Computable function
function whose values can be computed by an algorithm
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes the value of the function for every value of its argument. Because of the lack of a precise definition of the concept of algorithm, every formal definition of computability must refer to a specific model of computation.
Many such models of computation have been proposed, the major ones being Turing machines, register machines, lambda calculus and general recursive functions. Although these four are of a very different nature, they provide exactly the same class of computable functions, and, for every model of computation that has ever been proposed, the computable functions for such a model are computable for the above four models of computation.
The Church–Turing thesis is the unprovable assertion that every notion of computability that can be imagined can compute only functions that are computable in the above sense.
Before the precise definition of computable functions, mathematicians often used the informal term effectively calculable. This term has since come to be identified with the computable functions. The effective computability of these functions does not imply that they can be efficiently computed (i.e. computed within a reasonable amount of time).
Begin with the source’s own compact description: “Computable function” is function whose values can be computed by an algorithm. The dossier treats that line as a proposition to test through Computable, function and whose, not as a finished interpretation.
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This entry incorporates text from “Computable function” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.