Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Termination and Confluence of Higher-Order Rewrite Systems   In the last twenty years, several approaches to higher-order rewriting have
been proposed, among which Klop's Combinatory Rewrite Systems (CRSs), Nipkow's
Higher-order Rewrite Systems (HRSs) and Jouannaud and Okada's higher-order
algebraic specification languages, of which only the last one considers typed
terms. The later approach has been extended by Jouannaud, Okada and the present
author into Inductive Data Type Systems (IDTSs). In this paper, we extend IDTSs
with the CRS higher-order pattern-matching mechanism, resulting in simply-typed
CRSs. Then, we show how the termination criterion developed for IDTSs with
first-order pattern-matching, called the General Schema, can be extended so as
to prove the strong normalization of IDTSs with higher-order pattern-matching.
Next, we compare the unified approach with HRSs. We first prove that the
extended General Schema can also be applied to HRSs. Second, we show how
Nipkow's higher-order critical pair analysis technique for proving local
confluence can be applied to IDTSs.

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int