Reasoning about modular datatypes with Mendler induction

In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof assistants that are based on type theory, like Coq. The reason is that it involves type definitions, such as those of type-level fixpoint operators, that are not strictly positive. The known work-around of impredicative encodings is problematic, insofar as it impedes conventional inductive reasoning. Weak induction principles can be used instead, but they considerably complicate proofs. This paper proposes a novel and simpler technique to reason inductively about impredicative encodings, based on Mendler-style induction. This technique involves dispensing with dependent induction, ensuring that datatypes can be lifted to predicates and relying on relational formulations. A case study on proving subject reduction for structural operational semantics illustrates that the approach enables modular proofs, and that these proofs are essentially similar to conventional ones.Comment: In Proceedings FICS 2015, arXiv:1509.0282

Model-based Simulation of VoIP Network Reconfigurations using Graph Transformation Systems

We address the modelling and validation of P2P networks with special attention for problems related to VoIP services, focusing particularly on Skype. We use generalised stochastic graph transformation systems and associated stochastic simulation techniques based on generalised semi- Markov processes

Stochastic Graph Transformation with Regions

Graph transformation can be used to implement stochastic simulation of dynamic systems based on semi-Markov processes, extending the standard approach based on Markov chains. The result is a discrete event system, where states are graphs, and events are rule matches associated to general distributions, rather than just exponential ones. We present an extension of this model, by introducing a hierarchical notion of event location, allowing for stochastic dependence of higher-level events on lower-level ones

Domain-specific discrete event modelling and simulation using graph transformation

The final publication is available at Springer via http://dx.doi.org/10.1007/s10270-012-0242-3Graph transformation is being increasingly used to express the semantics of domain-specific visual languages since its graphical nature makes rules intuitive. However, many application domains require an explicit handling of time to accurately represent the behaviour of a real system and to obtain useful simulation metrics to measure throughputs, utilization times and average delays. Inspired by the vast knowledge and experience accumulated by the discrete event simulation community, we propose a novel way of adding explicit time to graph transformation rules. In particular, we take the event scheduling discrete simulation world view and provide rules with the ability to schedule the occurrence of other rules in the future. Hence, our work combines standard, efficient techniques for discrete event simulation (based on the handling of a future event set) and the intuitive, visual nature of graph transformation. Moreover, we show how our formalism can be used to give semantics to other timed approaches and provide an implementation on top of the rewriting logic system Maude.Work partially sponsored by the Spanish Ministry, under project “Go Lite” (TIN2011-24139) as well as by the R&D programme of the Community of Madrid, project “e-Madrid” (S2009/TIC-1650). We are grateful to the anonymous reviewers, which helped in improving previous versions of the paper

Resource-Bound Quantification for Graph Transformation

Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems

Towards an embedding of Graph Transformation in Intuitionistic Linear Logic

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 and transformations on one hand, formulas and proof terms on the other. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs and transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties

Morphological and molecular characterization of a Steinernema carpocapsae (Nematoda Steinernematidae) strain isolated in Veneto region (Italy)

Veneto region (North-East Italy). This new strain was named ItS-CAO1. Molecular and morphological analyses were performed. The ITS region and the 18S rRNA gene were amplified and sequenced. The ITS products were then digested with six restriction enzymes in order to unequivocally identify this species. Nematode virulence was tested against last instar of Galleria mellonella (L.) using different laboratory assays. Insect mortality of this new strain is very high in penetration (100%) and sand column assay (93.3%) and the percentage of penetrating infective juveniles was 57.6 and 42.9, respectively. Larval mortality in one-on-one quality assay was 50% and in exposure time assay it was 50% at 19 minutes. With the results of infectivity assays we can evaluate the possibility to use this new strain in biological control programs

Oscheius tipulae in Italy: Evidence of an Alien Isolate in the Integral Natural Reserve of Montecristo Island (Tuscany)

Montecristo Island is an integral natural reserve of the Tuscan Archipelago National Park (Central Italy), characterized by a peculiar assemblage of flora and fauna, with several endemic taxa, and also with a high number of alien species. During a soil survey, we found an alien Oscheius tipulae Lam &Webster, 1971 isolate, phylogenetically close to others from South America. In this article, we examined the possible pathways of introduction of this nematode. Because of the high number of alien plants in this protected area and the low desiccation survival ability of O. tipulae, we hypothesized that the presence of this alien nematode isolate may be related to the soil of introduced plants, although historical association with plant-associated invertebrates is also possible. Further studies with more populations and marker molecules are necessary to investigate the distribution of O. tipulae and the possible impact on this natural reserve