Computable functions are the basic objects of study in
computability theory. Computable functions are the formalized analogue of the intuitive notion of
algorithm, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. given an input of the function domain it can return the corresponding output. Computable functions are used to discuss computability without referring to any concrete
model of computation such as
Turing machines or
register machines. Any definition, however, must make reference to some specific model of computation but all valid definitions yield the same class of functions. Particular models of computability that give rise to the set of computable functions are the
Turing-computable functions and the
µ-recursive functions.