Volume 12, 2000

University of Bialystok

Copyright (c) 2000 Association of Mizar Users

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

- 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.

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

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Grzegorz Bancerek.
Cardinal numbers.
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Grzegorz Bancerek.
The fundamental properties of natural numbers.
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Segments of natural numbers and finite sequences.
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Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
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Jing-Chao Chen.
Computation and program shift in the SCMPDS computer.
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Jing-Chao Chen.
Computation of two consecutive program blocks for SCMPDS.
*Journal of Formalized Mathematics*, 11, 1999. - [9]
Jing-Chao Chen.
The construction and computation of conditional statements for SCMPDS.
*Journal of Formalized Mathematics*, 11, 1999. - [10]
Jing-Chao Chen.
The construction and shiftability of program blocks for SCMPDS.
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Jing-Chao Chen.
Recursive Euclide algorithm.
*Journal of Formalized Mathematics*, 11, 1999. - [12]
Jing-Chao Chen.
The SCMPDS computer and the basic semantics of its instructions.
*Journal of Formalized Mathematics*, 11, 1999. - [13]
Jing-Chao Chen.
The construction and computation of while-loop programs for SCMPDS.
*Journal of Formalized Mathematics*, 12, 2000. - [14]
Jing-Chao Chen and Piotr Rudnicki.
The construction and computation of for-loop programs for SCMPDS.
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Jaroslaw Kotowicz.
Functions and finite sequences of real numbers.
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Edmund Woronowicz.
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