Primitive Recursive Function

Primitive Recursive Function

The primitive recursive functions are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive). The term was coined by Rózsa Péter.

In computability theory, primitive recursive functions are a class of functions that form an important building block on the way to a full formalization of computability. These functions are also important in proof theory.

Most of the functions normally studied in number theory are primitive recursive. For example: addition, division, factorial, exponential and the nth prime are all primitive recursive. So are many approximations to real-valued functions. In fact, it is difficult to devise a computable function that is not primitive recursive, although some are known (see the section on Limitations below). The set of primitive recursive functions is known as PR in complexity theory.

Every primitive recursive function is a general recursive function.