For example, in the following lambda expression, λf . g(f(λx . x),x,y),
the variable x occurs three times. The first occurrence, since it immediately follows a λ, introduces a new “binding” of x, and is therefore called a binding occurrence. The second occurrence of x falls inside the “scope” of this binding and is therefore called a bound occurrence. The third x is not within the scope of any such binding and is therefore called a free occurrence. Equally, the variable f has a binding occurrence and a bound occurrence, while g and y just have one free occurrence each. Since only x, y, and g have free occurrences, they are referred to as the free variables of the expression. The value of the whole expression then depends on what values are given to these free occurrences.
Note that freeness depends on the expression under consideration; thus, although f does not occur free in the whole expression above, it does so in the subexpression g(f(λx . x),x,y).
"free variable." A Dictionary of Computing. . Encyclopedia.com. (February 21, 2019). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/free-variable
"free variable." A Dictionary of Computing. . Retrieved February 21, 2019 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/free-variable
Encyclopedia.com 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, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com 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 Encyclopedia.com 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.