VDM-10 Language Manual

Chapter 13. Statements
13.7 The While-Loop Statement
Syntax: statement = . . .
| while loop
| . . . ;
while loop = ‘while’, expression, ‘do’, statement ;
Semantics: The semantics for the while statement corresponds to the while statement from traditional
programming languages. The form of a while loop is:
✞
✡✝
while e do
s
where e is a boolean expression and s a statement. As long as the expression e evaluates to
true the body statement s is evaluated.
Examples: The while loop can be illustrated by the following example which uses Newton’s
method to approximate the square root of a real number r within relative error e.
✞
✡✝
SquareRoot : real * real ==> real
SquareRoot (r,e) ==
(dcl x:real := 1,
nextx: real := r;
while abs (x - nextx) >= e * x do
( x := nextx;
nextx := ((r / x) + x) / 2;
);
return nextx
);
✆
✆
13.8 The Nondeterministic Statement
Syntax: statement = . . .
| nondeterministic statement
| . . . ;
nondeterministic statement =
‘||’, ‘(’, statement,
{ ‘,’, statement }, ‘)’ ;
Semantics: The nondeterministic statement has the form:
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