Invariants, Patterns and Weights for Ordering Terms

✍ Scribed by Ursula Martin; Duncan Shand

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 488 KB
• Volume: 29
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1999.0333

✦ Synopsis

We prove that any simplification order over arbitrary terms is an extension of an order by weight, by considering a related monadic term algebra called the spine. We show that any total ground-stable simplification order on the spine lifts to an order on the full term algebra. Conversely, under certain restrictions, a simplification ordering on the term algebra defines a weight function on the spine, which in turn can be lifted to a weight order on the original ground terms which contains the original order. We investigate the Knuth-Bendix and polynomial orders in this light. We provide a general framework for ordering terms by counting embedded patterns, which gives rise to many new orderings. We examine the recursive path order in this context.