Theory exploration of binary trees

Dramnesc, Isabela; Jebelean, Tudor; Stratulat, Sorin

doi:10.1109/sisy.2015.7325367

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…Therefore the prover can rewrite parts of the goal or of the assumptions by replacing equivalent lists or by inferring new relations on lists which are equivalent to lists already related. Example: ( 12) - (13). IR-8: Two constants.…”

Section: Inference Rulesmentioning

confidence: 99%

“…However, in that pioneering work, the starting point of the synthesis (besides the specification of the desired function) is a specific algorithm scheme, while in our approach we use general Noetherian induction and cover-set decomposition. In our previous work we study proof-based algorithm synthesis in the theories of lists [9], sets [10] and binary trees [13] separately [7], [8], [14], [11], [15].…”

Section: Introductionmentioning

confidence: 99%

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Proof–Based Synthesis of Sorting Algorithms Using Multisets in Theorema

Dramnesc

Jebelean

2019

Electron. Proc. Theor. Comput. Sci.

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Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as a set of rewrite rules based on the witnesses found in the proof of the synthesis conjecture produced from the specification of the desired function (input and output conditions). The proofs are in natural style, using standard rules, but most importantly domain specific inference rules and strategies. In particular the use of multisets allows us to develop powerful strategies for the synthesis of arbitrarily structured recursive algorithms by general Noetherian induction, as well as for the automatic generation of the specifications of all necessary auxiliary functions (insert, merge, split), whose synthesis is performed using the same method.

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Section: Inference Rulesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Proof–Based Synthesis of Sorting Algorithms Using Multisets in Theorema

Dramnesc

Jebelean

2019

Electron. Proc. Theor. Comput. Sci.

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“…The simple scenario is when the proof succeeds, because the properties of the auxiliary functions which are necessary for the implementation of the algorithm are already present in the knowledge base. An example of knowledge base is given in [10]. The auxiliary algorithms used for tree sorting are Insert[a, A] (insert element a into sorted tree A, such that the result is sorted) and Merge[A, B] (merge two sorted trees into a sorted tree).…”

Section: Our Approachmentioning

confidence: 99%

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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“…From the generated proof, the corresponding algorithm is automatically extracted. The corresponding theory of binary trees is explored in [12].…”

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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Theory exploration of binary trees

Cited by 8 publications

References 12 publications

Proof–Based Synthesis of Sorting Algorithms Using Multisets in Theorema

Proof–Based Synthesis of Sorting Algorithms Using Multisets in Theorema

Proof–Based Synthesis of Sorting Algorithms for Trees

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

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