Interaction Nets Research Articles

Identifying Treatment Responders to Varenicline for Alcohol Use Disorder Using Two Machine-Learning Approaches

Varenicline has shown promise for treating alcohol use disorder (AUD); however, not everyone will respond to varenicline. Machine-learning methods are well suited to identify treatment responders. In the present study, we examined data from the National Institute on Alcohol Abuse and Alcoholism Clinical Intervention Group multisite clinical trial of varenicline using two machine-learning methods. Baseline characteristics taken from a randomized clinical trial of varenicline were examined as potential moderators of treatment response using qualitative interaction trees ( N = 199) and group least absolute shrinkage and selection operator interaction nets ( N = 200). Results align with prior research, highlighting smoking status, AUD severity, medication adherence, and drinking goal as predictors of treatment response. Novel findings included the interaction between age and cardiovascular health in predicting clinical response and stronger medication effects among individuals with lower craving. With increased integration of machine-learning methods, studies that effectively integrate methods and medication development have high potential to inform clinical practice.

Proceedings Tenth International Workshop on Computing with Terms and Graphs

This volume contains a selection of the papers presented at TERMGRAPH 2018, the tenth edition of the international workshop on computing with terms and graphs. Graphs, and graph transformation systems, are used in many areas within Computer Science: to represent data structures and algorithms, to define computation models, as a general modelling tool to study complex systems, etc. Research in this area addresses a range of theoretical and practical issues, including the modelling of first- and higher-order term rewriting by (acyclic or cyclic) graph rewriting, graphical frameworks such as interaction nets and sharing graphs (optimal reduction), rewrite calculi for the analysis of functional programs, graph reduction implementations of programming languages, graphical calculi modelling concurrent and mobile computations, object-oriented systems, graphs as a model of biological or chemical systems, and automated reasoning and symbolic computation systems working on shared structures. Previous editions of TERMGRAPH took place in Barcelona (2002), Rome (2004), Vienna (2006), Braga (2007), York (2009), Saarbrucken (2011), Rome (2013), Vienna (2014) and Eindhoven (2016). TERMGRAPH 2018 is affiliated with FSCD, which is part of FLOC.

Reduction Strategies for Program Extraction

We introduce Pure Type Systems with Pairs generalising earlier work on program extraction in Typed Lambda Calculus. We model the process of program extraction in these systems by means of a reduction relation called o-reduction, and give strategies for Bo-reduction which will be useful for an implementation of a proof assistant. More precisely, we give an algorithm to compute theo-normal form of a term in Pure Type System with Pairs, and show that this defines a prejection from Pure Type Systems with Pairs to standart Pure Type Systems. This result shows that o-reduction is an operational description of aprgram extraction that is independent of the particular Typed Lambda Calculus specified as a Pure Typoe System. For B-reduction, we define weak and strong reduction strategies using Interaction Nets, generalising well-know efficient strategies for the l-calculus to the general setting of Pure Type Systems.

A novel pseudo-centrosymmetric P[dbnd]O⋯H[sbnd]O[sbnd]H⋯O[dbnd]P synthon in crystal structures of azaheterocyclic phosphonates

Crystals of novel azaheterocyclic phosphonates were characterized by the X-ray diffraction analysis supplemented by detailed calculations on interactions stabilizing the molecular assemblies. Intermolecular energies were evaluated using CrystalExplorer CE-B3LYP method. Additionally, fingerprint plots derived from Hirshfeld surfaces were generated for each structure to characterize the crystal packing arrangement in detail. Supramolecular systems formed by investigated compounds may be conveniently described as molecular saw tooth ribbons linked by the pseudo-centrosymmetric PO⋯HOH⋯OP synthon which for the first time was introduced in this paper. Water molecules are disordered around inversion center over four positions and encapsulated by ethoxy and phosphoryl groups. The resulting pockets are connected by narrow linkers and form tunnels with periodically changing diameter. Therefore, the most likely water molecules enter the crystal during crystallization. Their further transport is limited by the tight channel aperture. Topology of intermolecular interactions as represented by energy frameworks showed similarity of interaction nets in all systems. The TG/DTG and DSC analyses indicate that thermal stability of investigated crystals is closely related to their packing behavior which is not disturbed by associated water molecules.

Shapely monads and analytic functors

In this paper, we give precise mathematical form to the idea of a structure whose data and axioms are faithfully represented by a graphical calculus; some prominent examples are operads, polycategories, properads, and PROPs. Building on the established presentation of such structures as algebras for monads on presheaf categories, we describe a characteristic property of the associated monads---the shapeliness of the title---which says that “any two operations of the same shape agree”. An important part of this work is the study of analytic functors between presheaf categories, which are a common generalisation of Joyal's analytic endofunctors on sets and of the parametric right adjoint functors on presheaf categories introduced by Diers and studied by Carboni--Johnstone, Leinster and Weber. Our shapely monads will be found among the analytic endofunctors, and may be characterised as the submonads of a universal analytic monad with “exactly one operation of each shape”. In fact, shapeliness also gives a way to define the data and axioms of a structure directly from its graphical calculus, by generating a free shapely monad on the basic operations of the calculus. In this paper we do this for some of the examples listed above; in future work, we intend to do so for graphical calculi such as Milner's bigraphs, Lafont's interaction nets, or Girard's multiplicative proof nets, thereby obtaining canonical notions of denotational model.

Proof Diagrams for Multiplicative Linear Logic

The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof in sequent calculus. In this paper we give an interpretation of proof nets in the syntax of string diagrams. Even though we lose standard proof equivalence, our construction allows to define a framework where soundness and well-typeness of a diagram can be verified in linear time.

The true concurrency of differential interaction nets

We analyse the reduction of differential interaction nets from the point of view of so-called ‘true concurrency,’ that is, employing a non-interleaving model of parallelism. More precisely, we associate with each differential interaction net an event structure describing its reduction. We show how differential interaction nets are only able to generate confusion-free event structures, and we argue that this is a serious limitation in terms of the concurrent behaviours they may express. In fact, confusion is an extremely elementary phenomenon in concurrency (for example, it already appears in CCS with just prefixing and parallel composition) and we show how its presence is preserved by any encoding respecting the degree of distribution and the reduction semantics. We thus infer that no reasonably expressive process calculus may be satisfactorily encoded in differential interaction nets. We conclude with an analysis of one such encoding proposed by Ehrhard and Laurent, and argue that it does not contradict our claims, but rather supports them.

Token-passing Optimal Reduction with Embedded Read-back

We introduce a new interaction net implementation of optimal reduction for the pure untyped lambda calculus. Unlike others, our implementation allows to reach normal form regardless of the interaction net reduction strategy using the approach of so-called token-passing nets and a non-deterministic extension for interaction nets. Another new feature is the read-back mechanism implemented without leaving the formalism of interaction nets.

Compiling Process Networks to Interaction Nets

Kahn process networks are a model of computation based on a collection of sequential, deterministic processes that communicate by sending messages through unbounded channels. They are well suited for modelling stream-based computations, but are in no way restricted to this application. Interaction nets are graph rewriting systems that have many interesting properties for implementation. In this paper we show how to encode process networks using interaction nets, where we model both networks and messages in the same framework.

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.

An Implementation Model for Interaction Nets

To study implementations and optimisations of interaction net systems we propose a calculus to allow us to reason about nets, a concrete data-structure that is in close correspondence with the calculus, and a low-level language to create and manipulate this data structure. These work together so that we can describe the compilation process for interaction nets, reason about the behaviours of the implementation, and study the efficiency and properties.

A Simple Parallel Implementation of Interaction Nets in Haskell

Due to their "inherent parallelism", interaction nets have since their introduction been considered as an attractive implementation mechanism for functional programming. We show that a simple highly-concurrent implementation in Haskell can achieve promising speed-ups on multiple cores.

Towards a GPU-based implementation of interaction nets

We present ingpu, a GPU-based evaluator for interaction nets that heavily utilizes their potential for parallel evaluation. We discuss advantages and challenges of the ongoing implementation of ingpu and compare its performance to existing interaction nets evaluators.

Bigraphical Nets

Interaction nets are a graphical model of computation, which has been used to define efficient evaluators for functional calculi, and specifically lambda calculi with patterns. However, the flat structure of interaction nets forces pattern matching and functional behaviour to be encoded at the same level, losing some potential parallelism. In this paper, we introduce bigraphical nets, or binets for short, as a generalisation of interaction nets using ideas from bigraphs and port graphs, and we present a formal notation and operational semantics for binets. We illustrate their expressive power by examples of applications.

Extending the Interaction Nets Calculus by Generic Rules

We extend the textual calculus for interaction nets by generic rules and propose constraints to preserve uniform confluence. Furthermore, we discuss the implementation of generic rules in the language inets, which is based on the lightweight interaction nets calculus.

Behavior Alignment and Control Flow Verification of Process and Service Choreographies

The representation of process and service choreographies has been recog- nized as an important requirement in service-oriented methodologies. The guarantee of alignment between process and service choreographies and the verification of the behavior of choreographies represent an important improvement for such methodolo- gies, since they enable the automatic generation of choreography service specifications from well-defined choreography process models. To deal with these issues, we propose a transformation pattern that guarantees behavior alignment between process and ser- vice choreographies, and a verification method for the control flow of choreographies, which can be applied to any choreography language. These approaches make use of the Global Interaction Nets (GI-Nets) language to formalize the behavior of process and service choreographies. This formal representation can then be used to conclude on the behavioral aspects of choreographies. In addition, we present a tool for the modeling, automatic generation and verification of GI-Nets, and apply the proposed approaches to the UP-ColBPIP and WS-CDL choreography languages.

Structured Operational Semantics for Graph Rewriting

Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in general. Hence, the goal of this article is to obtain a compositional semantics for graph transformation system in analogy to the structural operational semantics (SOS) for Milner's Calculus of Communicating Systems (CCS). The paper introduces an SOS style axiomatization of the standard labelled transition semantics for graph transformation systems. The first result is its equivalence with the so-called Borrowed Context technique. Unfortunately, the axiomatization is not compositional in the expected manner as no rule captures "internal" communication of sub-systems. The main result states that such a rule is derivable if the given graph transformation system enjoys a certain property, which we call "complementarity of actions". Archetypal examples of such systems are interaction nets. We also discuss problems that arise if "complementarity of actions" is violated.

A new graphical calculus of proofs

We offer a simple graphical representation for proofs of intuitionistic logic, which is inspired by proof nets and interaction nets (two formalisms originating in linear logic). This graphical calculus of proofs inherits good features from each, but is not constrained by them. By the Curry-Howard isomorphism, the representation applies equally to the lambda calculus, offering an alternative diagrammatic representation of functional computations.

Intuitionistic differential nets and lambda-calculus

We define pure intuitionistic differential proof nets, extending Ehrhard and Regnier’s differential interaction nets with the exponential box of Linear Logic. Normalization of the exponential reduction and confluence of the full one is proved. These results are directed and adjusted to give a translation of Boudol’s untyped λ-calculus with resources extended with a linear–nonlinear reduction à la Ehrhard and Regnier’s differential λ-calculus. Such reduction comes in two flavours: baby-step and giant-step β-reduction. The translation, based on Girard’s encoding A→B∼!A⊸B and as such extending the usual one for λ-calculus into proof nets, enjoys bisimulation for giant-step β-reduction. From this result we also derive confluence of both reductions.

An Explicit Framework for Interaction Nets

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on elementary properties of graph theory. We give here a more explicit presentation based on notions borrowed from Girard's Geometry of Interaction: interaction nets are presented as partial permutations and a composition of nets, the gluing, is derived from the execution formula. We then define contexts and reduction as the context closure of rules. We prove strong confluence of the reduction within our framework and show how interaction nets can be viewed as the quotient of some generalized proof-nets.