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Rice's theorem
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{{Short description|Theorem in computability theory}} In [[computability theory]], '''Rice's theorem''' states that all non-trivial semantic properties of programs are [[undecidable problem|undecidable]]. A ''semantic'' property is one about the program's behavior (for instance, "does the program [[halting problem|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 program analysis|static analysis]] of programs. It implies that it is impossible, for example, to implement a tool that checks whether any given program is [[correctness (computer science)|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]].
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