T. Sato and H. Tamaki. Transformational logic program synthesis. In Proceedings of the International Conference on Fifth Generation Computer Systems, pages 195  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[15] cannot express directly negative information, although negation is a useful speci cation tool. Since negation as failure does not t well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation introduced in [21] for Horn logic to a fragment of higher order HHF. This entails nding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and ....

....rst by Gabbay [8] the unrestricted combination of NF and embedded implication is particularly problematic, since it leads to the failure of basic logic principles such as cut elimination. The approach to negation that we adopt is transformational, also known as intensional negation, initiated in [21] and developed in Pisa [3] for Horn logic with negation and later extended to constraint logic programming [5] Roughly, given a clause with occurrences of negated predicates, say Q G; P; G 0 , where P is an already de ned atom, the aim is to derive a positive predicate, say non P which ....

T. Sato and H. Tamaki. Transformational logic program synthesis. In International Conference on Fifth Generation Computer Systems, 1984.

....decades there has been a fruitful interaction between unfold fold program transformation and program synthesis. To illustrate this point, let us recall here the program synthesis methods based on derivation rules, such as the one proposed by Hogger [32] and, along similar lines, those reported in [34,35,42,68,69] which make use of derivation rules similar to the unfold fold rules. In this regard, the speci c contribution of our chapter consists in providing a method for program synthesis which ensures the correctness w.r.t. the perfect model semantics. Also related to our rules and strategies approach, ....

T. Sato and H. Tamaki. Transformational logic program synthesis. In Proceedings of the International Conference on Fifth Generation Computer Systems, pages 195

.... for example: Darlington and Burstall have designed a research tool for the development of functional program transformation methodologies [Bur Darl 77, Darl 81] Tamaki and Sato have carried out similar research except they are concerned with the transformation of logic programs [Tamaki Sato 83, Tamaki Sato 84] Grant and Zang have developed heuristics for the automatic transformation of Prolog programs [Grant 88] However, all these prior approaches are concerned with the direct transformation of executable code and not with the transformation of constructive proof structures. The latter approach has ....

H. Tamaki and T.Sato. Transformational Logic Program Synthesis, Proceedings of the International Conference on Fifth Generation Computer Systems 1984 (edited by ICOT 1984).

....[12] cannot express directly negative information, although negation is a useful speci cation tool. Since negationas failure does not t well in a logical framework, especially one endowed with hypothetical and parametric judgments, we adapt the idea of elimination of negation introduced in [17] for Horn logic to a fragment of higher order HHF. This entails nding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and ....

....by Gabbay [6] the unrestricted combination of NF and embedded implication is particularly problematic, since it leads to the failure of basic logic principles such as cut elimination. The approach to negation that we adopt is transformational, also known as intensional negation, initiated in [17] and developed in Pisa [3] for Horn logic with negation. Roughly, given a clause with occurrences of negated predicates, say Q G; P; G 0 , where P is an already de ned atom, the aim is to derive a positive predicate, say non P which implements the complement of P , preserving operational ....

T. Sato and H. Tamaki. Transformational logic program synthesis. In International Conference on Fifth Generation Computer Systems, 1984.

....has been mechanically synthesized. This entails two major steps 1. Compute complement of heads of clauses in the predicate definition. 2. Bring definition in negation normal form the respecting operational semantics. While this approach has been investigated for first order Horn clauses [ST84,BMPT90] and CLP programs [BLLM94] the field has not been explored, at the best of our knowledge, w.r.t. higher order logics and logical frameworks. For the latter this notion of intensional negation is the most adequate, see [Momng] for a discussion. We cannot discuss item 2: here. We can suggest its ....

T. Sato and H. Tamaki. Transformational logic program synthesis. In International Conference on Fifth Generation Computer Systems, 1984.

....data representations, programs and proofs. Moreover, some remarks about related work and possible future research are given. 1 Introduction For many years a lot of work has been devoted to the study of program development in logical framework using techniques based on program transformation [17], or on theorem proving [11] Here we consider the latter with a particular approach which is programming with proofs using constructive (intuitionistic) logic and its applications to the activity of programming [5] Different theories related to this technique have been discussed in some ....

Sato, T., Tamaki, H., Transformational logic program synthesis, In International Conference on Fifth Generation Computer Systems, ICOT Tokyo, Japan, 1984.

.... non ground literals was tackled by various extensions of Negation As Failure, called constructive negation. Examples are intensional negation [3, 4] Chan s constructive negation [7, 8] fail substitutions [20] and fail answers [11, 10] The idea of intensional negation, originally sketched in [25] and then formalized for positive logic programs in [3, 4] is the following. Given a normal program P , we derive a new program P 0 , which contains clauses which allow us to compute the answers to negative queries. Example 1. Let P be the program feven(0) even(s(s(X) even(X)g. The new ....

T. Sato and H. Tamaki. Transformational Logic Programs Synthesis. In Proceedings of the International Conference of Fifth Generation Computer Systems, 1984, pages 195--201, 1984.

....negation means approaches to overcome the restrictions of negation as failure. step. Another extension in [Cha89, Stu91] is that not only literals can be selected but also some other negated formulae. The transformational approach to negation (Barbuti et al. BMPT90] Sato and Tamaki [ST84]) does not use the program completion explicitly. Instead it introduces new predicates to a program in order to express the negative information. The idea is to construct a definite program that defines both the original and the new predicates. However in many cases the resulting program contains ....

T. Sato and H. Tamaki. Transformational logic program synthesis. In Proceedings of the International Conference on Fifth Generation Computer Systems, pages 195--201, 1984.

....be divided into two main categories [27] 31] Deductive Synthesis (also known as Transformational Synthesis) meaning preserving transformations are applied to the specification, until an algorithm is obtained. Sample works are those of Clark [18] Hogger [48] Bibel et al. 6] Sato and Tamaki [73] [74] Lau and Prestwich [62] Kraan et al. 56] and so on. The theoretical foundations to deductive synthesis are being laid out by Lau and Ornaghi [58] 61] 1. Let s ignore here the problem that the intentions tend to be unknown or to change over time. Constructive Synthesis (also known ....

Taisuke Sato and Hisao Tamaki. Transformational logic program synthesis. In Proceedings of the International Conference on Fifth-Generation Computer Systems, pages 195--201, 1984.

....and induction choices. 1 Introduction The derivation of correct and efficient programs from formal specifications can be considered in different ways. An important one consists in using the transformation technique which is a method available in the case of functional [4] or logical programs [22] preserving semantics. The transformation methodology of program derivation is based on the idea of first writing an initial program version which corresponds to a given specification and then to derive by several transformation steps a new program version still correct and more efficient. For ....

.... holds) We will see that is beneficial to consider this definition or invariant as specification that is rather hard to find (eurekastep) 14] The proof transformation methodology has been introduced and applied for functional languages [4] but it can also be applied in the case of logic programs [22]. One basic idea of that methodology is the separation of efficiency requirement from the correctness requirement. The latter one is taken into account by allowing only transformation rules which are correctness preserving. The efficiency requirement is taken into account by considering heuristic ....

T. Sato and H. Tamaki. Transformational logic program synthesis. In International Conference on Fifth Generation Computer Systems, Tokyo, Japan, 1984. ICOT.

....transformations for definite clause programs so as to preserve the equivalence of programs in the sense of the least Herbrand model semantics. Many transformation systems for program optimization [Deb88, PP91] program specialization [BCD90] partial evaluation [LS91, PP93] and program synthesis [Sat90, ST84] are based on unfold fold transformations. An unfold fold program transformation system which extends the unfold fold transformations of Tamaki and Sato [TS84] is presented in this paper. The system consists of three transformation rules namely unfolding, simultaneous folding, and generalization ....

....the applicability of the folding rule. A proof of correctness of the transformations in the sense of the least Herbrand model semantics of the program is also presented. Besides the uses of Tamaki and Sato s transformations in optimization of logic programs [Deb88, PP91] and in program synthesis [ST84], the transformations that we propose may also be proved useful in optimization of nondeterministic logic programs as shown in the examples that we present. The application of This paper appears in the Proceedings of the Sixth International Symposium Programming Language Implementation and ....

T. Sato and H. Tamaki. Transformational logic program synthesis. In International Conference of Fifth Generation Computer Systems, pages 195--201, 1984.

....negation to other domains have been investigated in [26, 49] and could be applied to our technique. Nevertheless, this is beyond the spirit of the paper. Furthermore, the right framework for regular splitting (as well as for intensional negation) is a many sorted one, as already hinted in [41]. We need the following substitution lemma, whose easy proof is omitted: Lemma 38 In the PFDCA system for every proof Pi : L of and substitution , there is a proof Pi : L with height less or equal to Pi : L. In particular, the proof Pi : L may introduce eigenvariables in the ....

....[50] Formally, for a suitable derivability relation, this property holds when if 9xp(x) then there is a term t s.t. p(t) Accordingly, it is suggested that from 9x:p(x) the same property infers a term t s.t. p(t) We can roughly distinguish two approaches: i. Program Transformation: [41, 13, 5]. ii. Negation by Constraints: 51] for Datalog programs, 8, 9] for Prolog, extended to CLP in [49] Fail Substitutions: 45, 29] Historically, the original attempt to deal with negation was simply to try avoiding the floundering phenomenon: given that the latter is in general undecidable, one ....

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T. Sato and H. Tamaki. Transformational Logic Program Synthesis. In Proceeding of the International Conference on Fifth Generation Computer Systems, 1984.

.... shall explain it with an example: ffl For constructive synthesis, we shall base our description on the work by Bundy and Wiggins [1] ffl For deductive synthesis, we follow that of Lau and Ornaghi [8] For transformational synthesis by fold unfold, we will describe the work of Sato and Tamaki [11]. For transformational synthesis by partial deduction, we will describe the work of Komorowski [7] Transformational synthesis exemplifies the intricate relationship between synthesis and transformation. Here we shall discuss this relationship, and explain the precise distinction and similarities ....

T. Sato and H. Tamaki. Transformational Logic Program Synthesis. In Proc. International Conference on Fifth Generation Computer Systems, pages 195--201, 1984.

....negation to compute the complements of heads of clauses in the definition of a predicate, and intersection to combine results of negating individual clause heads. In this paper we have provided algorithms to compute both. While this approach has been investigated for first order Horn clauses [18, 2] and CLP programs [3] the field has been little explored with respect to higherorder logics and logical frameworks. This is the most important future work we are considering; the algorithms presented here provide the central foundation. We also plan to extend the results to dependent types to ....

T. Sato and H. Tamaki. Transformational logic program synthesis. In International Conference on Fifth Generation Computer Systems, 1984.

....cons cons cons cons nil cons cons X cons . cons cons expanded subgraph (b) After lazy copying Figure 13: Learned graphs The reduction mechanism is considered to provide an on the fly program transformation system of logic programs, in which unfolding (copying) and folding (sharing) (Sato and Tamaki, 1984) are crucial. Hasida (1994) presented a parsing mechanism based on Horn clauses denoted as a graphical representation, and proposed incremental copy of literals in order to speed up the parsing process. In this process, a non trivial check must be performed in order to determine whether two ....

Sato, T. and Tamaki, H. (1984). Transformational logic program synthesis.

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T. Sato and H. Tamaki. Transformational logic program synthesis. In Proceedings of the International Conference on Fifth Generation Computer Systems, pages 195

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Taisuke Sato and Hisao Tamaki. Transformational logic program synthesis. In ICOT, editor, Proceedings of the International Conference on Fifth Generation Computer Systems, pages 195--201, 1984.

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H. Tamaki and T.Sato. Transformational Logic Program Synthesis, Proceedings of the International Conference on Fifth Generation Computer Systems 1984 (edited by ICOT 1984). 21

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