term rewriting system
Let E be a set of equations such that, for each t = t′ ∈ E, the left-hand side t is not a variable. The pair (Σ,E) is called an equational TRS. The equations of E are used in derivations of terms where the reduction t →E t′ requires substitutions to be made in some equation e ∈ E and the left-hand side of e is replaced by the right-hand side of e in t to obtain t′.
The first set of properties of a term rewriting system (Σ,E) is now obtained from the properties of abstract reduction systems. The following are examples. (1) The term rewriting system (Σ,E) is complete if the reduction system →E on T(Σ) is Church–Rosser and strongly terminating.(2) Let ≡E be the smallest congruence containing →E and T(Σ,E) be the factor algebra T(Σ)|≡E. Then T(Σ,E) is the initial algebra of Alg(Σ,E). If (Σ,E) is a finite equational TRS specification that is complete, then T(Σ,E) is a computable algebra.
See also orthogonal term rewriting system.
"term rewriting system." A Dictionary of Computing. . Encyclopedia.com. (December 14, 2018). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/term-rewriting-system
"term rewriting system." A Dictionary of Computing. . Retrieved December 14, 2018 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/term-rewriting-system
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.