Overview
In an abstract rewriting system (ARS), an object is said to be in normal form if it cannot be rewritten any further, i.e. it is irreducible. An object is said to be in canonical form if it is presented in the “standard” representation (where “standard” is defined per field).
Examples of normal form include:
In most fields, a canoncial form specifies a unique representation.
Confluence
Confluence is the property by which two different terms can be further reduced to one common term. That is to say, confluence is a property of rewriting systems describing which terms in such a system can be rewritten in more than one way.
Bibliography
- “Canonical Form,” in Wikipedia, January 7, 2024, https://en.wikipedia.org/w/index.php?title=Canonical_form.
- “Confluence (Abstract Rewriting),” in Wikipedia, May 22, 2024, https://en.wikipedia.org/w/index.php?title=Confluence.
- Normal Form,” in Wikipedia, April 27, 2024, https://en.wikipedia.org/w/index.php?title=Normal_form.