Abstract
The notion of path is classical in graph theory but not directly used in the term rewriting community. The main idea of this work is to raise the notion of path to the level of first-order terms, i.e. paths become part of the terms and not just meta-information about them. These paths are represented by words of integers (positive or negative) and are interpreted as relative addresses in terms. In this way, paths can also be seen as a generalization of the classical notion of position for the first-order terms and are inspired by de Bruijn indexes.
In this paper, we define an original framework called Referenced Term Rewriting where paths are used to represent pointers between subterms. Using this approach, any term-graph rewriting systems can be simulated using a term rewrite-based environment.
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Ariola, Z.M., Blom, S.: Cyclic lambda calculi. In: Ito, T., Abadi, M. (eds.) TACS 1997. LNCS, vol. 1281, pp. 77–106. Springer, Heidelberg (1997)
Ariola, Z.M., Klop, J.W.: Equational term graph rewriting. Fundamenta Informaticae 26(3/4), 207–240 (1996)
Baader, F., Nipkow, T.: Term Rewriting and all That. Cambridge University Press, Cambridge (1998)
Balland, E., Brauner, P.: Term-graph rewriting in tom using relative positions. In: TermGraph 2007: International Workshop on Computing with Terms and Graphs (2007)
Balland, E., Moreau, P.-E.: Term-graph rewriting via explicit paths. Technical report (2008), http://hal.inria.fr/inria-00173535/fr/
Barendregt, H.P., van Eekelen, M., Glauert, J., Kennaway, J., Plasmeijer, M., Sleep, M.: Term graph rewriting. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) PARLE 1987. LNCS, vol. 259, pp. 141–158. Springer, Heidelberg (1987)
Benaissa, Z.-E.-A., Lescanne, P., Rose, K.H.: Modeling sharing and recursion for weak reduction strategies using explicit substitution. In: Kuchen, H., Swierstra, S.D. (eds.) PLILP 1996. LNCS, vol. 1140, pp. 393–407. Springer, Heidelberg (1996)
Corradini, A., Gadducci, F.: Cpo models for infinite term rewriting. In: Alagar, V.S., Nivat, M. (eds.) AMAST 1995. LNCS, vol. 936, pp. 368–384. Springer, Heidelberg (1995)
Corradini, A., Gadducci, F.: Rational term rewriting. In: Nivat, M. (ed.) ETAPS 1998 and FOSSACS 1998. LNCS, vol. 1378, pp. 156–171. Springer, Heidelberg (1998)
de Bruijn, N.G.: Lambda calculus notation with nameless dummies. a tool for automatic formula manipulation with application to the church-rosser theorem. Indagationes Mathematicae 34, 381–392 (1972)
Dougherty, D.J., Lescanne, P., Liquori, L.: Addressed term rewriting systems: Application to a typed object calculus. Mathematical Structures in Computer Science 16, 667–709 (2006)
Echahed, R., Peltier, N.: Narrowing data-structures with pointers. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 92–106. Springer, Heidelberg (2006)
Hoffmann, B., Plump, D.: Implementing term rewriting by jungle evaluation. RAIRO: Theoretical Informatics and Applications 25 (1991)
Kennaway, R.: On graph rewritings. TCS 52(1-2), 37–58 (1987)
Kirchner, C.: Strategic rewriting. In: International Workshop on Reduction Strategies in Rewriting and Programming - WRS. ENTCS, vol. 124 (2004)
Kirchner, C., Kirchner, H.: Rewriting, solving, proving. A preliminary version of a book (1999), www.loria.fr/~ckirchne/=rsp/rsp.pdf
Plump, D.: Term graph rewriting. In: Handbook of Graph Grammars and Computing by Graph Transformation, pp. 3–61. World Scientific Publishing, Singapore (1999)
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Balland, E., Moreau, PE. (2008). Term-Graph Rewriting Via Explicit Paths. In: Voronkov, A. (eds) Rewriting Techniques and Applications. RTA 2008. Lecture Notes in Computer Science, vol 5117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70590-1_3
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