W. Charatonik and A. Podelski. Directional Type Inference for Logic Programs. In G. Levi, editor, Proceedings of the International Symposium on Static Analysis. LNCS, pages 278--294, Springer-Verlag. 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Lakshman used regular sets of terms (see [9, 15, 12] They provided a procedure which checks whether a program is well typed with respect to a given set of directional types. The complexity of the type veri cation and inference in the Aiken Lakshman system was studied by Charatonik and Podelski [7] who gave an algorithm for the inferring directional types. Charatonik [6] showed that directional type checking is EXPTIME complete. Types in the Aiken Lakshman system are not polymorphic. J. Boye and J. Mauszyski in [3, 4] designed a system where directional types are merged with polymorphic ....

W. Charatonik and A. Podelski. Directional type inference for logic programs. In Proceedings of the Fifth International Static Analysis Symposium, LNCS 1503, pages 278294. Springer Verlag, 1998.

....combining set constraints with other analyses, in the framework of abstract interpretation. 8. 3 Complexity and Scalability Charatonik and Podelski remark that the worst case complexity of set based analysis is seldom encountered since types in user written programs tend to be relatively small [7]. This does indeed seem to be 12 true for type analysis applications of set constraints. However, for veri cation and planning problems, the types can grow very large since they can be combinatorial combinations of initial states present in the top goal. For instance, some of the planning ....

W. Charatonik and A. Podelski. Directional type inference for logic programs. In G. Levi, editor, Proceedings of the International Symposium on Static Analysis (SAS'98), Pisa, September 14 - 16, 1998, volume 1503 of Springer LNCS, pages 278-294. Springer-Verlag, 1998.

....in the constraint checking. The second one 2 translates the constraints into finite domain constraints and uses a finite domain solver for the constraint checking. Section 5 discusses alternative approaches: the use of model generators for first order logic [27, 28, 35, 24] of type analysis [19, 10] (a query fails if its inferred type is empty) and of program specialisation [22, 14] the query fails if the program for the given query can be specialised into the empty program) In section 6, the different approaches are compared. Finally, in section 7, we draw some conclusions. We ....

....proven if the types of shouldfail(X) are empty. Also set based analysis [20] can be used to approximate the success set. Set based analysis originates from [23] it was then studied (improved and implemented) in [20] The tool that we use is a composition of inference of a directional type (as in [10], based on set based analysis) with the theorem prover SPASS [34] Program specialisation. One could also employ program transformation, and more specifically program specialisation techniques to prove failure of the query. If for the given query, the program can be specialised in the empty ....

W. Charatonik and A. Podelski. Directional type inference for logic programs. In Giorgio Levi, editor, Proceedings of the Fifth International Static Analysis Symposium (SAS), LNCS 1503, pages 278--294, Pisa, Italy, 1998. Springer-Verlag.

....with every predicate a pair of sets that characterize, respectively, expected calls and successes of the predicate. Checking correctness of a logic program wrt directional types has been discussed by several authors (see e.g. Aiken Lakshman, 1994; Boye, 1996; Boye Ma luszy nski, 1997; Charatonik Podelski, 1998) and references therein) Their proposals can be seen as special cases of general verification methods of (Drabent Ma luszy nski, 1988; Bossi Cocco, 1989; Deransart, 1993) Technically, directional type checking consists in proving that the sets specified by given directional types of a ....

....from a finite collection of base sets. Term grammars and set constraints have been used by many authors for specifying and inferring types for logic programs (see among others (Mishra, 1984; Fruhwirth et al. 1991; Dart Zobel, 1992; Gallagher de Waal, 1994; Aiken Lakshman, 1994; Boye, 1996; Charatonik Podelski, 1998)) We show how the operations on discriminative term grammars can be extended to handle sets of constrained terms introduced by the extended discriminative term grammars. A solution to the second problem is an original contribution of this paper. We present a natural extension of the notion of ....

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Charatonik, W., & Podelski, A. (1998). Directional type inference for logic programs. Levi, G. (ed), Proc. of SAS'98. Lecture Notes in Computer Science. Springer-Verlag.

....uses techniques from finite domain constraint solving [20] to further prune the search. Also the suitability of alternative methods for solving this problem is analysed. The use of a general purpose model generation tool [16, 17] is evaluated. We have also explored whether tools for type inference [11, 5] can show that such queries have an empty success set and whether conjunctive partial deduction [13] can specialise such queries into a trivially failing program. Section 2 recalls the basics about pre interpretations and introduces a trivial example. Section 3, explains how a pre interpretation ....

....An example FINDER program can be found in appendix B. Regular approximations (RA) were computed with a system due to John Gallagher, conjunctive partial deduction (CPD) with a system due to Michael Leuschel. Witold Charatonik was so kind to run our examples on a tool (some info can be found in [5]) for set based analysis (SBA) he developed together with Harald Ganzinger, Christoph Meyer, Andreas Podelski and Christoph Weidenbach. Table 3 gives the results: For the abductive system the time and the number of backtracks (wrt. the choice made in the pre interpretation) for the constraint 6 ....

W. Charatonik and A. Podelski. Directional type inference for logic programs. In Proc. SAS'98, LNCS, Pisa, Italy, 1998. To appear.

....Theorem 4) The global suspension of a process is not necessarily a programming error. That a process must suspend forever in order to avoid a runtime error is, however, a problem worth diagnosing and reporting. Related Work. To our knowledge, set based analysis for logic programming (see e.g. [5, 18, 13, 14, 22, 23, 30]) has previously only been designed to approximate the success set (which can be characterized by the least model semantics) Mishra s analysis [30] is often cited as the historically first one here. Heintze and Jaffar [23] have shown that Mishra s analysis is less accurate than theirs in two ....

....solutions over the domain of non empty path closed sets of (finite or infinite) trees (see Remark 4) the proof of Theorem 2 goes through also for P instead of P , and the statements in this and the next section hold in the appropriate adaptation. One can prove that gSol( P ) gSol( P ) see [5]) i.e. the analysis using path closed constraints is less accurate than the one with co definite set constraints. Solving path closed constraints is still an open problem (both, for least and for greatest solutions) 5 Concurrent Constraint Programs We consider concurrent constraint (cc) ....

W. Charatonik and A. Podelski. Directional Type Inference for Logic Programs. In G. Levi, editor, Proceedings of the International Symposium on Static Analysis. LNCS, pages 278--294, Springer-Verlag. 1998.

....which they are translated. The connection is such that the type check is sound and complete for discriminative types (it is still sound for general regular types) Another decidability proof (without complexity analysis) for type checking for discriminative directional types is given in [13] In [19] we proved that directional type checking wrt. discriminative types is DEXPTIME complete and gave an algorithm for inferring (regular, not necessarily discriminative) directional types. The methods used in the mentioned papers are not strong enough to prove the decidability of directional type ....

....mentioned papers are not strong enough to prove the decidability of directional type checking wrt. general regular types. In Section 4, using automata on t dags, we prove the decidability of this problem. This improves the results by Aiken and Lakshman [5] Boye [13] and Charatonik and Podelski [19], where decidability is restricted to discriminative types. Set constraints. There are several kinds of automata used in solving systems of set constraints: tree set automata with free variables [24] tree set automata [25] Sigma graph automata [26] as well as standard tree automata [17, 18, ....

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W. Charatonik and A. Podelski. Directional type inference for logic programs. In G. Levi, editor, Proceedings of the Fifth International Static Analysis Symposium (SAS), LNCS 1503, pages 278--294, Pisa, Italy, 1998. Springer-Verlag.

....for combining types) Prescriptive and descriptive approaches. There are two main streams in the research on types in logic programming. In the prescriptive stream the user has to provide type declarations for predicates; these declarations form an This is an extended and revised version of [19, 13] integral part of the program. The system then checks if the program is welltyped, that is, if the type declarations are consistent. This approach can be found in particular in [46, 34, 42, 56, 44, 1] In the descriptive stream the types are inferred by the system and used to describe semantic ....

W. Charatonik and A. Podelski. Directional type inference for logic programs. In G. Levi, editor, Proceedings of the Fifth International Static Analysis Symposium (SAS), volume 1503 of LNCS, pages 278-294, Pisa, Italy, 1998. Springer-Verlag.

....of this clause by the set of triples h[ x; yi where x and y are any terms and thus loose the information that a second and third argument are of the same type. To overcome this problem, 24, 20] introduced approximations based on magic set transformation of the input program. It was observed in [12] that types of the magic set transformation of a program coincide with directional types of the initial program as they appear in [32, 8, 4, 2, 1, 3, 6, 5, 7] Directional types form a type system for logic programs which is based on the view of a predicate as a directional procedure which, when ....

....regular types, it is sound and complete only for discriminative ones. It is based on solving negative set constraints and thus runs in nondeterministic exponential time. Another algorithm (without complexity analysis) for type checking for discriminative directional types is given in [5] In [12] it is proved that directional type checking wrt. discriminative types is 2 DEXPTIME complete and an algorithm for inferring (regular, not necessarily discriminative) directional types is given. The methods used in the mentioned papers are not strong enough to prove the decidability of ....

[Article contains additional citation context not shown here]

W. Charatonik and A. Podelski. Directional type inference for logic programs. In G. Levi, editor, Proceedings of the Fifth International Static Analysis Symposium (SAS), LNCS 1503, pages 278-294, Pisa, Italy, 1998. Springer-Verlag.

....whether the problem is decidable at all. Below we recall the basic idea of the path closed analysis and show a small example exhibiting the di erence between the three (set based, path closed and path based) analyses. A further discussion on set based and path closed analyses can be found e.g. in [8]. A regular set of terms is called path closed if it is recognizable by a top down deterministic tree automaton. This is equivalent to other notions occurring in the literature: path closed sets are also called tuple distributive, discriminative or deterministic. The path closure operator PC ....

W. Charatonik and A. Podelski. Directional type inference for logic programs. In G. Levi, editor, Proceedings of the Fifth International Static Analysis Symposium (SAS), LNCS 1503, pages 278-294, Pisa, Italy, 1998. Springer-Verlag.

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