High Quality Content by WIKIPEDIA articles! In computability theory the smn theorem, (also called the translation lemma, parameter theorem, or parameterization theorem) is a basic result about programming languages (and, more generally, Godel numberings of the computable functions) (Soare 1987, Rogers 1967). It was first proved by Stephen Cole Kleene (Kleene 1943). In practical terms, the theorem says that for a given programming language and positive integers m and n, there is a particular algorithm that operates on the source code of programs with m+n free variables. This algorithm effectively binds m given values to the first m free variables in the program and leaves the rest free.

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