scholarly journals Term Rewrite Systems for Lattice Theory

1993 ◽  
Vol 16 (3) ◽  
pp. 279-288 ◽  
Author(s):  
Ralph Freese ◽  
J. Ježek ◽  
J.B. Nation
Keyword(s):  
Lattice Theory ◽  
Rewrite Systems ◽  
Term Rewrite Systems

Modular termination of prefix-constrained term rewrite systems

2022 ◽  
Vol 174 ◽  
pp. 106207
Author(s):  
Nirina Andrianarivelo ◽  
Pierre Réty
Keyword(s):  
Rewrite Systems ◽  
Term Rewrite Systems

Term rewrite systems and varieties of lattices

1995 ◽  
pp. 255-277
Author(s):  
Ralph Freese ◽  
Jaroslav Jezek ◽  
J. Nation
Keyword(s):  
Rewrite Systems ◽  
Varieties Of Lattices ◽  
Term Rewrite Systems

scholarly journals A proof-theoretic study of abstract termination principles

2019 ◽  
Vol 29 (8) ◽  
pp. 1345-1366 ◽  
Author(s):  
Thomas Powell
Keyword(s):  
Complexity Analysis ◽  
Theoretic Analysis ◽  
Rewrite Systems ◽  
Abstract Setting ◽  
Term Rewrite Systems ◽  
Recursive Path

Abstract We carry out a proof-theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of derivation trees that can be defined in Gödel’s system T plus bar recursion. We then carry out a complexity analysis of these terms and demonstrate how this can be applied to bound the derivational height of term rewrite systems.

REDEX CAPTURING IN TERM GRAPH REWRITING

1990 ◽  
Vol 01 (04) ◽  
pp. 369-386 ◽  
Author(s):  
WILLIAM M. FARMER ◽  
RONALD J. WATRO
Keyword(s):  
Fixed Point ◽  
Efficient Method ◽  
Natural Generalization ◽  
Linear Term ◽  
Time And Space ◽  
Graph Rewriting ◽  
Rewrite Systems ◽  
Arbitrary Structure ◽  
Term Rewrite Systems

Term graphs are a natural generalization of terms in which structure sharing is allowed. Structure sharing makes term graph rewriting a time- and space-efficient method for implementing term rewrite systems. Certain structure sharing schemes can lead to a situation in which a term graph component is rewritten to another component that contains the original. This phenomenon, called redex capturing, introduces cycles into the term graph which is being rewritten—even when the graph and the rule themselves do not contain cycles. In some applications, redex capturing is undesirable, such as in contexts where garbage collectors require that graphs be acyclic. In other applications, for example in the use of the fixed-point combinator Y, redex capturing acts as a rewriting optimization. We show, using results about infinite rewritings of trees, that term graph rewriting with arbitrary structure sharing (including redex capturing) is sound for left-linear term rewrite systems.

scholarly journals Polytool: Polynomial interpretations as a basis for termination analysis of logic programs

2010 ◽  
Vol 11 (1) ◽  
pp. 33-63 ◽  
Author(s):  
MANH THANG NGUYEN ◽  
DANNY DE SCHREYE ◽  
JÜRGEN GIESL ◽  
PETER SCHNEIDER-KAMP
Keyword(s):  
Logic Programs ◽  
Termination Analysis ◽  
Rewrite Systems ◽  
Analysis Techniques ◽  
Programming Paradigm ◽  
Generating Polynomial ◽  
Direct Generalization ◽  
Term Rewrite Systems

AbstractOur goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial interpretations—very well known in the context of term rewrite systems—to obtain new (nontransformational) termination analysis techniques for definite logic programs (LPs). This leads to an approach that can be seen as a direct generalization of the traditional techniques in termination analysis of LPs, where linear norms and level mappings are used. Our extension generalizes these to arbitrary polynomials. We extend a number of standard concepts and results on termination analysis to the context of polynomial interpretations. We also propose a constraint-based approach for automatically generating polynomial interpretations that satisfy the termination conditions. Based on this approach, we implemented a new tool, called Polytool, for automatic termination analysis of LPs.

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