A Modal Logic for Termgraph Rewriting

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs allow one to describe classical data-structures (possibly with pointers) such as doubly-linked lists, circular lists etc. We show how the proposed logic can faithfully describe (i) termgraphs as well as (ii) the application of a termgraph rewrite rule (i.e. matching and replacement) and (iii) the computation of normal forms with respect to a given rewrite system. We also show how the proposed logic, which is more expressive than propositional dynamic logic, can be used to specify shapes of classical data-structures (e.g. binary trees, circular lists etc.)

On a Dynamic Logic for Graph Rewriting

International audienceInitially introduced by P. Balbiani, R. Echahed and A.Herzig, this dynamic logic is useful to talk about properties on termgraphs and to characterize transformations on these graphs. Also are presented the deterministic labelled graphs for which the logical framework is designed. This logic has been the starting point of a formal development, using the Coq proof assistant, to design a logical and algorithmic framework useful for verifyin and proving graph rewriting. The formalization allowed us to figure out some ambiguities in the involved concepts. This formalization is not the topic here but the clear view brought to us by the formal work, so the results will be expressed using the original mathematical objects of this logic. Some problems of this logic are demonstrated, relatively to the representation of graph rewriting. Some are minor issues but some are far more important for the adequation between the formulas about graph rewriting and the actual rewriting systems. Invalidating some resulting propositions, solutions are given to reestablish the logical characterization of graph rewriting, which was the initial purpose

Higher-order port-graph rewriting

The biologically inspired framework of port-graphs has been successfully used to specify complex systems. It is the basis of the PORGY modelling tool. To facilitate the specification of proof normalisation procedures via graph rewriting, in this paper we add higher-order features to the original port-graph syntax, along with a generalised notion of graph morphism. We provide a matching algorithm which enables to implement higher-order port-graph rewriting in PORGY, thus one can visually study the dynamics of the systems modelled. We illustrate the expressive power of higher-order port-graphs with examples taken from proof-net reduction systems.Comment: In Proceedings LINEARITY 2012, arXiv:1211.348

Structure and Properties of Traces for Functional Programs

The tracer Hat records in a detailed trace the computation of a program written in the lazy functional language Haskell. The trace can then be viewed in various ways to support program comprehension and debugging. The trace was named the augmented redex trail. Its structure was inspired by standard graph rewriting implementations of functional languages. Here we describe a model of the trace that captures its essential properties and allows formal reasoning. The trace is a graph constructed by graph rewriting but goes beyond simple term graphs. Although the trace is a graph whose structure is independent of any rewriting strategy, we define the trace inductively, thus giving us a powerful method for proving its properties

In-place Graph Rewriting with Interaction Nets

An algorithm is in-place, or runs in-situ, when it does not need any additional memory to execute beyond a small constant amount. There are many algorithms that are efficient because of this feature, therefore it is an important aspect of an algorithm. In most programming languages, it is not obvious when an algorithm can run in-place, and moreover it is often not clear that the implementation respects that idea. In this paper we study interaction nets as a formalism where we can see directly, visually, that an algorithm is in-place, and moreover the implementation will respect that it is in-place. Not all algorithms can run in-place however. We can nevertheless still use the same language, but now we can annotate parts of the algorithm that can run in-place. We suggest an annotation for rules, and give an algorithm to find this automatically through analysis of the interaction rules.Comment: In Proceedings TERMGRAPH 2016, arXiv:1609.0301

Nested Term Graphs (Work In Progress)

We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent the nested scope structure of a higher-order term by a nested structure of term graphs. Based on a signature that is partitioned into atomic and nested function symbols, we define nested term graphs both in a functional representation, as tree-like recursive graph specifications that associate nested symbols with usual term graphs, and in a structural representation, as enriched term graph structures. These definitions induce corresponding notions of bisimulation between nested term graphs. Our main result states that nested term graphs can be implemented faithfully by first-order term graphs. keywords: higher-order term graphs, context-free grammars, cyclic lambda-terms, higher-order rewrite systemsComment: In Proceedings TERMGRAPH 2014, arXiv:1505.0681

Implementation of a Port-graph Model for Finance

In this paper we examine the process involved in the design and implementation of a port-graph model to be used for the analysis of an agent-based rational negligence model. Rational negligence describes the phenomenon that occurred during the financial crisis of 2008 whereby investors chose to trade asset-backed securities without performing independent evaluations of the underlying assets. This has contributed to motivating the search for more effective and transparent tools in the modelling of the capital markets. This paper shall contain the details of a proposal for the use of a visual declarative language, based on strategic port-graph rewriting, as a visual modelling tool to analyse an asset-backed securitisation market.Comment: In Proceedings TERMGRAPH 2018, arXiv:1902.0151

Ten virtues of structured graphs

This paper extends the invited talk by the first author about the virtues of structured graphs. The motivation behind the talk and this paper relies on our experience on the development of ADR, a formal approach for the design of styleconformant, reconfigurable software systems. ADR is based on hierarchical graphs with interfaces and it has been conceived in the attempt of reconciling software architectures and process calculi by means of graphical methods. We have tried to write an ADR agnostic paper where we raise some drawbacks of flat, unstructured graphs for the design and analysis of software systems and we argue that hierarchical, structured graphs can alleviate such drawbacks

Cellular Automata are Generic

Any algorithm (in the sense of Gurevich's abstract-state-machine axiomatization of classical algorithms) operating over any arbitrary unordered domain can be simulated by a dynamic cellular automaton, that is, by a pattern-directed cellular automaton with unconstrained topology and with the power to create new cells. The advantage is that the latter is closer to physical reality. The overhead of our simulation is quadratic.Comment: In Proceedings DCM 2014, arXiv:1504.0192

PORGY: Strategy-Driven Interactive Transformation of Graphs

This paper investigates the use of graph rewriting systems as a modelling tool, and advocates the embedding of such systems in an interactive environment. One important application domain is the modelling of biochemical systems, where states are represented by port graphs and the dynamics is driven by rules and strategies. A graph rewriting tool's capability to interactively explore the features of the rewriting system provides useful insights into possible behaviours of the model and its properties. We describe PORGY, a visual and interactive tool we have developed to model complex systems using port graphs and port graph rewrite rules guided by strategies, and to navigate in the derivation history. We demonstrate via examples some functionalities provided by PORGY.Comment: In Proceedings TERMGRAPH 2011, arXiv:1102.226