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Using multisets, we develop novel techniques for mechanizing the proofs ofthe synthesis conjectures for list-sorting algorithms, and we demonstrate themin the Theorema system. We use the classical principle of extracting thealgorithm as a set of rewrite rules based on the witnesses found in the proofof the synthesis conjecture produced from the specification of the desiredfunction (input and output conditions). The proofs are in natural style, usingstandard rules, but most importantly domain specific inference rules andstrategies. In particular the use of multisets allows us to develop powerfulstrategies for the synthesis of arbitrarily structured recursive algorithms bygeneral Noetherian induction, as well as for the automatic generation of thespecifications of all necessary auxiliary functions (insert, merge, split),whose synthesis is performed using the same method.

Proof-Based Synthesis of Sorting Algorithms Using Multisets in Theorema