Ulf Nilsson. Abstract interpretation: a kind of magic. Theoretical Computer Science, 142(1):125--138, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....triggering rule Pm . It can be proved [22] that In terms of natural deduction and similar systems, this is often called the inversion principle [27, ch. II] It was pointed out to us later that this construct is very similar to the magic set transformation used in logic programming [25]. Table 1 The weight function for BAN logic F F K 1 N p 1 1 P#X 2 X 3 #(X) 1 Q 2 K K P 2 (X ,Y ) 1 Y Theorem 1: For any set of hypotheses H and purported conclusion C for the proof system, H , # C . 3.3. The Decision ....

Ulf Nilsson. Abstract interpretation: a kind of magic. Theoretical Computer Science, 142(1):125--138, 1995.

....where possible completeness) w.r.t. the well founded model semantics [8, 15] In order to be prepared for the incorporation of constructive negation [3, 7] into our framework, we treat positive and negative literals symmetrically. This means that we do not impose a positivistic computation rule [14, 17] (i.e. one that always prefers positive literals) Moreover, in contrast to extensions of OLDT resolution for stratified programs [9, 19] we maintain only one table, where the entry for an atom can be used either positively or negatively. This is the main point where our research deviates from ....

U. Nilsson. Abstract interpretation: A kind of Magic. In Programming Language Implementation and Logic Programming 91, Lecture Notes in Computer Science 528, pages 299--309. Springer-Verlag, 1991. Extended version to appear in Theoretical Computer Science.

....(I) The properties of predicates are computed bottom up based on these operations. We restrict our attention to properties that are valid when a predicate succeeds. Properties that are dependent on some execution order can be obtained using transformation techniques such as Magic sets 3 [BMSU86, Nil91]. For every predicate p(X) in the program we associate a constraint p # (X) such that every substitution that satisfies p also satisfies p # . Hence p # is a necessary condition for p to succeed and therefore can be viewed as a property 1 of p. Given r # for every built in predicate r, ....

U. Nilsson. Abstract interpretation: A kind of magic. In International Symposium on Programming Language Implementation and Logic Programming, number 528 in LNCS, pages 299--309. Springer Verlag, 1991.

....grammars Tabling allows creation of chart parsers and can simulate Earley Recognition. Preference Logic Grammars create a powerful mechanism for handling ambiguities in Grammars To be discussed below 7 Overview ffl Program Analysis of Imperative, Functional, and Logic Programs: [90], 69] 68] 65] 100] 37] 14] 27] 66] ffl Abstraction of programs to be analyzed creates positive loops even when concrete programs do not loop Example: Groundness Analysis (from [26] append( Ys,Ys) append( X Xs] Ys, X Zs] append(Xs,Ys,Zs) gappend(g,Y,Y) ....

Ulf Nilsson. Abstract interpretation: A kind of magic. In PLILP91, pages 299--310, 1991.

....only formulations of evaluation strategies and not general theories of Datalog, updates, etc. Does not consider some newer areas such as Tabling Magic Sets and constraints. 7 Motivation ffl Practical and Research Applications Parsing [72] 1] 63] 62] Program Analysis [71], 58] 57] 86] 31] Software Verification [100] Graphics and Data Visualization [46] 26] Diagnosis Systems [32] 28] Other [13] 77] SQL3 Standard includes recursion. 8 Definite Programs Many formulations of tabling are more or less equivalent for definite programs. ....

Ulf Nilsson. Abstract interpretation: A kind of magic. In PLILP91, pages 299--310, 1991.

....conjoining functions. This speeds up computation and is simpler than more general query directed implementations of Pos . The transformation given here generalizes the well known magic set transformation, which can be used to compute information about the calls for a single query, see for example [19]. Codish and Demoen [4] have independently investigated query independent groundness analysis based on Pos . While they do not consider precision, Codish and Demoen have implemented their analysis. Their experimental results are most encouraging, especially as in the Codish Demoen approach, the ....

Nilsson, U. Abstract interpretation: A kind of magic. In J. Ma/luszy'nski and M. Wirsing, editors, Programming Language Implementation and Logic Programming (Lecture Notes in Computer Science 528), pages 299-309. Springer-Verlag, 1991. End of Paper; Total pages = 15. Words = 4953 plus abstract (81 words) plus bibliography.

....produce new items from tabulated ones. A subsumption test is done to avoid tabulating again redundant items. Rules are applied until a fixed point is reached. This general scheme encompasses various tabular algorithms appearing in the literature, such as [ASU86, Ear70, Tom87, Lan74] in Parsing, [Nil91, LCMVH91] in Abstract Interpretation, magic sets [BMSU86] and memoization [TS86, Vie87, SSW94] in Deductive Databases and [CF92] in Constraint Logic Programming. These algorithms have sometimes been designed independently. Each one required non trivial adequacy proofs. However, they are based on common ....

Ulf Nilsson. Abstract interpretation : A kind of magic. In Proc. of PLILP'91, 1991.

....with the reduction of backtracking phenomena when parsing. To attain this goal, authors often follow two different approaches: ffl Reduce the search space, using control techniques. Here, we distinguish between dynamic techniques when control is made by rewriting programs (Bancilhon et al. 1986; Nilsson 1991) and static ones when control is made by an external driver, which determines the action to be performed (Nilsson 1986) Some authors (Rosenblueth and Peralta 1994) try to integrate both strategies. ffl Incorporate dynamic programming techniques (Lang 1991; Pereira and Warren 1983) which ensure ....

....in consequence, linear parsing can be performed while local determinism is present. A Comparison with Previous Works We shall compare our work with some of the most representative approaches based on inference systems for logic programs. We take as reference the work of U. Nilsson (Nilsson 1986; Nilsson 1991), F. Bancilhon et al. Bancilhon et al. 1986) B. Lang (Lang 1991) E. Villemonte de la Clergerie (De la Clergerie 1993) and D. Rosenblueth and J. Peralta (Rosenblueth and Peralta 1994) U. Nilsson (Nilsson 1986) and D. Rosenblueth and J. Peralta (Rosenblueth and Peralta 1994) propose SLR(1) like ....

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Nilsson, Ulf. 1991. "Abstract interpretation: A kind of magic". Proc. of PLILP'91.

.... transformation for DATALOG programs [BMSU86, BR87, Ram88] It has been extended to PROLOG programs as the Magic Templates transformation [Ram88] and the Alexander Templates transformations [RLK86, Sek89] The formulation of the transformation rules differs slightly from [BR87] and takes after [Nil91]. In particular, the atoms call(A) resp. ret(A) are used in place of magic(A) resp. of A) 1. Each clause fl k of P is replaced by the n k 1 following clauses: ff) ret(A k:0 ) Gammacall(A k:0 ) ret(A k:1 ) ret(A k:n k ) fi) 8i 2 [0; n k Gamma 1] call(A k:i 1 ) Gammacall(A ....

U. Nilsson. Abstract interpretation : A kind of magic. In Proc. of PLILP'91, 1991.

....LR ones, differentiate the syntactic contexts in function of the state where the parsing process is, by virtue of the application of a predictive technique in the generation of the parser. The idea to consider bottom up evaluation with a top down predictive control is not new. The Magic Set [5, 6, 7, 8] techniques reduce the number of useless intermediate results produced by using a goal oriented bottom up evaluation. The main drawback of this approach is the extra cost these methods require. In effect, the addition of predictive control is made by re writing logic programs and introducing new ....

U. Nilsson, "Abstract interpretation: A kind of magic", in Proc. of PLILP'91, 1991.

....independent, parametric w.r.t. the (local) selection rule and allow us to characterize properties of the correct call patterns [61, 59] which are those call patterns which belong to successful derivations. A similar (yet goal dependent) result can be obtained by using a transformational approach [31, 99]. A program P and a goal G are transformed (by using a transformation similar to the magic set transformation) into a program P 0 , such that every call pattern of G in P is a success pattern of P 0 . An abstraction of the operator T Pi P 0 of definition 3.13 can now be used to compute in ....

U. Nilsson. Abstract Interpretation: A Kind of Magic. In J. Maluszy'nski and M. Wirsing, editors, Programming Language Implementation and Logic Programming, Proceedings 3rd Int'l Symposium PLILP'91, volume 528 of Lecture Notes in Computer Science, pages 299--309. SpringerVerlag, Berlin, 1991.

....in practice deals with the reduction of backtracking phenomena when parsing. To attain this goal, authors often follow two different approaches: ffl Reduce the search space, using control techniques. Here, we distinguish between dynamic techniques when control is performed by rewriting programs [1, 2], and static ones when control is applied by an external M. Vilares is with the Computer Science Department, University of Corunna, Campus de Elvi na s n, 15071 A Coru na, Spain. E mail: vilares dc.fi.udc.es. M. A. Alonso is currently at INRIA, Domaine de Voluceau, Rocquencourt, B.P.105, 78153 Le ....

....performed while local determinism is present. 1 the general case is not always decidable [6] 5 A comparison with previous works We shall compare our work with some of the most representative approaches based on inference systems for logic programs. We take as reference the work of Nilsson in [3, 2], Bancilhon et al. in [1] Lang and de la Clergerie in [5, 8] and Rosenblueth and Peralta in [4] Nilsson [3] and Rosenblueth and Peralta [4] propose SLR(1) like evaluators, more efficient than grammar oriented algorithms, as [6] because they drastically limit backtracking. The difference ....

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U. Nilsson, "Abstract interpretation: A kind of magic", in Proc. of PLILP'91, 1991.

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