Volume 11, 1999

University of Bialystok

Copyright (c) 1999 Association of Mizar Users

**Jing-Chao Chen**- Shanghai Jiaotong University

- This article describes the insert sorting algorithm using macro instructions such as if-Macro (conditional branch macro instructions), for-loop macro instructions and While-Macro instructions etc. From the viewpoint of initialization, we generalize the halting and computing problem of the While-Macro. Generally speaking, it is difficult to judge whether the While-Macro is halting or not by way of loop inspection. For this reason, we introduce a practical and simple method, called body-inspection. That is, in many cases, we can prove the halting problem of the While-Macro by only verifying the nature of the body of the While-Macro, rather than the While-Macro itself. In fact, we have used this method in justifying the halting of the insert sorting algorithm. Finally, we prove that the insert sorting algorithm given in the article is autonomic and its computing result is correct.

This research is supported by the National Natural Science Foundation of China Grant No. 69873033.

- Preliminaries
- Basic Property of {\bf while} Macro
- Insert Sort Algorithm

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