear logic. Results similar to those of this section are part of the folklore on CC languages [19, 31] but have not been published. Here we prove that 1) the stores of CC computations can be characterized in intuitionistic logic, and 2) both the stores and the successes of CC and LCC computations can be characterized in intuitionistic linear logic. Completeness results show that ILL can be used to ....

[Article contains additional citation context not shown here]

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

....the corresponding family of constraint solving algorithms in the spirit of cc(FD) i.e. from a set of elementary, combinable primitives aimed at abstracting its fundamental operations. In this paper, we show how Linear cc (lcc) a nonmonotonic extension of cc languages introduced in [14], in a spirit similar to [1] where the constraint system is axiomatized in linear logic and constraints are consumed by ask agents without maintenance or recomputation may be used to overcome the non monotony obstacle , and in so doing we provide the first example of practical use of the lcc ....

V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

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V. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Technical report, Xerox Parc, 1992.

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V.A. Saraswat and P. Lincoln. Higher-order linear concurrent constraint programming. Parc Xerox Technical Report, 1992.

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