G. Levi and P. Mancarella. The Unfolding Semantics of Logic Programs. Technical Report TR-13/38, Dipartimento di Informatica, Universit`a di Pisa, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of the semantics of CLP, obtained by defining various model notions, each corresponding to a specific operationally observable property, as firstly defined in [3] for the pure logic programming case. In this paper, we extend some results related to the pure logic programming and presented in [8], dealing with an alternative way to characterize the operational behaviour of logic programs. The main idea is that we can consider a possibly infinite collection of unit clauses as an alternative representation of the model. This set is obtained from the original program, via a program ....

....of view and for a deeper understanding of the logic programs semantics. In particular the immediate consequence operator T P can be defined in terms of the unfolding rule. The unfolding rule presented in this paper is an extension, in the area of constraint logic programs, of the one presented in [8]. 2 Preliminaries Let us recall some basic concepts about CLP. For a more complete treatment on the subject see [6, 5] In Constraint Logic Programming, the basic operational step is constraint solvability on a given domain. It follows that the algebraic approach to the semantics is natural for ....

[Article contains additional citation context not shown here]

G. Levi and P. Mancarella. The Unfolding Semantics of Logic Programs. Technical Report TR-13/38, Dipartimento di Informatica, Universit`a di Pisa, 1988.

....program. The compositional fixpoint semantics F Omega (P ) of P is defined as F Omega (P ) T Omega P . 7. 2 Equivalence results The equivalence between the operational and the fixpoint semantics can be proved by introducing the intermediate notion of unfolding semantics U Omega (P ) [35, 14] and following the lines of the similar proof in [7] U Omega (P ) is obtained as the limit of the (top down) unfolding process and is equivalent to the operational semantics O Omega (P ) The proof of this equivalence is straightforward since O Omega (P ) and U Omega (P ) are based on 27 ....

G. Levi and P. Mancarella. The Unfolding Semantics of Logic Programs. Technical Report TR-13/88, Dipartimento di Informatica, Universit`a di Pisa, 1988.

....3. 1 Unfolding semantics and equivalence results The equivalence between the operational semantics of an isa hierarchy HP and the fixpoint semantics of the corresponding HP can be proved in a concise and elegant way by introducing the intermediate notion of unfolding semantics U(P ) [18, 19, 8]. The unfolding semantics is obtained as the limit of the top down unfolding process. Definition 3.11 Let P be a h Sigma; Delta; Thetai program. Then we define the collection of cs interpretations P 1 = P Pn 1 = unf Pn (P [ Id Open(P ) The unfolding semantics U(P ) of the program P is ....

.... 1 ; A k ) H 1 ; H k ) fl jvar(G) # jvar(G) The proof of the above result can be carried out by using a straightforward inductive argoment, since U(P ) is based on a top down definition which mimics a parallel SLD derivation (the proof is essentially the same of those given in [19, 8] for the case of standard programs) Then, the desired equivalence can be stated in terms of the following Theorem 3.14 Let HP be an isa hierarchy, HP be the corresponding h Sigma; Delta; Thetai program and G = A 1 ; A k be a goal with P red(G) Sigma [ Delta [ Theta) Then: ....

G. Levi and P. Mancarella. The Unfolding Semantics of Logic Programs. Technical Report TR13 /88, Dipartimento di Informatica, Universit`a di Pisa, 1988.

.... can be computed both by a top down construction (a success set) and by a bottom up construction (the least fixpoint of suitable continuous immediate consequences operators on interpretations) The link between the top down and the bottom up constructions is given by an unfolding operator [82, 83]. The equivalence proofs can be stated in terms of simple properties of the unfolding and the immediate consequences operators [41] It is worth noting that the aim of the approach is not defining a new notion of model. We are simply unhappy with the traditional declarative semantics, because it ....

....the operational semantics. If this equivalence holds, the immediate consequences operator T P models the observable properties and may be used for bottom up program analysis. Concise and elegant equivalence proofs can be obtained by introducing the intermediate notion of unfolding semantics U [82, 83]. Unfolding is a well known program transformation rule which allows us to replace procedure calls by procedure definitions. The unfolding of the clauses of program P using the procedure definitions in program I is denoted by unfP (I) The unfolding and the operational semantics are strongly ....

[Article contains additional citation context not shown here]

G. Levi and P. Mancarella. The Unfolding Semantics of Logic Programs. Technical Report TR-13/88, Dipartimento di Informatica, Universit`a di Pisa, 1988.

....semantics, the analysis, and the transformation of logic programs. These include the semantics of concurrent logic languages [22, 6, 9, 13] the semantics of partial computations [10] the abstract interpretation of pure logic programs[1, 3, 18] correctness of program transformation techniques [23, 2], semantics of logic programs with negation [27] and the definition of a non ground finite failure set semantics [24] The same kind of applications can be developed in the CLP case by using our SS 3 (P; semantics. In particular we are currently investigating the abstract interpretation of CLP ....

G. Levi and P. Mancarella. The unfolding semantics of logic programs. Technical Report TR-13/38, Dipartimento di Informatica, Universit`a di Pisa, 1988.

....) p(a; a) r(X) q(X) r(a) s(Y ) q(Y ) s(a) g F Omega (P ) T Omega P 3 3 1.4. 1 Unfolding semantics and equivalence results The equivalence between the operational and the fixpoint semantics can be proved by introducing the intermediate notion of unfolding semantics U Omega (P ) [22, 23, 9]. U Omega (P ) is obtained as the limit of the (top down) unfolding process. Since the unfolding rule preserves computed answers in a compositional way, U Omega (P ) is equivalent to the operational semantics O Omega (P ) The proof of this equivalence is straightforward since O Omega (P ) ....

G. Levi and P. Mancarella. The Unfolding Semantics of Logic Programs. Technical Report TR-13/88, Dipartimento di Informatica, Universit`a di Pisa, 1988.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC