Download PDFOpen PDF in browserGeneralizations of Rice's Theorem, Applicable to Executable and Non-Executable Formalisms13 pages•Published: June 22, 2012AbstractWe formulate and prove two Rice-like theoremsthat characterize limitations on nameability of properties within a given naming scheme for partial functions. Such a naming scheme can, but need not be, an executable formalism. A programming language is an example of an executable naming scheme, where the program text names the partial function it implements. Halting is an example of a property that is not nameable in that naming scheme. The proofs reveal requirements on the naming scheme to make the characterization work. Universal programming languages satisfy these requirements, but also other formalisms can satisfy them. We present some non-universal programming languages and a non-executable specification language satisfying these requirements. Our theorems have Turing's well-known Halting Theorem and Rice's Theorem as special cases, by applying them to a universal programming language or Turing Machines as naming scheme. Thus, our proofs separate the nature of the naming scheme (which can, but need not, coincide with computability) from the diagonal argument. This sheds further light on how far reaching and simple the `diagonal' argument is in itself. Keyphrases: execution based computation formalisms, generalized rice theorem, halting theorem, specification based computation formalisms In: Andrei Voronkov (editor). Turing-100. The Alan Turing Centenary, vol 10, pages 168-180.
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