theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviated ARS) is a formalism...

In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible. Depending on the rewriting system, an...

in the most abstract setting of an abstract rewriting system. The usual rules of elementary arithmetic form an abstract rewriting system. For example...

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...

and mathematical logic a string rewriting system (SRS), historically called a semi-Thue system, is a rewriting system over strings from a (usually finite)...

object, an unlabeled transition system is identical with an (unindexed) abstract rewriting system. If we consider the rewriting relation as an indexed set...

can be validly manipulated. These are the "rewriting rules"—an integral part of an abstract rewriting system. A common question is whether it is possible...

The Abstract Rewriting Machine (ARM) is a virtual machine which implements term rewriting for minimal term rewriting systems. Minimal term rewriting systems...

Normalizing (abstract rewriting), an abstract rewriting system in which every object has at least one normal form Normalization property (abstract rewriting), a...

Note that the rewriting here is one-way. The word problem is the accessibility problem for symmetric rewrite relations, i.e. Thue systems. The accessibility...

satisfy the descending chain condition. Noetherian rewriting system, an abstract rewriting system that has no infinite chains. Noetherian scheme, a scheme...

both b and c can be reduced. Viewing the lambda calculus as an abstract rewriting system, the Church–Rosser theorem states that the reduction rules of...

approach to graph rewriting is term graph rewriting, which involves the processing or transformation of term graphs (also known as abstract semantic graphs)...

objects in these formal systems. Abstract rewriting systems can operate on these objects. Axiomatic systems, and logic systems build upon axioms, and upon...

Society Assemblea Regionale Siciliana, Sicilian Regional Assembly Abstract rewriting system in mathematical logic Acoustic resonance spectroscopy Acute radiation...

which states that if an (abstract) rewriting system is strongly normalizing and weakly confluent, then the rewriting system is confluent. So, if we can...

of rewriting systems, Newman's lemma, also commonly called the diamond lemma, states that a terminating (or strongly normalizing) abstract rewriting system...

pathways (P53), ecosystems, and enzyme systems by using his method, abstract rewriting system on multisets (ARMS). In the 1994 science-fiction novel Permutation...

The Maude system is an implementation of rewriting logic. It is similar in its general approach to Joseph Goguen's OBJ3 implementation of equational logic...

studied in the field of graph rewriting. The nomenclature term graph is associated with the field of term graph rewriting, which involves the transformation...

Turing machines Decision tree model Functional models include: Abstract rewriting systems Combinatory logic General recursive functions Lambda calculus...

means for a computation to converge or diverge. In abstract rewriting, an abstract rewriting system is called convergent if it is both confluent and terminating...

g., contextual analysis. Abstract syntax trees are also used in program analysis and program transformation systems. Abstract syntax trees are data structures...

get to it (they are confluent). More formally, a preordered set of term rewriting transformations are said to be convergent if they are confluent and terminating...

Iron Curtain: a history of the algebraic theory of semigroups" Abstract rewriting system Additive relation, a many-valued homomorphism between modules...

In rewriting, a reduction strategy or rewriting strategy is a relation specifying a rewrite for each object or term, compatible with a given reduction...

A formal system is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms by...

Greibach normal form Kuroda normal form Normal form (abstract rewriting), an element of a rewrite system which cannot be further rewritten in logic: Normal...

In computer science, an abstract data type (ADT) is a mathematical model for data types, defined by its behavior (semantics) from the point of view of...

parametrised modules and a functional system based on equations. OBJ3 is a version of OBJ based on order-sorted rewriting. OBJ3 is agent-oriented and runs...