Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999
Association of Mizar Users
The Construction and Computation of Conditional Statements for SCMPDS
-
Jing-Chao Chen
-
Shanghai Jiaotong University
Summary.
-
We construct conditional statements like
the usual high level program language by program blocks of SCMPDS.
Roughly speaking, the article justifies such a fact that
when the condition of a conditional statement is true (false), and
the true (false) branch is shiftable, parahalting and does not contain
any halting instruction, and the false branch is shiftable, then it is
halting and its computation result equals that of the true (false)
branch. The parahalting means some program halts for all states, this
is strong condition. For this reason, we introduce the notions of
"is\_closed\_on" and "is\_halting\_on". The predicate "A is\_closed\_on B"
denotes program A is closed on state B, and "A is\_halting\_on B" denotes
program A is halting on state B. We obtain a similar theorem to
the above fact by replacing parahalting by "is\_closed\_on" and
"is\_halting\_on".
This research is partially 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
[15]
[13]
[18]
[5]
[6]
[17]
[2]
[11]
[12]
[16]
[14]
[4]
[10]
[7]
[1]
[9]
[3]
[8]
-
Preliminaries
-
The Predicates of is\_closed\_on and is\_halting\_on
-
The Construction of Conditional Statements
-
The Computation of ``if var=0 then block1 else block2''
-
The Computation of ``if var=0 then block''
-
The Computation of ``if var<>0 then block''
-
The Computation of ``if var>0 then block1 else block2''
-
The Computation of ``if var>0 then block''
-
The Computation of ``if var<=0 then block''
-
The Computation of ``if var<0 then block1 else block2''
-
The Computation of ``if var<0 then block''
-
The Computation of ``if var>=0 then block''
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Received June 15, 1999
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