Synthesis of Programs in Computational Logic

Basin, David; Deville, Yves; Flener, Pierre; Hamfelt, Andreas; Nilsson, Jørgen Fischer

doi:10.1007/978-3-540-25951-0_2

Cited by 31 publications

(18 citation statements)

References 44 publications

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“…Our refinement calculus is similar in style to deductive logic program synthesis (surveys of which can be found in [3,11]). At the most fundamental level, logic program development is the manipulation of predicates from general logic to a subset that corresponds to code, and developing a logic program in either the refinement calculus or synthesis style will require similar manipulation.…”

Section: Discussionmentioning

confidence: 99%

Developing Logic Programs from Specifications Using Stepwise Refinement

Colvin

Groves

Hayes

et al. 2004

Program Development in Computational Logic

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Abstract.In this paper we demonstrate a refinement calculus for logic programs, which is a framework for developing logic programs from specifications. The paper is written in a tutorial-style, using a running example to illustrate how the refinement calculus is used to develop logic programs. The paper also presents an overview of some of the advanced features of the calculus, including the introduction of higher-order procedures and the refinement of abstract data types.

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Section: Discussionmentioning

confidence: 99%

Developing Logic Programs from Specifications Using Stepwise Refinement

Colvin

Groves

Hayes

et al. 2004

Program Development in Computational Logic

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show abstract

“…(Cohen et al, 2013) presents a different Coq library using datatype refinement to verify parameterized algorithms for which the soundness proof of some version can be deduced from that of a previous (less efficiently implemented) version. In (Basin et al, 2004) we find a comparison between three synthesis methods: constructive/deductive synthesis, schema-based synthesis and inductive synthesis. This complements the survey of logic program synthesis which has been done in (Deville and Lau, 1994) and (Flener, 2002).…”

Section: Algorithm Synthesismentioning

confidence: 99%

“…The work of (Gulwani, 2010) is a comprehensive overview of the most common approaches used to tackle the synthesis problem. In (Basin et al, 2004) we find a comparison between three synthesis methods: constructive/deductive synthesis, schema-based synthesis and inductive synthesis. We do not focus on the theoretical aspects of algorithm synthesis, but we follow an experimental approach in which we can find efficient proof methods.…”

mentioning

confidence: 99%

Mechanical synthesis of sorting algorithms for binary trees by logic and combinatorial techniques

Dramnesc

Jebelean

Stratulat

2019

Journal of Symbolic Computation

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We develop logic and combinatorial methods for automating the generation of sorting algorithms for binary trees, starting from input-output specifications and producing conditional rewrite rules. The main approach consists in proving (constructively) the existence of an appropriate output from every input. The proof may fail if some necessary sub-algorithms are lacking. Then, their specifications are suggested and their synthesis is performed by the same principles.Our main goal is to avoid the possibly prohibitive cost of pure resolution proofs by using a natural-style proving in which domain-specific strategies and inference steps lead to a significant increase of efficiency. In addition to classical techniques for natural-style proving, we introduce novel ones (priority of certain types of assumptions, transformation of elementary goals into conditions, special criteria for decomposition of the goal and of the assumptions), as well as methods based on the properties of domain-specific relations and functions. In particular, we use combinatorial techniques in order to generate possible witnesses, which in certain cases lead to the discovery of new induction principles. From the proof, the algorithm is extracted by transforming inductive proof steps into recursions, and case-based proof steps into conditionals.The approach is demonstrated in parallel using the Theorema system, by developing the theory, implementing the prover, and performing the proofs of the necessary properties and synthesis conjectures. It is also validated in the Coq system, which allows to compare the facilities of the two systems from the point of view of our application.

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“…Three of them: constructive/deductive synthesis, schema-based synthesis and inductive synthesis have been compared in [1] in the synthesis of a common program. A survey of logic program synthesis has been done in [7] and [14].…”

Section: A Related Workmentioning

confidence: 99%

A case study on algorithm discovery from proofs: The insert function on binary trees

Dramnesc

Jebelean

Stratulat

2016

2016 IEEE 11th International Symposium on Applied Computational Intelligence and Informatics (SACI)

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Abstract-We present a proof-based automatic synthesis experiment in the context of sorting binary trees, namely the synthesis of the function which inserts an element in a sorted binary tree at the appropriate place. The algorithm is automatically extracted from the automatically produced proof of the conjecture which expresses the existence of the desired output for each appropriate input of the function. This is a case study with the purpose of finding and illustrating general and domain specific inference rules and strategies for efficiently producing proofs from which the desired algorithms can be extracted.The construction of the necessary theory, of the provers, and the experiment itself are performed in the Theorema system.

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Synthesis of Programs in Computational Logic

Cited by 31 publications

References 44 publications

Developing Logic Programs from Specifications Using Stepwise Refinement

Developing Logic Programs from Specifications Using Stepwise Refinement

Mechanical synthesis of sorting algorithms for binary trees by logic and combinatorial techniques

A case study on algorithm discovery from proofs: The insert function on binary trees

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