scholarly journals From Linear Term Rewriting to Graph Rewriting with Preservation of Termination

2021 ◽  
Vol 350 ◽  
pp. 19-34
Author(s):  
Roy Overbeek ◽  
Jörg Endrullis
Keyword(s):  
Term Rewriting ◽  
Linear Term ◽  
Graph Rewriting

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 Modular termination of r-consistent and left-linear term rewriting systems

1995 ◽  
Vol 149 (2) ◽  
pp. 361-374 ◽  
Author(s):  
Manfred Schmidt-Schauß ◽  
Massimo Marchiori ◽  
Sven Eric Panitz
Keyword(s):  
Term Rewriting ◽  
Linear Term ◽  
Term Rewriting Systems ◽  
Rewriting Systems

Jungle Evaluation

1991 ◽  
Vol 15 (1) ◽  
pp. 37-60
Author(s):  
Annegret Habel ◽  
Hans-Jörg Kreowski ◽  
Detlef Plump
Keyword(s):  
Term Rewriting ◽  
Bipartite Graphs ◽  
Graph Grammar ◽  
Graph Rewriting ◽  
Structural Induction ◽  
Rewrite Rules ◽  
The Rich

Jungle evaluation is proposed as a new graph rewriting approach to the evaluation of functional expressions and, in particular, of algebraically specified operations. Jungles – being intuitively forests of coalesced trees with shared substructures – are certain acyclic hypergraphs (or equivalently, bipartite graphs) the nodes and edges of which are labeled with the sorts and operation symbols of a signature. Jungles are manipulated and evaluated by the application of jungle rewrite rules, which generalize equations or, more exactly, term rewrite rules. Indeed, jungle evaluation turns out to be a compromise between term rewriting and graph rewriting displaying some favorable properties: the inefficiency of term rewriting is partly avoided while the possibility of structural induction is maintained, and a good part of the existing graph grammar theory is applicable so that there is some hope that the rich theory of term rewriting is not lost forever without a substitute.

Term graph narrowing

1996 ◽  
Vol 6 (6) ◽  
pp. 649-676 ◽  
Author(s):  
Annegret Habel ◽  
Detlef Plump
Keyword(s):  
General Solution ◽  
Order Term ◽  
Term Rewriting ◽  
Term Rewriting Systems ◽  
Graph Rewriting ◽  
First Order ◽  
Improve Efficiency ◽  
Rewriting Systems ◽  
Solving Equations

We introduce term graph narrowing as an approach for solving equations by transformations on term graphs. Term graph narrowing combines term graph rewriting with first-order term unification. Our main result is that this mechanism is complete for all term rewriting systems over which term graph rewriting is normalizing and confluent. This includes, in particular, all convergent term rewriting systems. Completeness means that for every solution of a given equation, term graph narrowing can find a more general solution. The general motivation for using term graphs instead of terms is to improve efficiency: sharing common subterms saves space and avoids the repetition of computations.

A Characterization of Irreducible Sets Modulo Left-Linear Term Rewriting Systems by Tree Automata

1990 ◽  
Vol 13 (2) ◽  
pp. 211-226
Author(s):  
Z. Fülop ◽  
S. Vágvölgyi
Keyword(s):  
Term Rewriting ◽  
Linear Term ◽  
Tree Automata ◽  
Top Down ◽  
Term Rewriting Systems ◽  
Tree Language ◽  
Rewriting Systems ◽  
Term Rewriting System ◽  
Look Ahead

The concept of top-down tree automata with prefix look-ahead is introduced. It is shown that a tree language is the set of irreducible trees of a left-linear term rewriting system if and only if it can be recognized by a one-state deterministic top-down tree automaton with pre fix look-ahead.

scholarly journals Derivational Complexity and Context-Sensitive Rewriting

2021 ◽  
Author(s):  
Salvador Lucas
Keyword(s):  
Normal Forms ◽  
Term Rewriting ◽  
Linear Term ◽  
The Other ◽  
Term Rewriting Systems ◽  
Context Sensitive ◽  
Rewriting Systems ◽  
Other Hand

AbstractContext-sensitive rewriting is a restriction of rewriting where reduction steps are allowed on specific arguments $$\mu (f)\subseteq \{1,\ldots ,k\}$$ μ ( f ) ⊆ { 1 , … , k } of k-ary function symbols f only. Terms which cannot be further rewritten in this way are called $$\mu $$ μ -normal forms. For left-linear term rewriting systems (TRSs), the so-called normalization via$$\mu $$ μ -normalization procedure provides a systematic way to obtain normal forms by the stepwise computation and combination of intermediate $$\mu $$ μ -normal forms. In this paper, we show how to obtain bounds on the derivational complexity of computations using this procedure by using bounds on the derivational complexity of context-sensitive rewriting. Two main applications are envisaged: Normalization via $$\mu $$ μ -normalization can be used with non-terminating TRSs where the procedure still terminates; on the other hand, it can be used to improve on bounds of derivational complexity of terminating TRSs as it discards many rewritings.

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