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Logic Program Synthesis
, 1993
"... This paper presents an overview and a survey of logic program synthesis. Logic program synthesis is interpreted here in a broad way; it is concerned with the following question: given a specification, how do we get a logic program satisfying the specification? Logic programming provides a uniquely n ..."
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Cited by 38 (10 self)
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This paper presents an overview and a survey of logic program synthesis. Logic program synthesis is interpreted here in a broad way; it is concerned with the following question: given a specification, how do we get a logic program satisfying the specification? Logic programming provides a uniquely nice and uniform framework for program synthesis since the specification, the synthesis process and the resulting program can all be expressed in logic. Three main approaches to logic program synthesis by formal methods are described: constructive synthesis, deductive synthesis and inductive synthesis. Related issues such as correctness and verification as well as synthesis by informal methods are briefly presented. Our presentation is made coherent by employing a unified framework of terminology and notation, and by using the same running example for all the approaches covered. This paper thus intends to provide an assessment of existing work and a framework for future research in logic program synthesis.
MiddleOut Reasoning for Synthesis and Induction
, 1995
"... We develop two applications of middleout reasoning in inductive proofs: Logic program synthesis and the selection of induction schemes. Middleout reasoning as part of proof planning was first suggested by Bundy et al [Bundy et al 90a]. Middleout reasoning uses variables to represent unknown te ..."
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Cited by 26 (11 self)
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We develop two applications of middleout reasoning in inductive proofs: Logic program synthesis and the selection of induction schemes. Middleout reasoning as part of proof planning was first suggested by Bundy et al [Bundy et al 90a]. Middleout reasoning uses variables to represent unknown terms and formulae. Unification instantiates the variables in the subsequent planning, while proof planning provides the necessary search control. Middleout reasoning is used for synthesis by planning the verification of an unknown logic program: The program body is represented with a metavariable. The planning results both in an instantiation of the program body and a plan for the verification of that program. If the plan executes successfully, the synthesized program is partially correct and complete. Middleout reasoning is also used to select induction schemes. Finding an appropriate induction scheme during synthesis is difficult, because the recursion of the program, which is un...
Exploring Properties of Residue Classes
, 2000
"... We report on an experiment in exploring properties of residue classes over the integers with the combined effort of a multistrategy proof planner and two computer algebra systems. An exploration module classifies a given set and a given operation in terms of the algebraic structure they form. It th ..."
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Cited by 18 (11 self)
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We report on an experiment in exploring properties of residue classes over the integers with the combined effort of a multistrategy proof planner and two computer algebra systems. An exploration module classifies a given set and a given operation in terms of the algebraic structure they form. It then calls the proof planner to prove or refute simple properties of the operation. Moreover, we use different proof planning strategies to implement various proving techniques: from naive testing of all possible cases to elaborate techniques of equational reasoning and reduction to known cases.
On the Use of Inductive Reasoning in Program Synthesis: Prejudice and Prospects
 IN L. FRIBOURG AND F. TURINI (EDS), JOINT PROC. OF META'94 AND LOPSTR'94
, 1994
"... In this position paper, we give a critical analysis of the deductive and inductive approaches to program synthesis, and of the current research in these fields. From the shortcomings of these approaches and works, we identify future research directions for these fields, as well as a need for coopera ..."
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Cited by 13 (6 self)
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In this position paper, we give a critical analysis of the deductive and inductive approaches to program synthesis, and of the current research in these fields. From the shortcomings of these approaches and works, we identify future research directions for these fields, as well as a need for cooperation and crossfertilization between them.
Logic Frameworks for Logic Programs
, 1994
"... . We show how logical frameworks can provide a basis for logic program synthesis. With them, we may use firstorder logic as a foundation to formalize and derive rules that constitute program development calculi. Derived rules may be in turn applied to synthesize logic programs using higherorder re ..."
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Cited by 12 (7 self)
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. We show how logical frameworks can provide a basis for logic program synthesis. With them, we may use firstorder logic as a foundation to formalize and derive rules that constitute program development calculi. Derived rules may be in turn applied to synthesize logic programs using higherorder resolution during proof that programs meet their specifications. We illustrate this using Paulson's Isabelle system to derive and use a simple synthesis calculus based on equivalence preserving transformations. 1 Introduction Background In 1969 Dana Scott developed his Logic for Computable Functions and with it a model of functional program computation. Motivated by this model, Robin Milner developed the theorem prover LCF whose logic PP used Scott's theory to reason about program correctness. The LCF project [13] established a paradigm of formalizing a programming logic on a machine and using it to formalize different theories of functional programs (e.g., strict and lazy evaluation) and the...
Certifying solutions to permutation group problems
 In F. Baader, ed, CADE19, LNAI 2741
, 2003
"... Abstract. We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to pr ..."
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Cited by 12 (0 self)
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Abstract. We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to provide a full proof of correctness of the answer. To guarantee correctness we use proof planning techniques, which construct proofs in a humanoriented reasoning style. This gives the human mathematician the necessary insight into the computed solution, as well as making it feasible to check the solution for relatively large groups. 1
A Framework for Program Development Based on Schematic Proof
, 1993
"... Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that suppor ..."
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Cited by 11 (5 self)
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Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson's Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach.
SchemaGuided Synthesis of Constraint Logic Programs
 In D.F. Redmiles and B. Nuseibeh (eds), Proc. of ASE'98
, 1998
"... By focusing on the family of assignment problems (such as graph colouring, nQueens, etc), we show how to adapt D.R. Smith's Kids approach for the synthesis of constraint programs, rather than applicative Refine programs with explicit constraint propagation and pruning code. Synthesis is guided by a ..."
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Cited by 10 (8 self)
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By focusing on the family of assignment problems (such as graph colouring, nQueens, etc), we show how to adapt D.R. Smith's Kids approach for the synthesis of constraint programs, rather than applicative Refine programs with explicit constraint propagation and pruning code. Synthesis is guided by a global search program schema and can be fully automated with little effort, due to some innovative ideas. CLP(Sets) programs are equivalent in expressiveness to our input specifications. After optimisations, the synthesised programs would be competitive with handcrafted ones.
Program Development Schemata as Derived Rules
, 2000
"... This paper makes several contributions towards a clarified view of schemabased program development. First, we propose that schemata can be understood, formalized, and used in a simple way: program development schemata are derived rules. We mean this in the standard sense of a derived rule of infere ..."
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Cited by 9 (2 self)
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This paper makes several contributions towards a clarified view of schemabased program development. First, we propose that schemata can be understood, formalized, and used in a simple way: program development schemata are derived rules. We mean this in the standard sense of a derived rule of inference in logic. A schema like Figure i can be formulated as a rule stating that the conclusion follows from the premises defining F, G, and the applicability conditions. By deriving the rule in an axiomatic theory, we validate a semantic statement about it: the conclusion of the rule holds in every model where both the axioms of the theory and the premises of the rule are true. Hence, by selecting a language to work in we control which development schemata are formalizable, and by selecting a theory we determine which schemata are derivable
Generic System Support for Deductive Program Development
 In Tools and Algorithms for the Construction and Analysis of Systems (TACAS96), volume 1055 of LNCS
"... We report on a case study in using logical frameworks to support the formalization of programming calculi and their application to deductionbased program synthesis. Within a conservative extension of higherorder logic implemented in the Isabelle system, we derived rules for program development tha ..."
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Cited by 8 (5 self)
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We report on a case study in using logical frameworks to support the formalization of programming calculi and their application to deductionbased program synthesis. Within a conservative extension of higherorder logic implemented in the Isabelle system, we derived rules for program development that can simulate those of the deductive tableau proposed by Manna and Waldinger. We have used the resulting theory to synthesize a library of verified programs, focusing on sorting algorithms. Our experience suggests that the methodology we propose is well suited both to implement and use programming calculi, extend them, partially automate them, and even formally reason about their correctness. 1 Introduction Over the last few decades, a variety of methodologies for deductive software synthesis, transformation, and refinement from specification have been suggested, e.g., [4, 5, 8, 9, 12]. Our research investigates general frameworks that support such program development formalisms. That is, ...