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What (who) is rewrite system - definition

REPLACING SUBTERM IN A FORMULA WITH ANOTHER TERM

Term rewriting; Term rewriting system; Term-rewriting; Rewrite system; Rewrite rule; Phase-structure rule; Rewriting system; Term Rewriting System; Reducible expression; Redex; Rewrite rules; Transformational rule; Rewriting logic; Term rewrite system; Reduction system; Substitution system; Reduction systems; Termination (term rewriting); Termination (rewriting); Trace rewriting system; Tree rewriting; Rewriter

$'''Pic.2:''' Rule lhs term <math>x*(y*z)</math> matching in term <math>\frac{a*((a+1)*(a+2))}{1*(2*3)}</math>$
$'''Pic.1:''' Schematic triangle diagram of application of a rewrite rule <math>l \longrightarrow r</math> at position <math>p</math> in a term, with matching substitution <math>\sigma</math>$

term rewriting system

(TRS) A collection of rewrite rules used to transform terms (expressions, strings in some formal language) into equivalent terms. See reduction. (1994-11-04)

redex

Reducible Expression. An expression matching the left hand side of a reduction rule or definition.

Rewriting

In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines,

https://en.wikipedia.org/wiki/Rewriting

Wikipedia

Rewriting

In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects.

Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several theorem provers and declarative programming languages are based on term rewriting.

https://en.wikipedia.org/wiki/Rewriting