Abstract reduction system

An abstract reduction system (A, \rightarrow) consists of

• a set A
• a relation \mathbin{\rightarrow} \subseteq A \times A

Abstract reduction systems (ARSs) are the least setting in which we can talk about rewriting on a set A. The members of the set A can be considered as terms of some language. Instead of (a, b) \in A, we write a \rightarrow b, and say that a reduces to b.

References

• A textbook description is in chapter 2 of

@book{baader_1998,
	title = {Term {Rewriting} and {All} {That}},
	publisher = {Cambridge University Press},
	author = {Baader, Franz and Nipkow, Tobias},
	year = {1998},
	doi = {10.1017/CBO9781139172752}
}