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Well-Quasi-Orders
| Title: | Well-Quasi-Orders |
| Author: | Christian Sternagel |
| Submission date: | 2012-04-13 |
| Abstract: | Based on Isabelle/HOL's type class for preorders,
we introduce a type class for well-quasi-orders (wqo)
which is characterized by the absence of "bad" sequences
(our proofs are along the lines of the proof of Nash-Williams,
from which we also borrow terminology). Our main results are
instantiations for the product type, the list type, and a type of finite trees,
which (almost) directly follow from our proofs of (1) Dickson's Lemma, (2)
Higman's Lemma, and (3) Kruskal's Tree Theorem. More concretely:
|
| Change history: | [2012-06-11]: Added Kruskal's Tree Theorem. [2012-12-19]: New variant of Kruskal's tree theorem for terms (as opposed to variadic terms, i.e., trees), plus finite version of the tree theorem as corollary. [2013-05-16]: Simplified construction of minimal bad sequences. [2014-07-09]: Simplified proofs of Higman's lemma and Kruskal's tree theorem, based on homogeneous sequences. |
| BibTeX: |
@article{Well_Quasi_Orders-AFP,
author = {Christian Sternagel},
title = {Well-Quasi-Orders},
journal = {Archive of Formal Proofs},
month = apr,
year = 2012,
note = {\url{http://isa-afp.org/entries/Well_Quasi_Orders.shtml},
Formal proof development},
ISSN = {2150-914x},
}
|
| License: | BSD License |
| Depends on: | Abstract-Rewriting, Open_Induction, Regular-Sets |
| Used by: | Decreasing-Diagrams-II, Myhill-Nerode |
| Status: [skipped] | This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations. |
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