H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pages 134--142. ACM, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of Omega = we have the following version of previous theorem which shows the full abstraction of the s semantics. Theorem 2.8 [14] Let P 1 ; P 2 be programs. Then P 1 ; P 2 iff F ; P 1 ) F ; P 2 ) Finally note that, as shown by the following theorem (which generalize a theorem given in [17] for the case Omega = Pi) the composition of two Omega Gamma34 en programs induce the same equivalence on programs as the union of an Omega Gamma 3 en program with set of atoms whose predicates are in Omega Gamma Theorem 2.9 [16] Let P 1 ; P 2 be programs. Then P 1 P 2 iff there ....

....in each module are disjoint from those defined in the others. From a practical point of view the notion of predicate disjoint module is relevant since often module based implementations of logic programming languages assume this kind of separation. A similar restriction is also considered in [17] and in [9] A typical example of predicate disjoint program is provided by a Datalog program, where intensional and extensional predicates are disjoint, and where the extensional predicates are considered partially defined (see Section 4.2) Let us now prove the mentioned equality. an Omega ....

H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pages 134--142. ACM, 1989.

....technical problems. III. MODULAR SYSTEMS OVER A HETEROGENEOUS INSTITUTIONAL FRAMEWORK In this section we introduce the syntactic and semantic definition of the notions of module and heterogeneous modular system considered. The notion of module that we consider is inspired in the one defined in [8] and is quite close to the notion studied in [5] also used in [14] and to other module notions (e.g. 17] The intuition behind this concept is the following one: a module MOD is some kind of specification (or program) unit that not only consists of a specification BOD of the objects ....

H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logics programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pages 134--142, 1989.

....ning subprograms must be supported, which may be referred to at di erent places in a program. This requires appropriate scoping and abstraction mechanisms for program modules. This need has initiated a large number of investigations, which evolved into the area of modular logic programming, e.g. [32, 35, 29, 17, 22, 5]; see [5] for a comprehensive survey. The research on logic programming with modules has followed two mainstreams [5] The one is programming in the large, where compositional operators are provided for combining separate and independent modules, e.g. 35, 29, 17] Here, the approach is to provide ....

....logic programming, e.g. 32, 35, 29, 17, 22, 5] see [5] for a comprehensive survey. The research on logic programming with modules has followed two mainstreams [5] The one is programming in the large, where compositional operators are provided for combining separate and independent modules, e.g. [35, 29, 17]. Here, the approach is to provide operators which allow to algebraically combine programs, which does not need for an extension of the theory of logic programs. The other direction is programmingin the small, which aims at enhancing logic programming with abstraction and scoping mechanism ....

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H. Gaifman and E. Shapiro. Fully Abstract Compositional Semantics for Logic Programs. In Proceedings 16th Annual ACM Symposium on Principles of Programming Languages, pages 134-142. ACM Press, New York, 1989. 31

....stable models, expressive power 1 Introduction Structured Logic Programming requires the possibility to define subprograms along with scoping and abstraction mechanisms. This need has initiated a large number of investigations, which evolved into the area of modular logic programming, e.g. [26, 29, 23, 14, 17, 4]; see [4] for a comprehensive survey. The research on systems of logic program modules has followed two mainstreams [4] The one is programming in the large, where compositional operators are provided for combining separate and independent modules, e.g. 29, 23, 14] Extended Abstract, with ....

....programming, e.g. 26, 29, 23, 14, 17, 4] see [4] for a comprehensive survey. The research on systems of logic program modules has followed two mainstreams [4] The one is programming in the large, where compositional operators are provided for combining separate and independent modules, e.g. [29, 23, 14]. Extended Abstract, with most proofs omitted. An extended technical report including all proofs is available from the authors. Here, the approach is to provide operators which allow to algebraically combine programs, which does not need for an extension of the theory of logic programs. The ....

H. Gaifman and E. Shapiro. Fully Abstract Compositional Semantics for Logic Programs. In Proc. 16th ACM Symp. POPL, pp. 134--142. 1989

....of a transition system. As for compositionality is concerned, the very first and, up to our knowledge, unique example of construction of compositional semantics by abstract domain transformation is in [19] In this work, the authors proved that compositional semantics of logic programs in [2, 14] can be systematically designed by a generalization of Cousot s reduced cardinal power operation [9] from non compositional semantics of computed answer substitution. This work represents a starting point for our work, which generalizes the results in [19] to arbitrary programming languages whose ....

....compositional semantics are optimal, i.e. they are the most abstract solutions of simple domain equations. Clearly, our results can be specialized to the case of logic and constraint logic programming, obtaining in this way an enhanced theory for logic programming compositionality with respect to [2, 14, 19]. As for program manipulation, and in particular program slicing, is concerned, in [1, 3, 26, 29] we can find several approaches to lazy semantics for program dependence graphs. These kind of semantics are used in order to model program manipulation in a way such that the semantics of a slice ....

Gaifman, H., and Shapiro, E. Fully abstract compositional semantics for logic programs. In Conference Record of the 16th ACM Symp. on Principles of Programming Languages (POPL '89) (1989), ACM Press, New York, pp. 134--142.

....interpretations of logic programs. For example, one interesting issue is compositionality. Having a compositional semantic framework is indeed very convenient for formal reasoning on program properties and can facilitate the development of modular programs (Bossi et al. 1994a; Brogi et al. 1992; Gaifman Shapiro, 1989; Mancarella Pedreschi, 1987) We sketch here the main ideas concerning the role played by contexts in reduction systems, but for a more precise overview we invite the interested reader to join us in the little detour, from the logic programming world to the process description calculi area, ....

Gaifman, H., & Shapiro, E. (1989). Fully abstract compositional semantics for logic programs. Pages 134--142 of: Proceedings of popl'89. ACM.

....behaviour of programs more precisely (it is proved cas correct) and (ii) it provides a syntactic representation of the semantics (T P id) a kind of normal form representation for that functional semantics. The idea, which motivated also the definition of the semantics proposed in [14], is to use sets of clauses as the semantic objects used to interpret a program. Roughly, an Omega Gamma 5 en program P is a program where the predicates contained in Omega are considered being partially defined in P . The open semantics O Omega Gamma P ) of an Omega Gamma 4 en program P , is ....

....a meta linguistic mechanism. This idea gave way to the development of several proposals of modular systems based on the idea of program composition. The approach discussed by Bossi et al. in [3, 4] together with the compositional frameworks of Mancarella and Pedreschi ( 21] Gaifman and Shapiro ([14]) and of Brogi et al. 6] can in fact be seen as different formulations of this idea. The novelty of the proposal presented in this paper is in the type of composition mechanisms we have considered as well as in the domain chosen for the semantic characterization. The isa composition of ....

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H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. 16th Annual ACM Symp. on Principles of Programming Languages, pages 134--142. ACM, 1989.

....to IGC without stating any evaluation strategy or data structure. In what follows, GC denotes the set GC generated by a set (or multiset) computation and GC n denotes the set generated at step n of such a computation. GC is the minimal S model of P as defined by [10] It was recently shown [11, 12] that GC and IGC are fully abstract semantics for logic programs under an operational (respectively, declarative) definition of observable program behaviors. 9 We present algebraic definitions of some fixpoint evaluation strategies that are the focus of this paper, by instantiating the general ....

H. Gaifman and E. Shapiro, Fully Abstract Compositional Semantics for Logic Programs. In Proc. Principles of Programming Languages, 1989.

.... can be understood in logical terms since the set of all the (Herbrand) models is OR compositional [30] and correct wrt successful derivations) The only OR compositional semantics correct wrt computed answers are described in [24, 9, 8] while all the other OR compositional semantics [26, 33, 31, 30, 23] are only correct wrt successful derivations. Clearly, compositionality wrt program composition operators is a desirable property since it allows to define in a modular way and incrementally the semantics of structured programs. For example, a semantics compositional wrt a generalized composition ....

....The s semantics [17] was the first (non compositional) semantics correct wrt computed answers and which used sets of unit clauses as domain. Gaifman and Shapiro, following a proof theoretic approach, introduced the idea of using sets of non unit clauses to achieve ORcompositionality [23]. They then defined (using a different semantic domain) a fully abstract OR compositional semantics modeling computed answers [24] The Omega Gammae 394 tics [9, 8, 8] is the real compositional generalization of the s semantics and uses non unit clauses as domain. In this paper, following the ....

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H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pages 134--142. ACM, 1989.

....on q which allows us to infer that q(X) X = b is in the semantics of P 1 [ P 2 . Such an information is expressed by the clause q(X) true2p(X) Therefore, compositionality w.r.t. union of programs can be obtained by choosing a semantic domain based on clauses. This idea was first introduced in [24] and then further studied in 22 [8, 7] for the case of pure logic programs. In the following we show the application to CLP of this idea, essentially by lifting the definitions in [7] to the realm of constraints. Other compositional semantics based on a functional definition (e.g. the TP ....

H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pages 134--142. ACM, 1989.

....modules, mutual recursion between modules and virtual components. On the other hand, a considerable research e ort has been spent on modular logic programming over the past decade aiming at de ning mechanisms for structuring and reusing programs. Two di erent main approaches (see, for instance, [10, 7, 6]) have been followed. In the rst one emphasis is given to the programming in thelarge and to operators for composing programs which can be de ned without any need to extend the theory of Horn clauses; in the second one the attention is focused on the programming in the small in an attempt to ....

....Our comparison is mainly based on the papers by A. Brogi, P. Mancarella, D. Pedreschi and F. Turini [6] and by M. Bugliesi, E. Lamma and P. Mello [7] These papers provide a powerful synthesis of the main issues arising in algebraic composition of logic modules. We also take into consideration [10] for some evident similarities with our work. Mixin based modules for logic programming 11 We denote by BMPT lang, BLM lang and GS lang the language proposed in [6] 7] and [10] respectively. In the following of this section logic modules will be used for the expressions of BMPT lang, ....

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H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc.ACM Symposium on Principles of Programming Languages, pages 134-142. Austin, Texas, January 1989.

....for an initial goal in a highly efficient manner, once the goal independent phase of the analysis has been performed. 7 Related Work Several other compositional semantics for logic programs have been proposed in the literature. These include the work of Brogi and Turini [4] and Gaifmann et al. [20]. In [4] the compositional semantics is provided by composing the TP functions associated with program modules. Gaifmann et al. propose to adopt clauses as semantic objects in order to characterize partial computations (from the head to the body) and to enable different notions of composition. ....

H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pages 134--142. ACM, 1989.

.... To tackle this problem, several compositional semantics for logic programs have been studied by using higher order semantics [Fitting 1987; Lassez and Maher 1984; Maher 1988; Mancarella and Pedreschi 1988; O Keefe 1985] Herbrand models [Brogi et al. 1992] and notions such as full abstraction [Gaifman and Shapiro 1989]. A number of different approaches to modularizing logic programming have also been proposed. Some of them augment logic programming with constructs for declaring and using modules, much in the spirit of conventional programming languages. Typical examples are some of the existing commercial ....

Gaifman, H. and Shapiro, E. 1989. Fully abstract compositional semantics for logic programs. In Proc. 16th POPL, pp. 134--142. ACM Press.

....acting as denotations, like clauses, binary clauses, atoms, etc. which is instead the case in the standard s semantics approach for logic programming (cf. 8] In logic programming, for instance, likewise to Depr (S) one could consider Depr (H) as a variant of the compositional semantics in [32, 46], or, analogously, one can combine by reduced relative power the semantics for call patterns, partial answers, etc. Moreover, a semantic domain of functions like Depr (S) can be further approximated in different ways (e.g. by using binary relations, pointwise abstraction, etc. as suggested in ....

H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Conference Record of the 16th ACM Symp. on Principles of Programming Languages (POPL '89 ), pages 134--142. ACM Press, New York, 1989.

.... us to show that the specification frame associated to our semantic definition is equipped with the categorical constructions needed to apply the results in [21] to the class of normal logic programs, obtaining compositional and fully abstract (categorical) semantics for a number of program units [4,15]. The kind of compositionality results that can be achieved, using our semantics as the basis for defining the corresponding specification frame, are quite more powerful than the results presented in [8, 14, 19] In these papers different semantic definitions are provided for certain kinds of ....

....6.3. Theorem For any program P and any constrained literal p TMc: MP E p TMc Comp(P) E p TMc. 7 Compositionality The original aim of the approach introduced in this paper was to serve as a basis for providing compositional semantic definitions for different kinds of modular program units (e.g. [4, 15]) following the approach studied in [21] As said in the introduction, this approach consists of three steps. In the first step, one has to define and study the given units and the associated composition operations at an abstract level, making use of notions like institutions or specification ....

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H. Gaifman, and E. Shapiro, Fully abstract compositional semantics for logics programs, in Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, (1989) pp. 134-142.

....the predicates which are considered partially de ned. If P1 is an open program and P2 is an open program and pred(P 1) pred(P 2) and [ then the e 438 of P1 and P2, noted P1 [ P2, is the open program P1 [ P2. Otherwise P1 [ P2 is not de ned. The usual approach (see e.g. [4, 13]) for de ning a compositional semantics of logic program units consists in, rst, de ning as the semantic domain a class of clauses having only open or imported predicates in their tails and, second, de ning the semantics of a program P as the subset of this domain obtained by certain inferences ....

....open or imported predicates in their tails and, second, de ning the semantics of a program P as the subset of this domain obtained by certain inferences from P . For instance, in [4] the semantic domain considered is the class of all clauses having only open predicates in their tails, while in [13] the corresponding domain de ned for the kind of modules studied consists only of such clauses which are minimal. Then, in [4] the semantics of an open program is de ned as the set of all clauses in that semantic domain that can be obtained, by successive unfolding, from the given program. In this ....

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Gaifman, H., Shapiro, E., Fully abstract compositional semantics for logic programs, in: Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, 1989.

....for specification. This kind of work essentially started with the introduction of the notion of institution by Goguen and Burstall [13, 14] On the other hand, in the area of logic programming, in these years, a number of modular constructions for logic programming have been proposed (see, e.g. [2, 18, 19, 22, 23, 25]) These papers, after providing some semantic definition for their proposals, often study different kinds of properties associated to the given definition. One such property is compositionality of the semantics of the modular constructions, which holds if the semantics of the composition (for the ....

....level and, finally, if needed, providing a concrete representation of these algebraic constructions. In this paper we show the strength of this approach by studying some kinds of composition operations over corresponding kinds of (definite) logic program units already studied in the literature [2,18]. Being specific, first we study the operation of W union of open logic programs [2] then the operation of union of logic programs and, finally, a composition operation for a kind of logic programming modules [18] In all cases we provide an abstract algebraic semantics which is shown to be ....

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#H. Gaifman, and E. Shapiro, Fully abstract compositional semantics for logics programs, in Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, (1989) pp. 134142.

....P 0 . This is enough for de ning a speci cation frame of normal logic programs equipped with the categorical constructions needed to apply the results in [29] to the class of normal logic programs, obtaining compositional and fully abstract (categorical) semantics for a number of program units [8, 21]. In particular, we apply these results to provide a (categorical) semantics of arbitrary program fragments which is compositional and fully abstract with respect to (standard) union. In addition, we show that in the model class associated to every program there is a least model that can be seen ....

....in the subsection 3.2. As is well known, the least model semantics of logic programs is neither compositional nor fully abstract (in a compositional way) As a result, some form of more complex semantics must be considered if we intend to capture a compositional behaviour. For instance, [21] studies the (standard) union of logic programs and the composition of logic modules, where a logic module can be seen as a logic program 13 including an additional import export interface, with the restriction that clauses in the module do not include imported predicates in their heads. In both ....

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Gaifman, H., Shapiro, E., Fully abstract compositional semantics for logic programs, in: Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, 1989.

....operator for the rules only. The denotation of a grammar is the fixpoint of this operator, starting from the set of facts. This approach facilitates composition of programs, as the meaning of any composite sentence can be expressed in terms of the meanings of its immediate constituents. Gaifman and Shapiro (1989) observe that the classical Herbrand base semantics of logic programs is inadequate, as it identifies programs that should be distinguished and vice versa. They define the notions of compositional semantics and fully abstract semantics and show that the reason for the inadequacy of the standard ....

....a solution that incorporates a universal signature for logic programs, they change the notion of program equivalence by taking as invariant the set of all most general atomic logical consequences of the program. This definition of semantics is shown to be both compositional and fully abstract. Gaifman and Shapiro (1989) define compositional semantics as follows: let P be a class of programs (or program parts) let Ob be a function associating a set of objects, the observables, with a program P 2 P. Let Com be a class of composition functions over P such that for every n ary function f 2 Com and every set of n ....

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Gaifman, Haim and Ehud Shapiro. 1989. Fully abstract compositional semantics for logic programming.

....0 . This is enough for defining an specification frame of normal logic programs equipped with the categorical constructions needed to apply the results in [31] to the class of normal logic programs, obtaining compositional and fully abstract (categorical) semantics for a number of program units [7, 23]. In particular, we apply these results to provide a (categorical) semantics of arbitrary program fragments which is compositional and fully abstract with respect to (standard) union. In addition, we show that in the model class associated to every program there is a least model that can be seen ....

....in the subsection 3.2. As it is well known, the least model semantics of logic programs is neither compositional nor fully abstract (in a compositional way) As a result, some form of more complex semantics must be considered if we intend to capture a compositional behaviour. For instance, [23] studies the (standard) union of logic programs and the composition of logic modules, where a logic module can be seen as a logic program including an additional import export interface, with the restriction that clauses in the module do not include imported predicates in their heads. In both ....

[Article contains additional citation context not shown here]

Gaifman, H., Shapiro, E., Fully abstract compositional semantics for logic programs, in: Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, 1989.

....This model captures the results produced by terminating execution sequences. The S model generalises existing models of determinate constraint programming and (constraint) logic programming. In particular, for (constraint) logic programs, the model yields the set of minimal answers [FLMP89,GS89] This paper shows that the simple (constraint) logic programming view of programs discussed in these papers holds in the presence of synchronization. Furthermore, restricted to determinate programs, the semantics cuts down to the the semantics for determinate constraint programs, as discussed in ....

H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proceedings of Sixteenth ACM Symposium on Principles of Programming Languages, January 1989.

....answer semantics, are not compositional wrt Phi; consider for instance the modules M 1 and M 2 in Example 3. 4: they have the least D model, where M 1 Phi M and M 2 Phi M don t (the same reasoning applies for the answer constraint semantics of [14] Following an idea first introduced in [15], compositionality was then obtained by choosing a semantic domain based on clauses. As we discuss below the resulting semantics turns out to model the notion of resultant , hence its name. In order to define the semantic domain, we use the following equivalence relation, which, intuitively, is a ....

H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pages 134--142. ACM, 1989.

....x yi; heval(x ; y) fx ; yg ;i; heval(x ; y) eval(x 0 ; y 0 ) x x 0 ; y y 0 i 9 = 8 Related Work Several compositional semantics for logic programs have been proposed in the literature. These include Mancarella et al. 21] Gaifmann et al. [16] and Bossi et al. 4] In [21] the compositional semantics is provided by composing the TP functions associated with program modules. Gaifmann et al. propose to adopt clauses as semantic objects in order to characterize partial computations (from the head to the body) and to enable different ....

H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pp. 134--142. ACM, 1989.

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H. Gaifman and E. Shapiro. Fully abstract compositional semantics for logic programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pages 134--142. ACM, 1989.

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H. Gaifman and E. Shapiro. Fully Abstract Compositional Semantics for Logic Programs. In Proc. Sixteenth Annual ACM Symp. on Principles of Programming Languages, pp. 134--142. ACM, 1989.

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