Volume 10, 1998

University of Bialystok

Copyright (c) 1998 Association of Mizar Users

**Piotr Rudnicki**- University of Alberta, Edmonton
- This work was partially supported by NSERC Grant OGP9207 and NATO CRG 951368.

- The semantics of the {\tt times} macro is given in [2] only for the case when the body of the macro is parahalting. We remedy this by defining a new {\tt times} macro instruction in terms of {\tt while} (see [11], [14]). The semantics of the new {\tt times} macro is given in a way analogous to the semantics of {\tt while} macros. The new {\tt times} uses an anonymous variable to control the number of its executions. We present two examples: a trivial one and a remake of the macro for the Fibonacci sequence (see [13]).

- {\SCMFSA} Preliminaries
- Another {\tt times} Macro Instruction
- A Trivial Example
- A Macro for the Fibonacci Sequence

- [1]
Noriko Asamoto.
Constant assignment macro instructions of \SCMFSA. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [2]
Noriko Asamoto.
The \tt loop and \tt times macroinstruction for \SCMFSA.
*Journal of Formalized Mathematics*, 9, 1997. - [3]
Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec.
On the composition of macro instructions. Part II.
*Journal of Formalized Mathematics*, 8, 1996. - [4]
Noriko Asamoto, Yatsuka Nakamura, Piotr Rudnicki, and Andrzej Trybulec.
On the composition of macro instructions. Part III.
*Journal of Formalized Mathematics*, 8, 1996. - [5]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Grzegorz Bancerek.
K\"onig's theorem.
*Journal of Formalized Mathematics*, 2, 1990. - [7]
Grzegorz Bancerek and Piotr Rudnicki.
Two programs for \bf scm. Part I - preliminaries.
*Journal of Formalized Mathematics*, 5, 1993. - [8]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
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. - [11]
Jing-Chao Chen.
While macro instructions of \SCMFSA.
*Journal of Formalized Mathematics*, 9, 1997. - [12]
Yatsuka Nakamura and Andrzej Trybulec.
A mathematical model of CPU.
*Journal of Formalized Mathematics*, 4, 1992. - [13]
Piotr Rudnicki.
On the composition of non-parahalting macro instructions.
*Journal of Formalized Mathematics*, 10, 1998. - [14]
Piotr Rudnicki.
The \tt while macro instructions of \SCMFSA. Part II.
*Journal of Formalized Mathematics*, 10, 1998. - [15]
Piotr Rudnicki and Andrzej Trybulec.
Memory handling for \SCMFSA.
*Journal of Formalized Mathematics*, 8, 1996. - [16]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [17]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [18]
Andrzej Trybulec and Yatsuka Nakamura.
Some remarks on the simple concrete model of computer.
*Journal of Formalized Mathematics*, 5, 1993. - [19]
Andrzej Trybulec, Yatsuka Nakamura, and Noriko Asamoto.
On the compositions of macro instructions. Part I.
*Journal of Formalized Mathematics*, 8, 1996. - [20]
Andrzej Trybulec, Yatsuka Nakamura, and Piotr Rudnicki.
The \SCMFSA computer.
*Journal of Formalized Mathematics*, 8, 1996. - [21]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [22]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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