Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998
Association of Mizar Users
Another \tt times Macro Instruction
-
Piotr Rudnicki
-
University of Alberta, Edmonton
-
This work was partially supported by
NSERC Grant OGP9207 and
NATO CRG 951368.
Summary.
-
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]).
The terminology and notation used in this paper have been
introduced in the following articles
[16]
[21]
[17]
[6]
[5]
[22]
[8]
[9]
[10]
[7]
[12]
[18]
[20]
[19]
[3]
[15]
[4]
[1]
[11]
[13]
-
{\SCMFSA} Preliminaries
-
Another {\tt times} Macro Instruction
-
A Trivial Example
-
A Macro for the Fibonacci Sequence
Bibliography
- [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.
Received June 4, 1998
[
Download a postscript version,
MML identifier index,
Mizar home page]