Z. Manna and R. Waldinger. A Deductive Approach to Program Synthesis. TOPLAS, 2(1):90--121, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a side e ect of their use of proof synthesis to perform transformation. Early synthesis work [BM73, WL69] relied heavily on theorem proving techniques to ensure correctness. Later special purpose synthesis systems were built which did not utilise theorem proving [BD77, MW79] Manna and Waldinger [MW80] reunited synthesis and theorem proving combining uni cation, mathematical induction, and transformation rules. Barstow s knowledge based synthesis technique [Bar77] uses a large data base of information to perform program synthesis. Later Barstow [Bar79] proposed the introduction of a theorem ....

....Manna and Waldinger [MW79] abandoned the use of a theorem prover and implemented a system which directly used transformation rules to re ne a speci cation into a runnable program. Theorem proving systems became much more able to handle mathematical induction and subsequently Manna and Waldinger [MW80] again integrated their techniques with a theorem prover. The FUM presented by Burstall and Darlington [BD77] was designed as functional program transformation system. In [Dar78] Darlington shows how the same rules can be used for program synthesis. The practical aspects of Burstall and ....

Z. Manna and R.J. Waldinger. A deductive approach to program synthesis. Journal of Transactions on Programming Languages and Systems, 2(1):90-121, 1980.

....involving , but postpone the de nition of until the point where the descent conditions must be removed in order to nish the proof. The soundness of inductive contraction expansion is shown in [13] Section 5.4, and [15] Sections 3 and 4. 17 The general idea of deductive program synthesis [5, 9, 22] is to derive axioms ( programs) for a function or predicate f in the course of the proof of a correctness condition on f . For instance, one may want to derive axioms for a function f such that, for given functions g and h, f(x) g(h(x) x) holds true. By unfolding g and h, the equation is ....

Z. Manna, R. Waldinger, A Deductive Approach to Program Synthesis, ACM TOPLAS 2 (1980) 90-121

....cation. These terms are program fragments. Experiments show that the procedures synthesized by TOPS can reduce theorem proving search at least as much as hand tuning of the deductive synthesis system. 1 Introduction Deductive program synthesis technology has been known since the late 1960 s [3] [9]. However, construction of usable deductive synthesis systems is dicult. In the past thirty years, a great deal of progress has been made in the development of program synthesis systems based on theorem proving, transformations, and logic programming [3] 12] 4] However, in spite of this ....

Z. Manna and R. Waldinger, \A Deductive Approach To Program Synthesis," ACM Transactions on Programming Languages and Systems, Vol 2, No 1, Jan 1980, pp. 90-121.

....nitions more eciently, attempting to recover equivalences from clauses and treating them with speci c selection strategies for inferences. Admitting inferences on nonclausal formulas, the calculus described below is also related to the various calculi of nonclausal resolution and superposition [11, 12, 2, 4]. The main di erence here is that we also admit quanti ers, and that the local nature of classical superposition inferences is better preserved, facilitating the development of ecient implementations of our calculus in a theorem prover. In [1] the author argues, by discussing some examples, that ....

Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming Languages and Systems, 2(1), 1980.

....of components is also studied in that paper. The same authors also co designed a synthesis algorithm from MSCs to state machines, appearing in [16] 1.2.6. Synthesis from temporal logic The early work on this kind of synthesis considered closed systems, that do not interact with the environment [24, 10]. In this case a program can be extracted from a constructive proof that the formula is satisfiable. This approach is not suited to synthesizing open systems that interact with the environment, since satisfiability implies the existence of an environment in which the program satisfies the formula, ....

Manna, Z., and R.J. Waldinger, "A deductive approach to program synthesis" ACM Trans. Prog. Lang. Sys. 2 (1980), 90--121.

....and belongs to the class of brute force methods. Another approach to deductive planning in a resource conscious logic (Transition Logic) is given in [8] where also conversion from STRIPS like operators to a resource conscious representation is given. The list of deductive planners includes also [9, 66, 33, 7, 74]. Planning within a part of LL consisting only of tensor may be viewed as multiset rewriting as proposed in [96] In [19] a formalism has been given for deductively generating recursive plans in Linear Logic. This advancement is a step further to more general plans, which are capable to solve ....

Z. Manna, R. Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming Languages and Systems, Vol. 2, pp. 90-121, 1980.

....canonical set of rewrite rules, and does not exploit modes. Under the narrowing procedure, the programmer has little control over or intuition about the efficiency characteristics of unification. Tablog [Malachi 86] is a logic language based upon the Manna Waldinger deductivetableau proof system [Manna 80] This proof system explicitly handles equations as well as clauses. The language was designed and implemented as a demonstration that a logic programming language can be based upon something other than the resolution procedure. Its treatment of equality is incomplete, however, as it makes an ....

Z. Manna and R. Waldinger. A Deductive Approach to Program Synthesis. ACM Transactions on Programming Languages and Systems, 2(1):90--121, January 1980.

....for the theorem described by the program specification can be interpreted as a computational step. In principle, any method for automatic theorem proof can be used. A proposal for an approach based on automatic theorem proof that combines unification and mathematical induction is presented in [Manna and Waldinger, 1986]. There are two fundamental difficulties associated with this approach [Rich and Waters, 1988, McCartney, 1991] First, the proof procedures are very expensive. Deduction is basically a problem of searching for an inference path from some initial set of facts to a goal fact. The search is ....

Z. Manna and R. Waldinger. A deductive approach to program synthesis. In C. Rich and R.C. Waters, editors, Readings in artificial intelligence and software engineering, pages 3 34, Los Altos, CA, 1986. M. Kaufmann Publishers.

....new de nition: G 1 . genb(I ; J; Ks; M;N) b list(I ; J; Ks; M) b(I ; M;N) This clause is obtained by generalising the list [K 1 ] in clause E 2 and the list [K 1 ; K 2 ] in clause E 3 to the list variable Ks. Generalisation is a well known strategy for program derivation (see, for instance, [MaW80, Weg76]) and in our framework it allows us to construct the nite de nition trees needed for the derivation of new programs. Indeed, we expand a de nition tree when a folding step cannot be performed (see Point 3b of the tupling strategy) and by generalisation we introduce de nitions which allow ....

Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM Toplas, 2:90-121, 1980.

....new de nition: G 1 . genb(I ; J; Ks; M;N) b list(I ; J; Ks; M) b(I ; M;N) This clause is obtained by generalizing the list [K 1 ] in clause E 2 and the list [K 1 ; K 2 ] in clause E 3 to the list variable Ks. Generalization is a well known strategy for program derivation (see, for instance, [MaW80, Weg76]) and in our framework it allows us to construct the nite de nition trees needed for the derivation of new programs. Indeed, we expand a de nition tree when a folding step cannot be performed (see Point 3b of the tupling strategy) and by generalization we introduce de nitions which allow ....

Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM Toplas, 2:90-121, 1980.

....some cases, but fortunately, that incorrectness turns out not to be a problem in practice. The idea of programming and program development as a deduction from logical speci cations to executable expressions in a formal setting, has its roots in the works by Burstall Darlington and Manna Waldinger [10,49] for functional languages and in the works by Clark et al. Hogger, and Kowalski [11,12,32,39] for the case of logical languages. Similar ideas were proposed also in the case of imperative languages and one should mention, among others, the contributions of Dijkstra and Hoare (see, for instance, ....

....the equivalence of basic goals is decidable (see the goal replacement rule R9) 2 5 Related Work The idea of program development as a deductive activity in a formal theory has been very fertile in the eld of programming methodologies. Early results on this topic are reported, for instance, in [10,11,12,21,32,39,49]. Here we would like to mention some of the contributions to this eld, focusing on logic program transformation. In the pioneering work by Hogger [32] program transformation was intended as a particular form of deduction in rst order logic. Later, the approach based on the unfold fold ....

Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM Toplas, 2:90121, 1980.

....Introduction In system synthesis, we transform a speci cation into a system that is guaranteed to satisfy the speci cation. Early work on synthesis consider closed systems. There, a system that meets the speci cation can be extracted from a constructive proof that the speci cation is satis able [MW80, EC82]. As argued in [ALW89, Dil89, PR89a] such synthesis paradigms are not of much interest when applied to open systems, which interact with an environment. While synthesis that is based on satis ability assumes no environment or a cooperative one, synthesis of open systems should assume a hostile ....

Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM TOPLAS, 2(1):90-121, 1980.

....information concisely and to infer consequences quickly. It has built in facililties for fast temporal reasoning. It has answer extraction facilities, which allow it to answer questions instead of merely proving theorems. These facilities were developed for deductive program synthesis [Gre69] MW80] but apply as well to query answering. SNARK has a procedural attachment mechanism, which makes it possible to link symbols in the logic with procedures; when the symbol is employed in the proof, the corresponding procedure is executed. This enables us to invoke outside sources, including ....

Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming, Languages, and Systems, 2:90--121, 1980.

....information concisely and to infer consequences quickly. It has built in facilities for fast temporal reasoning. It has answer extraction facilities, which allow it to answer questions instead of merely proving theorems. These facilities were developed for deductive program synthesis [2] [6], but apply as well to query answering. SNARK has a procedural attachment mechanism, which makes it possible to link symbols in the logic with procedures; when the symbol is employed in the proof, the corresponding procedure is executed. This enables us to invoke outside sources, including web ....

Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming, Languages, and Systems, 2:90--121, 1980.

....Basin Waldinger s published examples, and, in particular, we have synthesized a variety of standard sorting algorithms. Full proofs scripts may be found in (Ayari, 1995) 2. Deductive Tableau Our account of the Deductive Tableau is based on Manna and Waldinger (1992) with additional input from (Manna and Waldinger, 1980; 1981; 1985; 1993) As explained in the introduction, the Deductive Tableau can be understood as a formal system with an associated methodology for program development. A program is speci ed by formalizing its behavior as a 8=9 formula in rst order logic, i.e. a formula with an initial pre x ....

....hypothesis contains occurrences of the function symbol f , which is the function that we are trying to synthesize. When the induction hypothesis is used in the proof, a recursive call, f(t) appears in the output entries. 2.4. The Front Last Example We take Manna Waldinger s front last example (Manna and Waldinger, 1980) as a running example. This example is simple to understand and illustrates both the Deductive Tableau methodology as well as its limitations. Later in Section 5, we return to this example to illustrate our approach and show how we overcome these limitations. The front last example builds upon a ....

Manna, Z., Waldinger, R. (1980). A deductive approach to program synthesis. TOPLAS, 2(1):90-121.

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Z. Manna and R. Waldinger. A Deductive Approach to Program Synthesis. TOPLAS, 2(1):90--121, 1980.

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Zohar Manna and Richard Waldinger, `A Deductive Approach to Program Synthesis', ACM Transactions on Programming Languages and Systems, 2(1), 90--121, (1980).

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Z. Manna and R. Waldinger. A Deductive Approach to Program Synthesis. ACM Transactions on Programming Languages and Systems, 2(1):90--121, 1980.

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Z. Manna and R. Waldinger, A deductive approach to program synthesis, Association for Computing Machinery Transactions on Programming Languages and Systems, vol. 2 (1980), no. 1, pp. 90--121.

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Zohar Manna and Richard Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming Languages and Systems, 2:90-121, Jan 1980.

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Z. Manna and R. Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming Languages and Systems, 2:90--121, 1980. 13

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Z. Manna and R. J. Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming Languages and Systems, 2(1):90--121, 1980.

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Z. Manna and R. J. Waldinger. A deductive approach to program synthesis. ACM Transactions on Programming Languages and Systems, 2(1), 1980.

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Manna, Z.---Waldinger, R.: A Deductive approach to program synthesis. ACM Trans. on Programming Languages and Systems, Vol. 2, Jan, 1980, No. 1, pp. 294-- 327,

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Manna, Z., and R. J. Waldinger, "A Deductive Approach to Program Synthesis," ACM Transactions on Programming Languages and Systems, 2(1980), 90--121.

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