Synthesis of list algorithms by mechanical proving

Dramnesc, Isabela; Jebelean, Tudor

doi:10.1016/j.jsc.2014.09.030

Cited by 16 publications

(11 citation statements)

References 21 publications

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“…This section introduces the algorithm synthesis problem and presents the proof-based synthesis techniques that we use, by adapting and improving inference rules and induction principles from [8].…”

Section: The Proof-based Synthesis Methodsmentioning

confidence: 99%

“…Synthesis methods and techniques similar to our proof-based approach are extensively presented in [8]. It can be noticed that most of the proof methods are based on expressive and undecidable logics that integrate induction principles.…”

Section: Related Workmentioning

confidence: 99%

“…The illustration of the induction principles and algorithm extraction in this subsection is similar to the one from [8], but the induction principles are adapted for trees and the extracted algorithms are more complex.…”

Section: Induction Principlesmentioning

confidence: 99%

“…In this paper, we apply the deductive approach to synthesize binary tree algorithms, extending similar results for lists [8]. In order to do this, we introduce new induction principles, proof strategies and inference rules based on properties of binary trees.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Proof–Based Synthesis of Sorting Algorithms for Trees

Dramnesc¹,

Jebelean²,

Stratulat³

2016

Language and Automata Theory and Applications

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Abstract. We develop various proof techniques for the synthesis of sorting algorithms on binary trees, by extending our previous work on the synthesis of algorithms on lists. Appropriate induction principles are designed and various specific prove-solve methods are experimented, mixing rewriting with assumption-based forward reasoning and goal-based backward reasoning à la Prolog. The proof techniques are implemented in the Theorema system and are used for the automatic synthesis of several algorithms for sorting and for the auxiliary functions, from which we present few here. Moreover we formalize and check some of the algorithms and some of the properties in the Coq system.

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Section: The Proof-based Synthesis Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Induction Principlesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proof–Based Synthesis of Sorting Algorithms for Trees

Dramnesc¹,

Jebelean²,

Stratulat³

2016

Language and Automata Theory and Applications

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“…Compared to our previous work on algorithm synthesis on lists [8], in this paper we use a similar proof-based approach, but different techniques to synthesize algorithms on binary trees. The authors apply in [9] combinatorial techniques in order to discover from proofs auxiliary algorithms, other than Insert, which are versions of an algorithm that merges two sorted binary trees into a sorted one.…”

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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Automatic Synthesis of Merging and Inserting Algorithms on Binary Trees Using Multisets in Theorema

Dramnesc

Jebelean

2020

Mathematical Aspects of Computer and Information Sciences

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Synthesis of list algorithms by mechanical proving

Cited by 16 publications

References 21 publications

Proof–Based Synthesis of Sorting Algorithms for Trees

Proof–Based Synthesis of Sorting Algorithms for Trees

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

Automatic Synthesis of Merging and Inserting Algorithms on Binary Trees Using Multisets in Theorema

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