We present an Isabelle formalization of abstract rewriting (see, e.g.,
the book by Baader and Nipkow). First, we define standard relations like
, 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
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.
[2010-09-17] Added theories defining several (ordered)
semirings related to strong normalization and giving some standard
[2013-10-16] Generalized delta-orders from rationals to Archimedean fields.