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Asked: 2026-05-22T19:29:02+00:00

Referring to the while rule for total correctness , WP seems to tell me

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Referring to the while rule for total correctness, WP seems to tell me that just finding a loop variant that strictly decreases is enough to prove termination. I can’t accept that, either because I’m missing something or the rule is wrong. Consider

int i = 1000;
while(true) i--;

in which the value of variable i is a strictly decreasing loop variant, but the loop certainly doesn’t terminate.

Surely the rule needs to have an additional precondition, something like i<0 → ¬B (where B is the loop condition in the axiom schema) so that the loop condition eventually ‘catches’ the loop variant and exits.

Or have I missed something?

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1 Answer

  1. Editorial Team

    The loop-variant must be a natural number. A natural number cannot decrease past zero. Using big words, the loop variant is a value that is monotonically decreasing with respect to a well-founded relation. It’s the well-foundedness that’s missing from your reasoning.

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