Volume 10, 1998

University of Bialystok

Copyright (c) 1998 Association of Mizar Users

**Jing-Chao Chen**- Shanghai Jiaotong University
**Yatsuka Nakamura**- Shinshu University, Nagano

- Up to now, many properties of macro instructions of {\SCMFSA} are described by the parahalting concepts. However, many practical programs are not always halting while they are halting for initialization states. For this reason, we propose initialization halting concepts. That a program is initialization halting (called ``InitHalting'' for short) means it is halting for initialization states. In order to make the halting proof of more complicated programs easy, we present ``InitHalting'' basic properties of the compositions of the macro instructions, if-Macro (conditional branch macro instructions) and Times-Macro (for-loop macro instructions) etc.

Contents (PDF format)

- [1]
Noriko Asamoto.
Conditional branch macro instructions of \SCMFSA. Part I.
*Journal of Formalized Mathematics*, 8, 1996. - [2]
Noriko Asamoto.
Conditional branch macro instructions of \SCMFSA. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [3]
Noriko Asamoto.
Constant assignment macro instructions of \SCMFSA. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [4]
Noriko Asamoto.
The \tt loop and \tt times macroinstruction for \SCMFSA.
*Journal of Formalized Mathematics*, 9, 1997. - [5]
Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec.
On the composition of macro instructions. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [6]
Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec.
On the composition of macro instructions. Part III.
*Journal of Formalized Mathematics*, 8, 1996. - [7]
Grzegorz Bancerek.
Cardinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Grzegorz Bancerek and Piotr Rudnicki.
Development of terminology for \bf scm.
*Journal of Formalized Mathematics*, 5, 1993. - [11]
Grzegorz Bancerek and Andrzej Trybulec.
Miscellaneous facts about functions.
*Journal of Formalized Mathematics*, 8, 1996. - [12]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [14]
Czeslaw Bylinski.
A classical first order language.
*Journal of Formalized Mathematics*, 2, 1990. - [15]
Czeslaw Bylinski.
The modification of a function by a function and the iteration of the composition of a function.
*Journal of Formalized Mathematics*, 2, 1990. - [16]
Yatsuka Nakamura and Andrzej Trybulec.
A mathematical model of CPU.
*Journal of Formalized Mathematics*, 4, 1992. - [17]
Piotr Rudnicki and Andrzej Trybulec.
Memory handling for \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [18]
Yasushi Tanaka.
On the decomposition of the states of SCM.
*Journal of Formalized Mathematics*, 5, 1993. - [19]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [20]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [21]
Andrzej Trybulec and Yatsuka Nakamura.
Some remarks on the simple concrete model of computer.
*Journal of Formalized Mathematics*, 5, 1993. - [22]
Andrzej Trybulec and Yatsuka Nakamura.
Computation in \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [23]
Andrzej Trybulec and Yatsuka Nakamura.
Modifying addresses of instructions of \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [24]
Andrzej Trybulec and Yatsuka Nakamura.
Relocability for \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [25]
Andrzej Trybulec, Yatsuka Nakamura, and Noriko Asamoto.
On the compositions of macro instructions. Part I.
*Journal of Formalized Mathematics*, 8, 1996. - [26]
Andrzej Trybulec, Yatsuka Nakamura, and Piotr Rudnicki.
The \SCMFSA computer.
*Journal of Formalized Mathematics*, 8, 1996. - [27]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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