Rice's Theorem
Version 1.0.0 · Updated 2026-07-28
CORE DEFINITION
Rice's theorem is a theorem in computability theory, proposed by Henry Gordon Rice in 1953. It states that all non-trivial properties of recursively enumerable languages are undecidable. A property is 'non-trivial' if it is possessed by only some recursively enumerable languages.
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Reduce cognitive load
Rice's theorem is a theorem in computability theory, proposed by Henry Gordon Rice in 1953. It states that all non-trivial properties of recursively enumerable languages are undecidable. A property is 'non-trivial' if it is possessed by only some recursively enumerable languages.
Anchor fast decisions
For any non-trivial semantic property of program behavior, there is no uniform decision algorithm (Turing undecidable). Self-referential diagonalization can be constructed on program behavior, causing any 'decider' to fall into contradiction.
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