Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

The Construction and Shiftability of Program Blocks for SCMPDS

Jing-Chao Chen
Shanghai Jiaotong University

Summary.

In this article, a program block is defined as a finite sequence of instructions stored consecutively on initial positions. Based on this definition,any program block with more than two instructions can be viewed as the combination of two smaller program blocks. To describe the computation of a program block by the result of its two sub-blocks, we introduce the notions of paraclosed, parahalting, valid, and shiftable, the meaning of which may be stated as follows: \begin{itemize} \item[-] a program is paraclosed if and only if any state containing it is closed, \item[-] a program is parahalting if and only if any state containing it is halting, \item[-] in a program block, a jumping instruction is valid if its jumping offset is valid, \item[-] a program block is shiftable if it does not contain any return and saveIC instructions, and each instruction in it is valid. \end{itemize} When a program block is shiftable, its computing result does not depend on its storage position.

This research is partially supported by the National Natural Science Foundation of China Grant No. 69873033.

MML Identifier: SCMPDS_4

The terminology and notation used in this paper have been introduced in the following articles [14] [13] [20] [15] [21] [4] [6] [18] [2] [5] [9] [10] [11] [16] [12] [3] [8] [19] [17] [7] [1]

Contents (PDF format)

1. Definition of a Program Block and its Basic Properties
2. Combining two Consecutive Blocks into One Program Block
3. Combining a Block and a Instruction into One Program Block
4. The Notions of Paraclosed, Parahalting and their Basic Properties
5. Shiftability of Program Blocks and Instructions

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