Skip to main content

partial function

partial function Roughly, a function f : ST

that holds for only a proper subset of S. Strictly, if the subset over which it holds is R, then f : RT

is a function. However it may be more convenient to work with S rather than with R. The set U, U = SR,

is nonempty, and f has no value (or rather has the undefined value) at points in U; f is then said to be undefined on U and defined for all elements in the subset R of S, i.e. in S but not in U.

Partial functions arise naturally in computing. When recursive definitions of functions are given, the definition can sometimes loop for certain parameters. Definitions of functions can also give rise to overflow or exception situations. In these cases it is convenient to talk about partial functions. Compare total function.

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

  • MLA
  • Chicago
  • APA

"partial function." A Dictionary of Computing. . 21 Mar. 2019 <>.

"partial function." A Dictionary of Computing. . (March 21, 2019).

"partial function." A Dictionary of Computing. . Retrieved March 21, 2019 from

Learn more about citation styles

Citation styles gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, cannot guarantee each citation it generates. Therefore, it’s best to use citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

The Chicago Manual of Style

American Psychological Association

  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.