I have heard of some people mentioning the general rule that says that you can only ever guarantee that a program will not capture the negative cases but you can never guarantee that it captures all the positive cases.

I am only roughly summarizing what i heard and don't know the exact definition or exact phrase but the meaning remains the same as mentioned.

I am wondering if there is any formal theory or proof for the same or even if this incorrect.

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    $\begingroup$ It's not exactly what you want, but related: "Program testing can be used to show the presence of bugs, but never to show their absence!" Edsger Dijkstra said it. $\endgroup$ – Rick Decker Nov 15 '17 at 0:23
  • $\begingroup$ @RickDecker Yes something like that. For example, if i am to validate an input, i can sort of guarantee that i can positively guard against all known(to me) invalid inputs, but i cannot guarantee that the given input will be 100% in all other cases valid. $\endgroup$ – rapidclock Nov 15 '17 at 0:31
  • $\begingroup$ I'm not sure what exactly you mean, but it sounds like common sense to me, not a mathematical fact. $\endgroup$ – Raphael Nov 15 '17 at 7:21

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