Skip to main content
Select Source:

primitive recursive function

primitive recursive function A function that can be obtained from certain initial functions by a finite number of applications of composition and primitive recursion. The initial functions are normally the zero function, successor function, and projection (or generalized identity) functions, where all functions are defined on the nonnegative integers. Primitive recursive functions are total functions, defined in a simple way by induction. There is also a notion of primitive recursive set, namely one whose characteristic function is primitive recursive.

The arithmetic functions of addition and multiplication are examples of primitive recursive functions. Indeed most of the functions and sets on natural numbers that we wish to compute are primitive recursive.

The idea can be generalized: for example, a primitive recursive function on lists satisfies a definition analogous to the one given above, with the successor function adding an element to the front of a list.

See also recursive function.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"primitive recursive function." A Dictionary of Computing. . Encyclopedia.com. 27 Jul. 2017 <http://www.encyclopedia.com>.

"primitive recursive function." A Dictionary of Computing. . Encyclopedia.com. (July 27, 2017). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/primitive-recursive-function

"primitive recursive function." A Dictionary of Computing. . Retrieved July 27, 2017 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/primitive-recursive-function

primitive recursion

primitive recursion In the study of effective computability, a particular way of defining a new function in terms of other simpler ones. The functions involved are functions over the nonnegative integers. Primitive recursion is then the process of defining a function f of n+1 variables in the following manner: f(x1,x2,…xn,0) = g(x1,x2,…xn), f(x1,x2,…xn,y+1) = h(x1,x2,…xn,y,f(x1,…xn,y))

where g and h are functions of n and n+2 variables respectively. See also primitive recursive function.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"primitive recursion." A Dictionary of Computing. . Encyclopedia.com. 27 Jul. 2017 <http://www.encyclopedia.com>.

"primitive recursion." A Dictionary of Computing. . Encyclopedia.com. (July 27, 2017). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/primitive-recursion

"primitive recursion." A Dictionary of Computing. . Retrieved July 27, 2017 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/primitive-recursion