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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Notes
- 1.
The square brackets have been used for function and predicate applications instead of round brackets.
- 2.
- 3.
Each predicate and function symbol applies to a certain combination of types of argument.
- 4.
The full Coq script is available at: http://web.info.uvt.ro/~idramnesc/LATA2016/coq.v.
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Acknowledgments
Isabela Drămnesc: This work was partially supported by the strategic grant POSDRU/159/1.5/S/137750, Project Doctoral and Postdoctoral programs support for increased competitiveness in Exact Sciences research cofinanced by the European Social Fund within the Sectoral Operational Programme Human Resources Development 2007–2013.
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Drămnesc, I., Jebelean, T., Stratulat, S. (2016). Proof–Based Synthesis of Sorting Algorithms for Trees. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_43
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