J.R. KENNAWAY, On 'On graph rewritings', Th. Comp. Sci., 52, 37-58, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....graph G consisting of a single node which is the only root, i.e. G I R I G . Another example of reduction of a circular redex is the rewriting G 3 R2 G 4 at the end of Section 1. It is worth mentioning that other definitions of term graph rewriting agree with ours on circular redexes (see [1, 12, 34, 40] 7 ) and that many authors already discussed the disagreement of various definitions of rewriting in the handling of circular redexes. In our opinion, this disagreement is due to the operational nature of most definitions, which leaves some degree of freedom in the handling of pathological ....

J.R. Kennaway. On `On Graph Rewritings'. Theoret. Comput. Sci., 52:37--58, 1980.

....0;1 (ff(R I ) tr 1 0;1 (r 1 (I Omega id 1 ) tr 1 0;1 (r 1 ) 1 0, which goes from the arrow representing the I loop to that representing . It is worth mentioning that other definitions of term graph rewriting proposed in the literature agree with ours on circular redexes (see [17, 1, 6] 4 ) and that many authors already discussed the disagreement of various definitions of term graph rewriting in the handling of circular redexes. However, to our knowledge it is the first time that the correctness of the proposed construction is verified against a more declarative, categorical ....

J.R. Kennaway. On `On Graph Rewritings'. Theoret. Comput. Sci., 52:37--58, 1980.

....compared with our rewritings of relational (labeled) graph. Moreover a more general sufficient condition for two rewritings to commute and a theorem concerning critical pairs useful to demonstrate the confluency of graph rewriting systems are also given. 1 Introduction There are many researches [1 7,9,13,14,16 18,20 22] on graph grammars and graph rewritings which have a lot of applications including software specification, data bases, analysis of concurrent systems, developmental biology and many others. In these one of the advantages of categorical graph rewritings is to produce a universal reduction which ....

....the semantics of rewriting rules. Gluing conditions are investigated by Ehrig and Kreowski [4] and Kawahara [9] Using single pushouts and regarding production rules as partial functions preserving graph structures, another framework of graph rewritings were formalized by Raoult [22] and Kennaway [13]. Recently Ehrig and Lowe [3, 16, 18] studied rewritings based on single pushouts in Sig algebras and proved pushout completeness for restricted signatures with monadic operator symbols only. In this note we treat the category of (simple) graphs (with or without labeled edges) and partial ....

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R. Kennaway, On "On graph rewritings". Theoretical Computer Science 52(1987), 37--58.

....space and time of copying complex data structures. However, since this technique is orthogonal to and at a different level than the concept of reduction strategy, it is not discussed here. The step from reduction semantics to a graph reduction semantics in the spirit of Raoult and Kennaway ([17]) should be small. Obviously a complete reduction strategy does not need to reduce all redexes which are reduced by the po reduction strategy. Many approximations of a subset of needed redexes will spring to the reader s mind. The concept of gaining predicates enables easy proofs of ....

R. Kennaway. On "On graph rewritings". Theoretical Computer Science, 52:37--58, 1987.

....bound variables used relation algebraic notation from the beginning, we have been able to complete the proofs in a way that is still readable and at the same time su#ciently formal to support confidence in the correctness. On the other hand, the algebraic approach to term graph rewriting itself [35, 27, 28, 31, 5] had to be extended, but that is outside the scope of the present article. This paper provides a more gentle introduction to the fundamental rationale behind the relational formalisation of term graphs developed in [21, 22] and goes on to extend this formalisation even more into the relational ....

Richard Kennaway. On "On Graph Rewritings". Theoretical Computer Science, 52:37--58, 1987.

....The existence theorem of pushout complements in a topos including the category of graph was generally proved by Kawahara[7] Lowe and Ehrig[3, 11] also formulated graph rewritings using a single pushout in the category of graphs based on sets and partial functions. Raoult and Kennaway s approach[13, 9] was different from Ehrig s formalization of graph rewritings. The graph structure in [13] is a function from a vertex set V to the set V 3 of finite strings of vertices and Raoult defined graph rewritings by a single pushout square using partial functions. This paper generalizes Raoult s ....

R. Kennaway. On "On graph rewritings". Theoretical Computer Science, 52:37--58, 1987.

....enough to avoid the implementation details of particular machines, and yet concrete enough to serve as an intermediate target language for compilers. Graph rewriting provides one promising area within which to search for such models [43, 32, 15, 41] and colimits seem to be quite useful here [10, 58, 44]. Graph rewriting is also important for the unification grammars that are now popular in linguistics [60, 22] There seem to be many opportunities for further research in these areas. 6.3 Initiality. The simplest possible diagram is the empty diagram. Its colimit is an initial object , which is ....

Richard Kennaway. On `On graph rewritings'. Theoretical Computer Science, 52:37--58, 1987.

....Rewriting R. Banach 7.1 INTRODUCTION In this chapter, we re examine the problem of providing a categorical semantics for the core of the general term graph rewriting language DACTL. Partial success in this area has been obtained by describing graph rewrites as certain kinds of pushout. See [Ken87, HP88, HKP88, Ken91] Nevertheless, none of these constructions successfully describe the whole of the operational models of [BvEG 87] where term graph rewriting was introduced, or of its generalization in the language DACTL itself [GKSS88, GHK 88, GKS91, Ken90] The main stumbling blocks ....

....kinds of pushout. See [Ken87, HP88, HKP88, Ken91] Nevertheless, none of these constructions successfully describe the whole of the operational models of [BvEG 87] where term graph rewriting was introduced, or of its generalization in the language DACTL itself [GKSS88, GHK 88, GKS91, Ken90]. The main stumbling blocks for all of these attempts have been examples such as the I combinator root:I[a] a when applied to a circular instance of itself x:I[x] None of the hitherto proposed categorical formulations of TGR adequately capture the DACTL version of the rewrite (which is, ....

J.R. Kennaway. On "on graph rewritings". Theor. Comput. Sci. 52, pp. 37-58.

....from G to L is usually required to be a monomorphism (i.e. injective) An important result of the double pushout approach is that existence of a pushout complement H is equivalent to the validity of the gluing condition. L . R A . B . Raoult[1984] and Kennaway [1987; 1990] and independently Lowe [1990] developed the approach of the single pushout by moving to the corresponding category of graphs with partial morphisms . The only application condition is that the embedding of the left hand rule side into the application graph is a total morphism; no ....

....with an additional morphism tacked onto the lower left corner was introduced by Ehrig and ParisiPresicce [1991; 1993] under the name of restricting derivations . Parisi Presicce [1993] showed that this approach is strictly more powerful then the single pushout approach. One of the motivations [Kennaway, 1987] for developing the single pushout had already come from the context of algebraic modelling of the graph rewriting language DACTL [Glauert et al. 1990] fiberr.tex; 9 05 1997; 19:27; no v. p.3 4 Wolfram Kahl L R A H B H As a further development of this approach, Banach [1993a; ....

Richard Kennaway. On "On Graph Rewritings". Theoretical Computer Science, 52:37--58, 1987.

....rewriting. Establishing confluence was not altogether trivial since it faced the need for solving the problem of cyclic collapsing terms [Ari92, Ari93, FW91] a g a Y b g Figure 1. Previous definitions of term graph rewriting tend to use one of two ways: 1) categorytheory oriented [Ken87, Ken88, Ken90, Rao84] 2) implementation oriented [PvE93] The first describes graph rewrite steps as push outs in a category, and some papers have been devoted to analyzing whether this can be done by single or double push out constructions [Lo93] The second uses notions like pointers, redirections, ....

J. R. Kennaway. Corrigendum on `on graph rewriting'. Theoretical Computer Science, 61:317--320, 1988.

....environment, so there is an incentive to find a clean formulation for the whole of the semantics. The heart of the problem is the contraction building and redirection phases of a rewrite. Partial success in this area has been obtained by describing graph rewrites as certain kinds of pushout. See Kennaway (1987), Hoffmann and Plump (1988) Habel Kreowski and Plump (1988) and Kennaway (1991) Nevertheless none of these constructions successfully describe the whole of the operational models of Barendregt et al. 1987) where term graph rewriting was introduced, or of its generalisation in the general term ....

...., so by changing the permitted arrows there we can modify the arrows of G(P, Rew) Making the fibers G P into discrete categories effectively gets rid of non trivial f s. However non trivial f s are useful for certain purposes. In Hoffmann and Plump (1988) Habel, Kreowski and Plump (1988) and Kennaway (1987), the desirablity of identifying identical subgraphs of the execution graph is expounded. This is useful for non linear rewrite rules, or for maximal sharing of identical subgraphs to improve execution efficiency. By restricting the arrows of G P to be (maximal) onto rigid homomorphisms we see ....

Kennaway J.R. (1987), On "On Graph Rewritings". Theor. Comput. Sci. 52 37-58.

....[13, 14] for object oriented languages based on asynchronous communication [22, 24, 20, 21] and in logic programming [5, 28] Within the algebraic (or categorical) school the classical double pushout approach (c.f. 9] among many others) has been accompanied by the single pushout approach [31, 25, 26]. We combine the theory [2, 32] and specification [1, 3] of partial algebras with a single pushout approach to graph grammars [26] and apply the results obtained to the specification of conceptual objects as they occur in information system design traditionally employing semantic data models [33, ....

R. Kennaway. On "On graph rewriting". Theoretical Computer Science, 52:37--58, 1987.

....evaluation. Term graph rewriting was first studied by Staples [Sta80] who demonstrated a correspondence with term rewriting, for finitary orthogonal rewrite systems and acyclic graphs. Bar87] extended this by establishing results about normalising strategies. Raoult [Rao84] refined by Kennaway [Ken87], studied the relationship between graph rewriting and term rewriting using a category theoretic description of term graph rewriting. Hoffmann and Plump [Hof88] gave an equivalent description in a different category of graphs. All of the above treatments of the subject considered only acyclic ....

J.R. KENNAWAY, On 'On graph rewritings', Th. Comp. Sci., 52, 37-58, 1987.

....of partial morphisms Richard Kennaway School of Information Systems, University of East Anglia, Norwich NR4 7TJ, U.K. Abstract: We present a definition of term graph rewriting as the taking of a pushout in a category of partial morphisms, adapting the rather ad hoc definitions we gave in [Ken87] so as to use a standard category theoretic concept of partial morphism. This single pushout construction is shown to coincide with the well known double pushout description of graph rewriting whenever the latter is defined. In general, the conditions for the single pushout to exist are weaker ....

....by ESPRIT basic research action no. 3074 (Semagraph) SERC grant no. GR F 91582, and an SERC Advanced Fellowship. 2 diagram of Figure 1, so as to make both squares pushouts. Conditions are imposed on the rule and the occurrence to ensure that this can be done uniquely, up to isomorphism. In [Rao84, Ken87], a definition of graph rewriting is given using a more complicated category of graphs but a simpler definition of rewriting. A rule is a morphism LR, an occurrence of this rule in a graph G is a morphism LG (of a restricted class) and the rewrite is performed by taking the pushout shown in ....

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J.R. Kennaway "On `On graph rewritings"', Th. Comp. Sci. 52, 37--58, 1987.

....evaluation. Term graph rewriting was first studied by Staples [Sta80] who demonstrated a correspondence with term rewriting, for finitary orthogonal rewrite systems and acyclic graphs. Bar87] extended this by establishing results about normalising strategies. Raoult [Rao84] refined by Kennaway [Ken87], studied the relationship between graph rewriting and term rewriting using a category theoretic description of term graph rewriting. Hoffmann and Plump [Hof88] gave an equivalent description in a different category of graphs. All of the above treatments of the subject considered only acyclic ....

J.R. KENNAWAY, On `On graph rewritings', Th. Comp. Sci., 52, 37--58, 1987.

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Richard Kennaway. On "On graph rewritings". Theoretical Computer Science, 52:37--58, 1987.

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Richard Kennaway. On "On graph rewritings". Theoretical Computer Science, 52:37--58, 1987.

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Richard Kennaway. On "On graph rewritings". Theoretical Computer Science, 52:37--58, 1987.

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