N. Dershowitz, "Synthesis by completion," in Proc. The 9th Int. Joint Conf. Artificial Intelligence, 1985, pp. 208--214.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....tools for synthesis of IIR filters including MATLAB and SPW. Algorithm selection and design has been a popular research topic in a number of research fields, particularly in artificial intelligence where four main directions have emerged: first order logicbased methods [Gre69] rewrite systems [Der85], transformational approaches [Dar81] and schema based programming [Wil83] While the proposed techniques are strategically and algorithmically very different, they all share a common weakness in their inability to scale to problems of practical importance. Several VLSI DSP efforts have also ....

N. Dershowitz, "Synthesis By Completion," The Ninth Int. Joint Conference on Artificial Intelligence, pp. 208-214, 1985.

....such as Artificial Intelligence have made algorithm selection and design a popular research topic. There are four main directions that have emerged in this area: first order logic based methods [Gre69] transformational approaches [Dar81] schema based programming [Wil83] and rewrite systems [Der85]. All of these techniques share one common weakness, the inability to scale to problems of practical importance, even though the techniques are very different in terms of strategy and algorithm. Oppenheim and Nawab [Opp92] and Proudler et al. Pro96] addressed the algorithm selection and design ....

N. Dershowitz, "Synthesis by Completion", The Ninth Int. Joint Conference on Artificial Intelligence, pp. 208-214, 1985.

....tools for synthesis of IIR filters including MATLAB and SPW. Algorithm selection and design has been a popular research topic in a number of research fields, particularly in artificial intelligence where four main directions have emerged: first order logicbased methods [Gre69] rewrite systems [Der85], transformational approaches [Dar81] and schema based programming [Wil83] While the proposed techniques are strategically and algorithmically very different, they all share a common weakness in their inability to scale to problems of practical importance. Several VLSI DSP efforts have also ....

N. Dershowitz, "Synthesis By Completion," The Ninth Int. Joint Conference on Artificial Intelligence, pp. 208-214, 1985.

....the area of traditional program transformation and belong to the eld of logic program synthesis. There are also techniques by which program synthesis may be viewed as part of program transformation. Among those techniques we would like to mention the so called completion techniques presented in [57]. By completion a new program can be derived from an old one by successive applications of semantics preserving rewriting steps each of which can be viewed as a program transformation step. Recent developments have indicated a new interesting way of considering the process of program development ....

N. Dershowitz. Synthesis by completion. In Proc. 9th International Joint Conference on Articial Intelligence, pages 208214, 1985.

....nonhomogeneous array R(l; y) consisting in one function and one list, is determined by the need for folding. There are also techniques by which program synthesis may be viewed as part of program transformation. Among those techniques we would like to mention the so called completion techniques [Dershowitz 85] In that paper it is shown how a new program can be derived from an old one by successive applications of semantics preserving rewriting steps each of which can be viewed as a program trasformation step. Recent developments have indicated a new interesting way of considering the process of ....

Dershowitz, N.: Synthesis by Completion. Proc. 9th International Joint Conference on Artificial Intelligence 1 (1985) 208--214

.... of this system is a component of the tool suite that support a Method for Software Design for Reliability and Reuse developed in the Pacific Software Research Center [2] The underlying methodology is folding unfolding [9] Synthesis of a new program version is done by a completion procedure [13, 14, 3]. The programs in the sequence P 0 ; P 1 ; P n are presented by a terminating, constructor based and orthogonal first order rewrite system. The transformation strategies that are automated are: fusion or deforestation (elimination of useless intermediate data structures) and two loops ....

N. Dershowitz. Synthesis by Completion. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 208--214, Los Angeles, 1985.

....of the divide and conquer strategy determined by the recursive construction of objects. Several well known transformation techniques (e.g. split of postcondition to introduce an invariant, finite differencing) have been implemented in the PROSPECTRA transformation system [585] Dershowitz [273], Kodratoff [561] and Perdrix [778] have advocated the use of completion techniques for the purpose of deriving executable specifications from both the specification of the problem domain and of the requirements for the solution. From the completeness properties of the completion process it ....

N. Dershowitz. Synthesis by completion. In Proc. 9th Intl. Joint Conf. on Artificial Intelligence, pages 208--214, 1985.

....and unfolding of definitions, depending upon the orientation of the equations as rules. Critical pair computation performs both instantiation and unfolding, hence providing an implemention for transformation by the unfold fold methodology. This technique has been called synthesis by completion [11, 12]. In Astre, synthesis by completion is used as a mechanism to transform R 0 into a sequence of rewrite systems R 1 ; R 2 ; Rn to get from a functional program P 0 to a new, semantically equivalent program Pn that is more efficient. Astre translates Rn into an SML program where functions ....

N. Dershowitz. Synthesis by completion. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 208--214, Los Angeles, 1985.

....we do not really want to limit the transformation process to terminating programs. However, we are limited if we want to do automatic proofs about enrichments. ro ram ransforma ion Dershowitz has shown how completion can be applied to the task of program synthesis from specifications in [7, 9]. The transformation process can be viewed as a partial unfailing completion. Example 3 Let us take the well known example of the transformation of the specification of the function reverse in example 2 [7] We want a more efficient implementation of reverse. In an attempt to find one, we enrich ....

....how completion can be applied to the task of program synthesis from specifications in [7, 9] The transformation process can be viewed as a partial unfailing completion. Example 3 Let us take the well known example of the transformation of the specification of the function reverse in example 2 [7]. We want a more efficient implementation of reverse. In an attempt to find one, we enrich the specification with the definition of a new function motivated by a generalization of the right hand side of equation 4. h : list 2 list 7 list h(u; v) append(reverse(u) v) 5) Overlaps between the ....

N. Dershowitz. Synthesis By Completion. Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 208-214, Los Angeles, 1985.

....process. This requires a full formalization of all its parts in order to get an understanding of the mechanisms involved. Many formal approaches for the automated synthesis of programs have been developed and implemented during the last years (see e.g. BD77, MW79, MW80, Bib80, Hog81, BH84, Der85, BC85, Fra85, CH88, NFK89, PM89, SL89, SL90, Gal90] The KIDS system [SL90] most mature of the realized ones, is even be lieved close to the point where it can be used for routine programming. Current implementations of program synthesis systems, however, more or less underly the same ....

....resolution are used, the method a program is constructed appears to be quite unnatural. Furthermore, there is only little practical experience in constructing AE proofs for a larger class of programming problems. ffl In transformation based approaches (see e.g. BD77, MW79, Bib80, Hog81, BH84, Der85, SL89, SL90] a specification is treated as if it were already some kind of logic program, though an inefficient one. Instead of constructing a correct program the main aspect is to improve efficiency which shall be achieved by adapting methods from the field of program transformations. Starting ....

N. Dershowitz. Synthesis by completion. In IJCAI 85, pages 208--214, 1985.

....how every value of the ADT can be generated. This is done in a two step process. First, the Knuth Bendix completion procedure [KB70] is applied to the axioms describing the operations of the ADT; it determines if the patterns on the LHSs of the rules cover all possible (variable free) input values [Der85]. The programmer supplies a precedence ordering between the symbols that is a well founded ordering to the Knuth Bendix completion procedure. The precedences provide the partial ordering to rewrite equations of the form x = y, such that the LHS of an equation is greater in precedence than the ....

Nachum Dershowitz. Synthesis by completion. Fifth International Joint Conference Artificial Intelligence, 1:208--214, 1985.

....process. This requires a full formalization of all it parts in order to get an understanding of the mechanisms involved. Many formal approaches for the automated synthesis of programs have been developed and implemented during the last years (see e.g. BD77, MW79, MW80, Bib80, BH84, Hog81, Der85, Smi88, SL89] the most mature of them currently being the KIDS system [Smi88] which also aims at a strong theoretical foundation. However, program synthesis systems built so far underly the same problems as conventional software. Despite the fact that they aim at a formalization and ....

Nachum Dershowitz. Synthesis by completion. In A. Joshi, editor, IJCAI-85 --- Proceedings of the 9 th International Joint Conference on Artificial Intelligence, Los Angeles, August 1985, pages 208--214, 1985.

....allows both folding and unfolding of definitions, depending upon the orientation of the equations as rules. Critical pair computation performs both instantiation and unfolding and hence can implement transformations by the unfold fold technique. This has been called synthesis by completion [10, 11]. In Astre, synthesis by completion is used as a mechanism to transform R 0 into a sequence of rewrite systems R 1 ; R 2 ; Rn to get from a functional program P 0 to a new, semantically equivalent program Pn that is more efficient. Astre translates Rn into an SML program in which ....

N. Dershowitz. Synthesis by completion. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 208--214, Los Angeles, 1985.

.... induction differs considerably from that of Michalski and Stepp [ 9 ] Rendell [ 16 ] and Fu and Buchanan [ 5 ] and can be more easily compared to the deductive transformational programming techniques of Burstall and Darlington [ 2 ] Burstall and Darlington, and later Dershowitz [ 3 ] suggest that deductive program synthesis can be carried out by gradual truth preserving transformations of a program specification. At first sight, these techniques seem not to be applicable to inductive inference, which by definition progresses by performing non truth preserving ....

....wings. This concept is named bird . When asked to search for another operator application Duce comes back with the message, No applicable transformation , meaning that none of the operators reduce the rule base. The time between each prompt in this example is in the order of one second. Figure 3 shows the result of the transformations. Not only is the rule base more compact but also the new concepts have made the rules more conceptually transparent. For example, a blackbird is simply defined as a bird which is black. Note that the illustrative examples are propagated to all new rules. 6 ....

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N. Dershowitz. Synthesis by completion. In IJCAI85, pages 208--214, Los Altos, CA, 1985. Kaufmann.

.... s(s(d(x) The first rule, for instance, is the result of orienting the two normal forms of 0 0 (in the only direction possible) The latter term is obtained by unifying the left hand sides of the specification and first rule for addition. For more details of completion based synthesis, see [Dershowitz, 1985b] We need to show that the two generated rules form a correct and complete system for doubling. To define correctness, we need to make precise what was meant earlier by equal according to S. There are two notions of equality that are relevant: a) deductive equality, meaning provable by ....

....have been designed and perform better; see, for example, Bachmair et al. 1989] Regardless of which version of completion is employed, it may generate an infinite number of relevant program rules. What to do in such a case, is the subject of the next section. Inductive Synthesis In [Dershowitz, 1985b] and [Reddy, 1989a] it was argued that with an appropriate ordering completion will always generate a program from a given specification. The catch is that the guaranteed program may be of infinite length. Indeed, running completion without the third addition rule, s(x) y s(x y) ....

Dershowitz, N. Synthesis by completion. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 208--214, Los Angeles, CA, August 1985.

....: 3 . ro ra transfor ation an re ritin Dershowitz [7, 9] has shown how the completion procedure can be applied to program transformation by automatizing the instanciation, folding and unfolding processes originated by Burstall and Darlington [4] But no attempt has been made to apply the completion to design a program transformation system. We think ....

N. Dershowitz. Synthesis By Completion. Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 208-214, Los Angeles, 1985.

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N. Dershowitz, "Synthesis by completion," in Proc. The 9th Int. Joint Conf. Artificial Intelligence, 1985, pp. 208--214.

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