We present an Isabelle formalization of abstract rewriting (see, e.g., the book by Baader and Nipkow). First, we define standard relations like joinability, meetability, conversion, etc. Then, we formalize important properties of abstract rewrite systems, e.g., confluence and strong normalization. Our main concern is on strong normalization, since this formalization is the basis of CeTA (which is mainly about strong normalization of term rewrite systems). Hence lemmas involving strong normalization constitute by far the biggest part of this theory. One of those is Newman's lemma.
- October 16, 2013
- Generalized delta-orders from rationals to Archimedean fields.
- September 17, 2010
- Added theories defining several (ordered)
semirings related to strong normalization and giving some standard