Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

## Insert Sort on SCMPDS

Jing-Chao Chen
Shanghai Jiaotong University

### Summary.

The goal of this article is to examine the effectiveness of ``for-loop'' and ``while-loop'' statements on SCMPDS by insert sort. In this article, first of all, we present an approach to compute the execution result of ``for-loop'' program by ``loop-invariant'', based on Hoare's axioms for program verification. Secondly, we extend the fundamental properties of the finite sequence and complex instructions of SCMPDS. Finally, we prove the correctness of the insert sort program described in the article.

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

#### MML Identifier: SCPISORT

The terminology and notation used in this paper have been introduced in the following articles [20] [5] [6] [19] [2] [16] [18] [4] [12] [7] [1] [10] [8] [9] [11] [3] [14] [13] [17] [15]

#### Contents (PDF format)

1. Preliminaries
2. Computing the Execution Result of For-Loop Program by Loop-Invariant
3. A Program for Insert Sort
4. The Property of Insert Sort and Its Correctness

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