scholarly journals Lifting Infinite Normal Form Definitions From Term Rewriting to Term Graph Rewriting

2007 ◽  
Vol 72 (1) ◽  
pp. 17-29
Author(s):  
Stefan Blom
Keyword(s):  
Normal Form ◽  
Term Rewriting ◽  
Graph Rewriting

Graph rewriting for the π-calculus

2007 ◽  
Vol 17 (3) ◽  
pp. 407-437 ◽  
Author(s):  
FABIO GADDUCCI
Keyword(s):  
Normal Form ◽  
Graph Rewriting ◽  
Π Calculus ◽  
Standard Graph

We propose a graphical implementation for (possibly recursive) processes of the π-calculus, encoding each process into a graph. Our implementation is sound and complete with respect to the structural congruence for the calculus: two processes are equivalent if and only if they are mapped into graphs with the same normal form. Most importantly, the encoding allows the use of standard graph rewriting mechanisms for modelling the reduction semantics of the calculus.

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.

scholarly journals On the adequacy of graph rewriting for simulating term rewriting

1994 ◽  
Vol 16 (3) ◽  
pp. 493-523 ◽  
Author(s):  
J. R. Kennaway ◽  
J. W. Klop ◽  
M. R. Sleep ◽  
F. J. de Vries
Keyword(s):  
Term Rewriting ◽  
Graph Rewriting

Convergence in infinitary term graph rewriting systems is simple

2018 ◽  
Vol 28 (8) ◽  
pp. 1363-1414
Author(s):  
PATRICK BAHR
Keyword(s):  
Term Rewriting ◽  
Unified Framework ◽  
Lazy Evaluation ◽  
Efficient Manner ◽  
Graph Rewriting ◽  
Rewriting Systems ◽  
Finite Term ◽  
Natural Generalisation ◽  
Graph Rewriting Systems ◽  
Ideal Completion

Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by emulating duplication via sharing. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can be used to model non-strict evaluation. In this paper, we unify term graph rewriting and infinitary term rewriting thereby addressing both components of lazy evaluation: non-strictness and sharing. In contrast to previous attempts to formalise infinitary term graph rewriting, our approach is based on a simple and natural generalisation of the modes of convergence of infinitary term rewriting. We show that this new approach is better suited for infinitary term graph rewriting as it is simpler and more general. The latter is demonstrated by the fact that our notions of convergence give rise to two independent canonical and exhaustive constructions of infinite term graphs from finite term graphs via metric and ideal completion. In addition, we show that our notions of convergence on term graphs are sound w.r.t. the ones employed in infinitary term rewriting in the sense that convergence is preserved by unravelling term graphs to terms. Moreover, the resulting infinitary term graph calculi provide a unified framework for both infinitary term rewriting and term graph rewriting, which makes it possible to study the correspondences between these two worlds more closely.

scholarly journals Term Graph Rewriting and Parallel Term Rewriting

2011 ◽  
Vol 48 ◽  
pp. 3-18 ◽  
Author(s):  
Andrea Corradini ◽  
Frank Drewes
Keyword(s):  
Term Rewriting ◽  
Graph Rewriting
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