Test
Dynamic logic associates to every proposition an action called a test. When holds, the test acts as a NOP, changing nothing while allowing the action to move on. When is false, acts as BLOCK. Tests can be axiomatized as follows.
A8.
The corresponding theorem for is:
T8.
The construct if p then a else b is realized in dynamic logic as . This action expresses a guarded choice: if holds then is equivalent to, whereas is equivalent to BLOCK, and is equivalent to . Hence when is true the performer of the action can only take the left branch, and when is false the right.
The construct while p do a is realized as . This performs zero or more times and then performs . As long as remains true, the at the end blocks the performer from terminating the iteration prematurely, but as soon as it becomes false, further iterations of the body are blocked and the performer then has no choice but to exit via the test .
Read more about this topic: Dynamic Logic (modal Logic)
Famous quotes containing the word test:
“Utopias are presented for our inspection as a critique of the human state. If they are to be treated as anything but trivial exercises of the imagination. I suggest there is a simple test we can apply.... We must forget the whole paraphernalia of social description, demonstration, expostulation, approbation, condemnation. We have to say to ourselves, “How would I myself live in this proposed society? How long would it be before I went stark staring mad?””
—William Golding (b. 1911)
“It is the test of a novel writer’s art that he conceal his snake-in-the-grass; but the reader may be sure that it is always there.”
—Anthony Trollope (1815–1882)
“The face we see was never young,
Nor could it ever have been old.
For he, to whom we had applied
Our shopman’s test of age and worth,
Was elemental when he died,
As he was ancient at his birth:”
—Edwin Arlington Robinson (1869–1935)