In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
,
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
and
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
, convergence is the idea that different sequences of transformations come to a conclusion in a finite amount of time (the transformations are
terminating), and that the conclusion reached is independent of the path taken to get to it (they are
confluent
In geography, a confluence (also: ''conflux'') occurs where two or more flowing bodies of water join to form a single channel. A confluence can occur in several configurations: at the point where a tributary joins a larger river (main stem); o ...
).
More formally, a
preorder
In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. Preorders are more general than equivalence relations and (non-strict) partial orders, both of which are special c ...
ed set of
term 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 reduc ...
transformations are said to be convergent if they are
confluent
In geography, a confluence (also: ''conflux'') occurs where two or more flowing bodies of water join to form a single channel. A confluence can occur in several configurations: at the point where a tributary joins a larger river (main stem); o ...
and
terminating.
See also
*
Logical equality
Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value ''true'' if both functional arguments have the same logical value, ...
*
Logical equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending on ...
*
Rule of replacement
In logic, a rule of replacementMoore and Parker is a transformation rule that may be applied to only a particular segment of an logical expression, expression. A logical system may be constructed so that it uses either axioms, rules of inference ...
References
Rewriting systems
{{plt-stub