Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999
Association of Mizar Users
Insert Sort on \SCMFSA
-
Jing-Chao Chen
-
Shanghai Jiaotong University
Summary.
-
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.
The terminology and notation used in this paper have been
introduced in the following articles
[25]
[24]
[35]
[26]
[8]
[15]
[36]
[13]
[14]
[16]
[12]
[7]
[10]
[9]
[21]
[28]
[11]
[23]
[31]
[29]
[30]
[22]
[5]
[6]
[3]
[1]
[17]
[2]
[32]
[34]
[18]
[27]
[4]
[20]
[19]
[33]
-
Preliminaries
-
Basic Property of {\bf while} Macro
-
Insert Sort Algorithm
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Received March 13, 1999
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