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. The proof techniques are implemented in the Theorema system and generate 8 sorting algorithms and 19 auxiliary functions.

使用多集，我们开发了新颖的技术来机械化列表排序算法的综合猜想的证明，并在Theorema中进行了证明。系统。我们基于提取算法的经典原理，将其作为一组重写规则，基于从所需函数的规范（输入和输出条件）产生的合成猜想的证明中找到的证人。证明采用自然风格，使用标准规则，但最重要的是针对特定领域的推理规则和策略。特别是多集的使用使我们能够开发强大的策略，以通过通用Noetherian归纳法合成任意结构的递归算法，以及自动生成所有必要辅助功能（插入，合并，拆分）的规范，其综合使用相同的方法执行。证明技术在定理中实现 系统并生成8种排序算法和19种辅助功能。