Interaction nets: programming language design and implementation

This paper presents a compiler for interaction nets, which, just like term rewriting systems, are user-definable rewrite systems which offer the ability to specify and program. In the same way that the lambda-calculus is the foundation for functional programming, or horn clauses are the foundation for logic programming, we give in this paper an overview of a substantial software system that is currently under development to support interaction based computation, and in particular the compilation of interaction nets

Combining interaction nets with externally defined programs

Many calculi, for instance the lambda-calculus and term rewriting systems, have benefitted from extensions, especially to include data structures and operations which are more naturally defined in another language. A simple example of this is PCF where the lambda-calculus is extended to include natural numbers and some basic functions over this type, which avoids having to use inefficient encodings of numbers. In this paper we present a generalization of interaction nets along these lines. We begin by adding a fixed set of constants and predefined functions, before presenting the main contribution of the paper which is a system of interaction nets combined with an external language where functions and richer data types can be defined

Graph Creation, Visualisation and Transformation

We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting

Strategic programming on graph rewriting systems

We describe a strategy language to control the application of graph rewriting rules, and show how this language can be used to write high-level declarative programs in several application areas. This language is part of a graph-based programming tool built within the port-graph transformation and visualisation environment PORGY.Comment: In Proceedings IWS 2010, arXiv:1012.533

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

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

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.Comment: In Proceedings DCM 2012, arXiv:1403.757

An Implementation of Nested Pattern Matching in Interaction Nets

Reduction rules in interaction nets are constrained to pattern match exactly one argument at a time. Consequently, a programmer has to introduce auxiliary rules to perform more sophisticated matches. In this paper, we describe the design and implementation of a system for interaction nets which allows nested pattern matching on interaction rules. We achieve a system that provides convenient ways to express interaction net programs without defining auxiliary rules

Labelled Lambda-calculi with Explicit Copy and Erase

We present two rewriting systems that define labelled explicit substitution lambda-calculi. Our work is motivated by the close correspondence between Levy's labelled lambda-calculus and paths in proof-nets, which played an important role in the understanding of the Geometry of Interaction. The structure of the labels in Levy's labelled lambda-calculus relates to the multiplicative information of paths; the novelty of our work is that we design labelled explicit substitution calculi that also keep track of exponential information present in call-by-value and call-by-name translations of the lambda-calculus into linear logic proof-nets