Are pure functions always computable functions?
In computer programming, a Pure function is a function that has the following properties:
(1) the function return values are identical for identical arguments (no variation with local static variables, non-local variables, mutable reference arguments or input streams), and
(2) the function application has no side effects (no mutation of local static variables, non-local variables, mutable reference arguments or input/output streams).
Computable functions are the basic objects of study in computability theory.
Computable functions are the formalized analogue of the intuitive notion of algorithms, 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.
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