The Pullback-Pushout Approach to Algebraic Graph Transformation

Corradini, Andrea; Duval, Dominique; Echahed, Rachid; Prost, Frédéric; Ribeiro, Leila

doi:10.1007/978-3-319-61470-0_1

Cited by 6 publications

(14 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Particularly, the object D in Definition 1 could be constructed following different algebraic methods such as DPO [18] or SqPO [10]. Extension to recent approaches such as AGREE [8] or PBPO [9] is rather straightforward. This opens the possibility to integrate, in one parallel step, rules written in different approaches.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

Parallel Coherent Graph Transformations

Tour

Echahed

2021

Recent Trends in Algebraic Development Techniques

Self Cite

View full text Add to dashboard Cite

Cellular automata as well as simultaneous assignments in Python can be understood as the parallel application of local rules to a grid or an environment that can be easily represented as an attributed graph. Since the result of such transformations cannot generally be obtained by a sequential application of the involved rules, this situation infringes the standard notion of parallel independence. An algebraic approach with production rules of the form L Ð K Ð I Ñ R is adopted and a condition of parallel coherence more general than parallel independence is formulated, that enable the definition of the Parallel Coherent Transformation (PCT). This transformation supports a generalisation of the Parallelism Theorem in the theory of adhesive HLR categories, showing that the PCT yields the expected result of sequential rewriting steps when parallel independence holds. Categories of finitely attributed structures are proposed, in which PCTs are guaranteed to exist. These notions are introduced and illustrated on several detailed examples.

show abstract

Section: Conclusion and Related Workmentioning

confidence: 99%

Parallel Coherent Graph Transformations

Tour

Echahed

2021

Recent Trends in Algebraic Development Techniques

Self Cite

View full text Add to dashboard Cite

show abstract

“…More general port graph rewrite rules that include bridge ports with connections 1 to n and wire ports in the arrow node are more permissive, but then rewriting steps do not correspond directly to the SPO construction. We leave for future work the definition of a semantics handling these more permissive rules, with general user-defined conditions, following more general approaches such as the Span-categories of Löwe (2010), the Pullback-Pushout approach of Corradini et al (2017), or the symbolic attributed graphs of Orejas and Lambers (2010).…”

Section: Attributed Port Graph Rewriting and Spo Approach To Graph Trmentioning

confidence: 99%

“…To formally define the transformation (i.e., rewriting) relation generated by the rules, it is necessary to give a formal semantics for rules and for their application. The most well-known approaches are algebraic (that is, based on an algebraic construction, as in the double pushout (Ehrig et al 1973), SPO (Kennaway 1987;Löwe 1993;Raoult 1984) or pullback-pushout (Corradini et al 2017) semantics) or algorithmic (that is, the application of rules is described as a sequence of atomic operations, as we have done in this paper). Although algorithmic, our rewriting semantics follows the SPO approach, as shown in Section 2.4.…”

Section: Related Workmentioning

confidence: 99%

Strategic port graph rewriting: an interactive modelling framework

Fernández

Kirchner

Pinaud

2018

Math. Struct. Comp. Sci.

View full text Add to dashboard Cite

Abstract. We present strategic port graph rewriting as a basis for the implementation of visual modelling tools. The goal is to facilitate the specification and programming tasks associated with the modelling of complex systems. A system is represented by an initial graph and a collection of graph rewrite rules, together with a user-defined strategy to control the application of rules. The traditional operators found in strategy languages for term rewriting have been adapted to deal with the more general setting of graph rewriting, and some new constructs have been included in the strategy language to deal with graph traversal and management of rewriting positions in the graph. We give a formal semantics for the language, and describe its implementation: the graph transformation and visualisation tool Porgy.

show abstract

“…Readers familiar with algebraic approaches to graph transformation may recognize the cloning flexibility provided by the recent PBPO (pullback-pushout) approach of [10]. The parameters of the clone action reflect somehow the typing morphisms of [10]. Cloning a node according to the approach of Sesquipushout If α = addC(i, c) then:…”

Section: Definition 2 (Elementary Action Actionmentioning

confidence: 99%

On the Verification of Logically Decorated Graph Transformations

Brenas,

Echahed,

Strecker

2018

Preprint

Self Cite

View full text Add to dashboard Cite

We address the problem of reasoning on graph transformations featuring actions such as addition and deletion of nodes and edges, node merging and cloning, node or edge labelling and edge redirection. First, we introduce the considered graph rewrite systems which are parameterized by a given logic L. Formulas of L are used to label graph nodes and edges. In a second step, we tackle the problem of formal verification of the considered rewrite systems by using a Hoare-like weakest precondition calculus. It acts on triples of the form {Pre}(R, strategy){Post} where Pre and Post are conditions specified in the given logic L, R is a graph rewrite system and strategy is an expression stating how rules in R are to be performed. We prove that the calculus we introduce is sound. Moreover, we show how the proposed framework can be instantiated successfully with different logics. We investigate first-order logic and several of its decidable fragments with a particular focus on different dialects of description logic (DL). We also show, by using bisimulation relations, that some DL fragments cannot be used due to their lack of expressive power.

show abstract

The Pullback-Pushout Approach to Algebraic Graph Transformation

Cited by 6 publications

References 20 publications

Parallel Coherent Graph Transformations

Parallel Coherent Graph Transformations

Strategic port graph rewriting: an interactive modelling framework

On the Verification of Logically Decorated Graph Transformations

Contact Info

Product

Resources

About