Theorems in theory of computation | Computability theory

Smn theorem

In computability theory the S mn theorem, (also called the translation lemma, parameter theorem, and the parameterization theorem) is a basic result about programming languages (and, more generally, Gödel numberings of the computable functions) (Soare 1987, Rogers 1967). It was first proved by Stephen Cole Kleene (1943). The name S mn comes from the occurrence of an S with subscript n and superscript m in the original formulation of the theorem (see below). In practical terms, the theorem says that for a given programming language and positive integers m and n, there exists a particular algorithm that accepts as input the source code of a program with m + n free variables, together with m values. This algorithm generates source code that effectively substitutes the values for the first m free variables, leaving the rest of the variables free. (Wikipedia).

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Primitive recursive function | Kleene's recursion theorem | Partial evaluation | Stephen Cole Kleene | Computable function | Computability theory | Algorithm | Gödel numbering | Currying