Proof–Based Synthesis of Sorting Algorithms Using Multisets in Theorema

Isabela Drămnesc
(Department of Computer Science West University Timisoara, Romania)
Tudor Jebelean
(Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria)

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.

In Mircea Marin and Adrian Crăciun: Proceedings Third Symposium on Working Formal Methods (FROM 2019), Timişoara, Romania, 3-5 September 2019, Electronic Proceedings in Theoretical Computer Science 303, pp. 76–91.
Published: 2nd September 2019.

ArXived at: http://dx.doi.org/10.4204/EPTCS.303.6 bibtex PDF

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