(en.wikipedia.org) Rice's theorem - Wikipedia

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In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about the program's behavior (for instance, "does the program terminate for all inputs?"), unlike a syntactic property (for instance, "does the program contain an if-then-else statement?"). A non-trivial property is one which is neither true for every program, nor false for every program.

The theorem generalizes the undecidability of the halting problem. It has far-reaching implications on the feasibility of static analysis of programs. It implies that it is impossible, for example, to implement a tool that checks whether any given program is correct, or even executes without error (it is possible to implement a tool that always overestimates or always underestimates, so in practice one has to decide what is less of a problem).

The theorem is named after Henry Gordon Rice, who proved it in his doctoral dissertation of 1951 at Syracuse University.