Maurice Bruynooghe, Wim Vanhoof, and Michael Codish. Pos(T) : Analyzing dependencies in typed logic programs. In Perspectives of System Informatics, 4th International Andrei Ershov Memorial Conference, PSI 2001, Revised Papers, volume 2244 of LNCS, pages 406-420. Springer-Verlag, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....programming (see e.g. 1, 5, 7, 9] Termination proofs often are based on the concept of a norm (a level mapping) a function mapping terms (atoms) of the program to the natural numbers. Recently, using type information became a prominent trend in termination analysis for symbolic computations [2, 3, 13]. On the other hand, the study of termination of numerical programs led to the emerging of the adorning technique [11, 12] Both approaches are based on the idea of distinguishing between different subsets of values for variables, and deriving norms and level mappings based on these subsets. ....

M. Bruynooghe, W. Vanhoof, and M. Codish. Pos(T): Analyzing dependencies in typed logic programs. In D. Bjrner, M. Broy, and A. V. Zamulin, editors, Perspectives of System Informatics, 4th International Andrei Ershov Memorial Conference, PSI 2001, Akademgorodok, Novosibirsk, Russia, July 2-6, 2001, Revised Papers, volume 2244 of Lecture Notes in Computer Science. Springer Verlag, 2001.

....a structured way to automatically derive suited norms. The problems encountered in the derivation of relations between typed norms [8] inspired us to explore a di erent way of representing these relations. This work complements our earlier work on deriving type based instantiation dependencies [4], which are a necessary ingredient for a type based termination analysis. In recent work [16] we have developed a binding time analysis for logic programs that makes heavy use of termination analysis in order to decide what calls can be safely unfolded during specialisation. For this ....

....termination quickly by searching in a structured way through a number of possible norms without requiring the user to assist in the construction of these norms may be more suited than a heavy analysis employing dedicated norms. In Section 2 we recall the basics of the instantiatedness analysis of [4] and develop a type based size abstraction. In section 3 we introduce a type based termination condition and we conclude in Section 4. 2 Characterising Terms 2.1 About Terms and Types We assume familiarity with logic programming concepts [11, 1] We use T erm = T ( V ) to denote the set of ....

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Maurice Bruynooghe, Wim Vanhoof, and M Codish. Pos(T) : Analyzing dependencies in typed logic programs. In Proceedings of Andrei Ershov Fourth International Conference \Perspectives of System Informatics", 2001. accepted.

....# (denoted as # # #) if there is f #1 . # n## # F and a type substitution # such that ## = # and # i # = # for some i # 1, n . The transitive, reflexive closure of # is denoted as # # . If # # # #, then # is a subterm type of #. We had defined these relations previously [15] In [2], subterm types are called constituents. We now discuss two problems related to the generalisation to polymorphism. They have been mentioned previously [15] and are illustrated here with examples. Example 3.6. Whenever we give a particular typed language, K is given implicitly as the set of ....

....to U in the same way as k(str) relates to str . To rule out this anomaly, we impose the following condition on K, F . Flat Range Condition: For all f #1 . # n## # F , # is a flat type. In Mercury (and in ML and Haskell) this condition is enforced by the syntax. In the recent work of [2], we also find similar conditions. So from now on, we assume that any typed language meets these two conditions. 3.3 Labelling as Presented in [11] Labellings can be used to characterise the degree of instantiation of a term taking its type into account, i.e. analyse a term on a per role basis ....

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M. Bruynooghe, W. Vanhoof, and M. Codish. POS(T ): Analyzing dependencies in typed logic programs. In D. Bjrner, M. Broy, and A. Zamulin, editors, Preproceedings of the Andrei Ershov Fourth International Conference, pages 212--218. Final version to appear in LNCS series of Springer-Verlag, 2001.

....a structured way to automatically derive suited norms. The problems encountered in the derivation of relations between typed norms [9] inspired us to explore a di erent way of representing these relations. This work complements our earlier work on deriving type based instantiation dependencies [3], which are a necessary ingredient for a type based termination analysis. In recent work [27] we have developed a binding time analysis for logic programs that makes heavy use of termination analysis in order to decide what calls can be safely unfolded during specialisation. For this ....

....termination quickly by searching in a structured way through a number of possible norms without requiring the user to assist in the construction of these norms may be more suited than a heavy analysis employing dedicated norms. In Section 2 we recall the basics of the instantiatedness analysis of [3] and develop a type based size abstraction. In Section 3 we present the actual analysis of size relations in a monomorphic as well as a polymorphic setting. Next, we introduce a type based termination condition in Section 4 and conclude in Section 5 with a discussion and comparison with related ....

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Maurice Bruynooghe, Wim Vanhoof, and Michael Codish. Pos(T): Analyzing dependencies in typed logic programs. In Dines Bjrner, Manfred Broy, and Alexander V. Zamulin, editors, Perspectives of System Informatics, PSI 2001, Revised Papers, volume 2244 of LNCS, pages 406-420. Springer, 2001.

....polymorphic typed variables need not be considered. All of the information required for termination analysis relevant to such types can be reconstructed from the polymorphic types. A preliminary investigation of the reuse of rigidity and size information based on polymorphic types are described in [6] and [26] respectively. However, these works focus mainly on monomorphic types and contain preliminary ideas for polymorphic types applicable only for simple instances of the polymorphic types. The reuse of analysis results about polymorphic predicates is an important step in supporting modular ....

....rigidity information. This gives a nite approximation of the calls and loops from which the analyzer can try to determine that the program terminates. Rigidity can be represented in the domain Pos of positive Boolean functions [20] as shown in [15] A type based rigidity analysis is developed in [6]. Size relations express linear information about the sizes of terms with respect to a given norm function. Termination analysis for logic programs can be based (examples are in [7, 18, 22] on a technique termed abstract compilation. The program to be analysed is rst abstracted, using the ....

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M. Bruynooghe, W. Vanhoof, and M. Codish. Pos(t): Analyzing dependencies in typed logic programs. In Perspectives of System Informatics, 4th International Andrei Ershov Memorial Conference, (PSI). Lecture Notes in Computer Science, vol. 2244. Springer-Verlag, 406-420.

....and nally, if there are several Combining Norms to Prove Termination 11 candidate norms and it is not clear which (linear combination of di erent norms) is suitable then our system can nd it automatically. The use of types to re ne other program analyses has recently been considered in [5] and [17] In those papers the authors observe that if a program is well typed then only subterms of the same type can be uni ed. Hence, type information is used to re ne the analysis of uni cations in a program by considering for each type which of subterms can be matched. The idea of multiplying ....

Maurice Bruynooghe, Wim Vanhoof, and Michael Codish. Pos(t): Analyzing dependencies in typed logic programs. Technical report, Presented at the Andrei Ershov Fourth International Conference on Perspectives of System Informatics, July 2001. Source available from http://www.cs.bgu.ac.il/ mcodish/Papers/Pages/TypedPos.html.

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Maurice Bruynooghe, Wim Vanhoof, and Michael Codish. Pos(T) : Analyzing dependencies in typed logic programs. In Perspectives of System Informatics, 4th International Andrei Ershov Memorial Conference, PSI 2001, Revised Papers, volume 2244 of LNCS, pages 406-420. Springer-Verlag, 2001.

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M. Bruynooghe, W. Vanhoof, and M. Codish. Pos(T) : Analyzing dependencies in typed logic programs. PSI, LNCS 2244:406--420, 2001.

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