H. P. Barendregt, M. C. J. D. van Eekelen, J. R. W. Glauert, J. R. Kennaway, M. J. Plasmeijer and M. R. Sleep. Term graph rewriting. In PARLE '87 volume II, number 259 in LNCS, pp. 191--231. Springer Verlag, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....as in rational equations, to model recursion, and ii) multiple edges, to model sharing. Sharing is fundamental in obtaining e#ciency, as computations in a shared subterm need only be performed once, rather than one time for each occurrence. Traditionally, term graphs are defined by labelled graphs [4], but we feel the definition of a term graph as an X F coalgebra is considerably cleaner, as the arity information made explicit in the usual definition is hidden inside the structure map of the coalgebra, and is usually automatically verified when working with coalgebras. We also choose to ....

H. P. Barendregt, M. C. J. D. van Ekelen, J. R. W. Glauert, J. R. Kennaway, M. J. Plasmeijer, and M. R. Sleep. Term graph rewriting. In Proc. PARLE 87, number 259 in LNCS, pages 141-- 158. Springer Verlag, 1987.

....we are not concerned with optimality questions, and we restrict our attention to argument sharing in a language which is simpler than the calculus. Much of the past work on graph rewriting has been to prove its correctness with respect to either the calculus [20] or Term Rewriting Systems [7, 8, 9, 16]. In contrast, this paper explores graph rewriting as a system in its own right, and makes no attempt to prove the correctness of a graph implementation with respect to a tree (or unshared) view of the computation. Motivated by what we have observed in real implementations of functional ....

....view of the computation. Motivated by what we have observed in real implementations of functional languages, we explore syntactic and semantic properties of graphs with cycles, and rewriting rules that recognize or create cycles. In this respect our calculus goes farther than either [20] or [8] where only acyclic graphs are considered. Without cyclic graphs some important implementation ideas are ruled out. More recently, Klop et al. 15] have extended the Barendregt s graph rewriting system to deal with cycles. However, their approach is significantly different from ours in that they ....

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H. Barendregt, M. van Eekelen, J. Glauert, J. Kennaway, M. Plasmeijer, and M. Sleep. Term Graph Rewriting. In Proceedings of the PARLE Conference, Eindhoven, The Netherlands, Springer-Verlag LNCS 259, June 1987.

....the right hand sides of the rules. 1 Introduction Graph rewriting is being considered in many different areas ; see for instance [8, 17] The contributions of this paper are theoretical results which concern graph rewriting as operational semantics of functional or algebraic programming languages [15, 5]. There are many straightforward reasons which motivate the use of graphs in the setting of declarative languages. For instance, graphs allow to represent expressions in a compact way thanks to the sharing of sub expressions; they also permit to handle efficiently cyclic graphs which represent ....

....of the main results. 2 Definitions and notations Many different notations are used in the literature to investigate graph rewriting [8, 19, 16] The aim of this section is to recall briefly some key definitions in order to make easier the understanding of the paper. We are mostly consistent with [5]. Some precise definitions which are omitted can be found in [6] A many sorted signature Sigma = hS; Omega i consists of a set S of sorts and an S indexed family of sets of operation symbols Omega = s2S Omega s with Omega s = w;s)2S ThetaS Omega w;s . We shall write f : s 1 : s ....

[Article contains additional citation context not shown here]

H. Barendregt, M. van Eekelen, J. Glauert, R. Kenneway, M. J. Plasmeijer, and M. Sleep. Term graph rewriting. In PARLE'87, pages 141--158. LNCS 259, 1987.

....to the appendix. 2 Preliminaries Many di erent notations are used in the literature to investigate graphs (see [11, 22] for a compilation) The aim of this section is to give brie y some key de nitions in order to make easier the understanding of the paper. Our notations are similar to those of [7, 16]. We are consistent with [9, 8] A many sorted signature = hS; i consists of a set S of sorts and an S indexed family of sets of operation symbols = s2S s with s = w;s)2S S w;s . We shall write f : s 1 : s n s whenever f 2 s 1 : s n ;s and say that f is of sort s ....

....g 2 are bisimilar, denoted g 1 : g 2 , i they represent the same (in nite) tree when one unravels them [5] We write g 1 g 2 when the term graphs g 1 and g 2 are equal up to renaming of nodes. As the formal de nition of graphs is not useful to give examples, we introduce a linear notation [7]. In the following grammar, the variable A (resp. n) ranges over the set [ X (resp. N ) Graph : Node j Node Graph Node : n:A(Node, Node) j n The set of roots of a graph de ned with a linear expression contains the rst node of the expression and all the nodes appearing just ....

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H. Barendregt, M. van Eekelen, J. Glauert, R. Kenneway, M. J. Plasmeijer, and M. Sleep. Term graph rewriting. In PARLE'87, pages 141-158. LNCS 259, 1987.

....we refer to [75, 43, 51, 61, 23, 89] In the literature there exists a variety of definitions of term graphs. Besides hypergraphs, directed graphs, terms with labels, and recursion equations have been used as underlying structures. Acyclic graphs have been dealt with in [34, 95, 96, 97] while [83, 92, 59, 15, 37, 63, 32] also consider cyclic graphs. By equipping function symbols with additional labels, sharing of different occurrences of a subterm in a term can be expressed through identical labels. Such labelled terms correspond to acyclic term graphs and have been studied in [76, 74, 82] In [36, 4, 2, 67] ....

.... Sigmat after removing all edges labelled with variables is denoted by Sigmat. For example, Figure 6 shows the graphs Mf(x,x) Sigmaf(x,x) and Sigmaf(x,x) Note that the latter graph is not a term graph according to Definition 3.1. It may be regarded as a term graph with an open node . In [15, 89], such graphs are also regarded as term graphs, and term graphs without open nodes are said to be closed. f x x f x f Figure 6: The graphs Mf(x,x) Sigmaf(x,x) and Sigmaf(x,x) For each node v in a term graph G, we denote by G[v] the (standard) term graph isomorphic to the subgraph of G ....

[Article contains additional citation context not shown here]

Hendrik Barendregt, Marko van Eekelen, John Glauert, Richard Kennaway, Rinus Plasmeijer, and Ronan Sleep. Term graph rewriting. In Proc. Parallel Architectures and Languages Europe, volume 259 of Lecture Notes in Computer Science, pages 141--158. Springer-Verlag, 1987.

....I I Graph reduction has been used to implement non strict functional languages such as JOHNSSON s lazy ML (1984) JONES s Gofer (1992) and TURNER s Miranda (1985) It is discussed in PEYTON JONES s textbook (1987) However, there has been little work in the formal semantics of graph reduction. BARENDREGT et al. 1987) have shown that graph reduction is sound and complete with respect to term reduction. LESTER (1989) has shown that the G machine of AUGUSTSSON (1984) and JOHNSSON (1984) is adequate wrt a denotational model of the lazy l calculus. In this paper, we provide an alternative presentation of graph ....

BARENDREGT, H. P., VAN EEKELEN, M. C. J. D., GLAUERT, J. R. W., KENNAWAY, J. R., PLASMEIJER, M. J., and SLEEP, M. R. (1987). Term graph rewriting. In Proc. PARLE 87, volume 2, pages 141--158. SpringerVerlag. LNCS 259.

....I I Graph reduction has been used to implement non strict functional languages such as JOHNSSON s lazy ML (1984) JONES s Gofer (1992) and TURNER s Miranda (1985) It is discussed in PEYTON JONES s textbook (1987) However, there has been little work in the formal semantics of graph reduction. BARENDREGT et al. 1987) have shown that graph reduction is sound and complete with respect to term reduction. LESTER (1989) has shown that the G machine of AUGUSTSSON (1984) and JOHNSSON (1984) is adequate wrt a denotational model of the lazy l calculus. In this paper, we provide an alternative presentation of graph ....

BARENDREGT, H. P., VAN EEKELEN, M. C. J. D., GLAUERT, J. R. W., KENNAWAY, J. R., PLASMEIJER, M. J., and SLEEP, M. R. (1987). Term graph rewriting. In Proc. PARLE 87, volume 2, pages 141--158. Springer-Verlag. LNCS 259.

....= P; x = X; y = p; x = p; if (p) x = y; g f p = 0; x = 1; y = p; x = p; if (p) x = y; g f p = P; y = p; x = p; if (p) x = y; g f p = 0; y = p; x = p; if (p) x = y; g f p = P; y = P; x = P; g P1 P2 P3 P4 P5 Fig. 1. Some simple C programs. A directed term graph [3] form of the PIM representation of P1 , SP 1 , is depicted in Fig. 4. SP 1 is generated by a simple syntax directed translation, complete details of which may be found in [4] A term graph may be viewed as a term by traversing it from its root and replacing all shared subgraphs by separate copies ....

....term by traversing it from its root and replacing all shared subgraphs by separate copies of their term representations. Shared PIM subgraphs are constructed systematically as a consequence of the translation process, or as a side effect of the natural extension of term rewriting to term graphs [3]. Parent nodes in PIM term graphs will be depicted below their children to emphasize the correspondence between program constructs and corresponding PIM subgraphs. This orientation also corresponds to the manner in which compiler IR graphs are commonly rendered. In the sequel, only a small number ....

[Article contains additional citation context not shown here]

BARENDREGT, H., VAN EEKELEN, M., GLAUERT, J., KENNAWAY, J., PLASMEIJER, M., AND SLEEP, M. Term graph rewriting. In Proc. PARLE Conference, Vol. II: Parallel Languages (Eindhoven, The Netherlands, 1987), vol. 259 of Lecture Notes in Computer Science, Springer-Verlag, pp. 141--158.

....two domains: the first one is the operational semantics of logico functional programming languages. This area led to various extensions of the rewriting concept, like order sorted rewriting [29] conditional rewriting [16] priority rewriting [38] concurrent rewriting [18] or graph rewriting [11] : The second domain is automated theorem proving where rewriting techniques are of primarily use in provers using demodulation or simplification inference rules to prune the search space. In this context, it appears that most of interesting proofs in mathematical structures, set and graph ....

H. P. Barendregt et al. Term graph rewriting. In Proc. of PARLE'87, volume 259 of Lecture Notes in Computer Science. Springer-Verlag, 1987.

....variables, with respect to the matching out (G 1 ) i] in (G 2 ) i] for i = 1: n, of the variables in the merged interfaces of G 1 and G 2 . Note that this matching can introduce unexpected chains of links, e.g. when y ## ## W [1] W [1] ## ## W [2] 2 L 1 and W [2] ## ## W [3] ; W [3] ## ## x 2 L 2 . It is worth remarking that this de nition preserves the transitive closure property (5) of De nition 3.2 on links. The following technical lemmas will be useful for proving Proposition 3.7. Lemma 3.4 Given a list of names W and two sets of links L 1 and L 2 whose ....

....with respect to the matching out (G 1 ) i] in (G 2 ) i] for i = 1: n, of the variables in the merged interfaces of G 1 and G 2 . Note that this matching can introduce unexpected chains of links, e.g. when y ## ## W [1] W [1] ## ## W [2] 2 L 1 and W [2] ## ## W [3] W [3] ## ## x 2 L 2 . It is worth remarking that this de nition preserves the transitive closure property (5) of De nition 3.2 on links. The following technical lemmas will be useful for proving Proposition 3.7. Lemma 3.4 Given a list of names W and two sets of links L 1 and L 2 whose underlying ....

[Article contains additional citation context not shown here]

H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W. Glauert, J.R. Kennaway, M.J. Plasmeijer, and M.R. Sleep. Term graph rewriting. In J.W. de Bakker, A.J. Nijman, and P.C. Treleaven, editors, Proc. of PARLE'87, Parallel Architectures and Languages Europe, volume 259 of Lect. Notes in Comp. Science, pages 141{ 158. Springer Verlag, 1987.

....a Sigma ) h Sigma , that intuitively represent the same term h(a; a) are different. In fact, in the PhD thesis [10] of the first author it is shown that a fundamental property of correspondence holds between smonoidal theories and term graphs (as defined e.g. in the introductory chapter of [8]) each arrow t Sigma : n m identifies a term graph t over Sigma with a specified m tuple of roots and a specified n tuple of variables nodes, and arrow composition is graph replacement. The incremental description of algebraic theories has received little attention in the literature (see ....

M.C.J.D. van Eekelen, M.J. Plasmeijer, M.R. Sleep, Term Graph Rewriting, Theory and Practice, John Wiley & Sons, 1993.

....structure. Figure 1 shows the effects of these two different representations of the role. Repeat Cons Cons Repeat 1 The correctness of the graph rewriting implementation of term rewriting is a piece of well known folklore. For acyclic graphs the formal relationship has been studied in [Sta80, Bar87, Far89, Far90]. Only the last two of these consider cyclic graphs at all. In an obvious and intuitive sense, acyclic graphs can be unravelled to trees the syntax trees of terms. Cyclic graphs can be similarly unravelled, but give rise to infinite trees, which we can regard as infinite terms. A single ....

....term and term graph rewriting, and a notion of one rewrite system implementing another. We show that for orthogonal systems of rewrite rules, finitary graph rewriting implements in this sense a restricted version of infinitary term rewriting. This subsumes and makes more precise the result of [Bar87] that for orthogonal systems, finitary acyclic graph rewriting implements finitary term rewriting. We show by means of a counterexample that, surprisingly, infinitary graph rewriting does not implement infinitary term rewriting. Our present definition of an implementation by one system of another ....

[Article contains additional citation context not shown here]

H.P. BARENDREGT, M.C.J.D. VAN EEKELEN, J.R.W. GLAUERT, J.R KENNAWAY, M.J. PLASMEIJER and M.R. SLEEP, Term graph rewriting, Proc. PARLE'87 Conference II, LNCS 259, 141-158, (Springer-Verlag 1987).

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H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W. Glauert, J.R. Kennaway, M.J. Plasmeijer, and M.R. Sleep. Term graph rewriting. In Proceedings of PARLE 87, volume 2, pages 141--158. Springer-Verlag LNCS 259, Eindhoven, The Netherlands, June 1987.

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H. P. Barendregt, M. C. J. D. van Eekelen, J. R. W. Glauert, J. R. Kennaway, M. J. Plasmeijer and M. R. Sleep. Term graph rewriting. In PARLE '87 volume II, number 259 in LNCS, pp. 191--231. Springer Verlag, 1987.

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Henk Barendregt, M. C. J. D. van Eekelen, J. R. W. Glauert, J. R. Kennaway, M. J. Plasmeijer, and M. R. Sleep. Term graph rewriting. In Proceedings of the European Workshop on Parallel Architectures and Languages, volume 259 of Lecture Notes in Computer Science, pages 141-158, Berlin, 1987. Springer-Verlag.

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Henk Barendregt, Marko van Eekelen, John Glauert, Richard Kennaway, Rinus Plasmeijer, and Ronan Sleep. Term graph rewriting. In Proc. Parallel Architectures and Languages Europe, volume 259 of Lecture Notes in Computer Science, pages 141-158. Springer-Verlag, 1987.

No context found.

H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W. Glauert, J.R. Kennaway, M.J. Plasmeijer, and M.R. Sleep. Term Graph Rewriting. In J.W. de Bakker, A.J. Nijman, and P.C. Treleaven, editors, Proc. of 2nd Conference on Parallel Architectures and Languages Europe, PARLE'87, LNCS 259:141-158, Springer-Verlag, Berlin, 1987.

No context found.

H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W. Glauert, J.R. Kennaway, M.J. Plasmeijer, and M.R. Sleep. Term graph rewriting. In PARLE, Eindhoven, The Netherlands. LNCS 259, pages 141--158, 1987.

No context found.

Barendregt H.P., van Eekelen M.C.J.D., Glauert J.R.W., Kennaway J.R, Plasmeijer M.J., Sleep M.R., Term Graph Rewriting. in: Proc. PARLE-87, de Bakker, Nijman (eds.), LNCS 259, 141-158, Springer, (1987).

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Hendrik Barendregt, Marko van Eekelen, John Glauert, Richard Kennaway, Rinus Plasmeijer, and Ronan Sleep. Term graph rewriting. In Proc. Parallel Architectures and Languages Europe, volume 259 of Lecture Notes in Computer Science, pages 141--158. Springer-Verlag, 1987.

No context found.

H.P. Barendregt, M.C.J.D. van Eekelen, J.R.W. Glauert, J.R. Kennaway, M.J. Plasmeijer, and M.R. Sleep. Term Graph Rewriting. In Proc. Parallel Architectures and Languages Europe (PARLE'87), pp. 141--158. Springer LNCS 259, 1987.

No context found.

H. P. Barendregt, M. C. J. D. Van Eekelen, J. R. W. Glauert, J. R. Kennaway, M. J. Plasmeijer, and M. R. Sleep. Term Graph Rewriting. In Parallel Architectures and Languages Europe, number 259 in Lecture Notes in Computer Science, pages 141-158. Springer-Verlag, 1987.

No context found.

Barendregt,H.P., Eekelen, M.C.J.D., Glauert, J.R.W.J., Kennaway, R., Plasmeijer, M.J. and Sleep, M.R. (1987) Term graph rewriting, in PARLE87, Eindhoven, The Netherlands, 15--19 June, Lecture Notes in Computer Science 259, Springer-Verlag, Berlin, pp. 141--58.

No context found.

Hendrik Barendregt, Marko van Eekelen, John Glauert, Richard Kennaway, Rinus Plasmeijer, and Ronan Sleep. Term graph rewriting. In Proc. Parallel Architectures and Languages Europe, volume 259 of Lecture Notes in Computer Science, pages 141{ 158. Springer-Verlag, 1987.

No context found.

H. P. Barendregt, M. C. J. D. Van Eekelen, J. R. W. Glauert, J. R. Kennaway, M. J. Plasmeijer, and M. R. Sleep. Term Graph Rewriting. In Proc. of PARLE '87, number 259 in Lecture Notes in Computer Science, pages 141158. SpringerVerlag, 1987.

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