Rices Theorem

Essentially states that all non-trivial properties over partial functions are, in general, undecidable. 'Partial function' here refers to functions that allow divergence (non-termination) or error. Trivial properties are only those true or false of all functions in general.

See: http://en.wikipedia.org/wiki/Rice%27s_theorem

See also: GoedelsIncompletenessTheorem, HaltingProblem, TotalFunctionalProgramming