We address the problem of cyclic termgraph rewriting. We propose a new framework where rewrite rules are tuples of the form (L,R, τ, σ) such that L and R are termgraphs representing the left-hand and the right-hand sides of the rule, τ is a mapping from the nodes of L to those of R and σ is a partial function from nodes of R to nodes of L. τ describes how incident edges of the nodes in L are co...

In a recent paper, mimicking Winskel's construction for Petri nets, a concurrent semantics for (double-pushout) DPO graph grammars has been provided by showing that each graph grammar can be unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. This paper faces the problem of p...

Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs / transformations and formulas / proof terms. With linear implication representing ru...

This paper introduces a formal approach to the specification of constraint-aware model transformation which is suitable for language translation. The proposed approach extends graph transformations with the ability to specify and transform constraints by transformation rules. In particular, it uses non-deleting rules which are typed over the metamodel of a joined language which is constructed f...

The graph-manipulating core of the general term graph rewriting language DACTL, namely contraction building and redirection, is reexamined from a categorical viewpoint. The essentials of this rather complex two-phase operational semantics is recast as a Grothendieck opfibration of a category of graph rewrites over a base of rewrite rules. This generalises previous attempts to categorise contrac...

This paper deals with model transformations based on attributed graphs transformation. Our approach is based on the categorical approach called Single Pushout. The principal goal being to strengthen the attribute computation part, we generalize our earlier approach based on the use of typed lambda-terms with inductive types and recursion to represent attributes and computation functions. The ge...

The dynamics of process calculi, e.g. CCS, have often been defined using a labelled transition system (LTS). More recently it has become common when defining dynamics to use reaction rules —i.e. unlabelled transition rules— together with a structural congruence. This form, which I call a reactive system, is highly expressive but is limited in an important way: LTSs lead more naturally to operat...

We tackle the problem of data-structure rewriting including global and local pointer redirections. Eachbasic rewrite step may perform three kinds of actions: (i) Local redirection, the aim of which is to redirectspecific pointers determined by means of a pattern ; (ii) Replacement, that may add new information todata-structures ; (iii) Global redirection, which is aimed at redirecti...

Several applications of graph rewriting systems (notably, some encodings of calculi with name passing) require rules which, besides deleting and generating graph items, are able to coalesce some parts of the graph. This latter feature forbids the development of a satisfactory concurrent semantics for rewrites (intended as a partial order description of the steps in a computation). This paper pr...