Corollary: The set of WHILE-computable functions is included in the set of partially WHILE-computable functions

(related to Definition: WHILE-Computable Functions)

There are functions \(f : \mathbb N^k \to \mathbb N\), which are partially WHILE-computable, but are not WHILE-computable. In particular, the set of all WHILE-computable functions is a proper subset of the set of all partially WHILE-computable functions:

\[W H I L E\subset W H I L E^{part}.\]

Note: This corollary actually makes sure that partially WHILE-computable functions are well-defined.

Proofs: 1

Theorems: 1

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  1. Erk, Katrin; Priese, Lutz: "Theoretische Informatik", Springer Verlag, 2000, 2nd Edition