Term Graph Rewriting and Garbage Collection Using Ppfibrations

The categorical semantics of (an abstract version of) the general term graph rewriting language DACTL is investigated. The operational semantics is reformulated in order to reveal its universal properties. The technical dissonance between the matchings of left-hand sides of rules to redexes, and the properties of rewrite rules themselves, is taken as the impetus for expressing the core of the model as a Grothendieck opfibration of a category of general rewrites over a base of general rewrite rules. Garbage collection is examined in this framework in order to reconcile the treatment with earlier approaches. It is shown that term rewriting has particularly good garbage-theoretic properties that do not generalise to all cases of graph rewriting and that this has been a stumbling block for aspects of some earlier models for graph rewriting.

[1]  Hartmut Ehrig,et al.  Introduction to the Algebraic Theory of Graph Grammars (A Survey) , 1978, Graph-Grammars and Their Application to Computer Science and Biology.

[2]  Jan Willem Klop,et al.  Transfinite Reductions in Orthogonal Term Rewriting Systems , 1995, Inf. Comput..

[3]  Richard Kennaway.  On "On Graph Rewritings" , 1987, Theor. Comput. Sci..

[4]  Eugenio Moggi.  A Cateogry-Theoretic Account of Program Modules , 1991, Math. Struct. Comput. Sci..

[5]  Hartmut Ehrig,et al.  Graph rewriting with unification and composition , 1986, Graph-Grammars and Their Application to Computer Science.

[6]  Marko C. J. D. van Eekelen,et al.  Term Graph Rewriting , 1987, PARLE.

[7]  Hartmut Ehrig,et al.  Algebraic Approach to Graph Transformation Based on Single Pushout Derivations , 1991, WG.

[8]  Pim van den Broek.  Algebraic Graph Rewriting Using a Single Pushout , 1991, TAPSOFT, Vol.1.

[9]  Jean-Claude Raoult,et al.  On graph rewritings , 1984, Bull. EATCS.

[10]  Richard Kennaway,et al.  Implementing Term Rewrite Languages in Dactl , 1990, Theor. Comput. Sci..

[11]  Jean Benabou,et al.  Fibered categories and the foundations of naive category theory , 1985, Journal of Symbolic Logic.

[12]  Berthold Hoffmann,et al.  Jungle Evaluation for Efficient Term Rewriting , 1988, ALP.

[13]  John Staples,et al.  Optimal Evaluations of Graph-Like Expressions , 1980, Theor. Comput. Sci..

[14]  Annegret Habel,et al.  Jungle evaluation , 1988, Fundam. Informaticae.

[15]  Simone Martini,et al.  Categorical Models of Polymorphism , 1992, Inf. Comput..

[16]  Michael Barr,et al.  Category theory for computing science , 1995, Prentice Hall International Series in Computer Science.

[17]  John Staples.  Speeding up Subtree Replacement Systems , 1980, Theor. Comput. Sci..

[18]  William M. Farmer,et al.  Redex Capturing in Term Graph Rewriting , 1990, Int. J. Found. Comput. Sci..

[19]  John Staples,et al.  Computation on Graph-Like Expressions , 1980, Theor. Comput. Sci..

[20]  Richard Kennaway,et al.  Graph Rewriting in Some Categories of Partial Morphisms , 1990, Graph-Grammars and Their Application to Computer Science.

[21]  Hartmut Ehrig,et al.  Tutorial introduction to the algebraic approach of graph grammars , 1986, Graph-Grammars and Their Application to Computer Science.

[22]  Glynn Winskel,et al.  Domain Theoretic Models of Polymorphism , 1989, Inf. Comput..

[23]  A. Grothendieck.  Technique de descente et théorèmes d'existence en géométrie algébrique. I. Généralités. Descente par morphismes fidèlement plats , 1960 .