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

Iterators and interaction

Eigth International Workshop on Computing with Terms and Graphs (TERMGRAPH’09), 2009We propose a method for encoding iterators (and recursion operators in general) using interaction nets. There are two main applications for this: the method can be used to obtain a visual notation for functional programs, in a visual programming system; and it can be used to extend the existing translations of the λ-calculus into interaction nets (that have been proposed as efficient implementation mechanisms) to languages with recursive types. This work can also be seen as a study of the relation between interaction net programming and functional programming

A Type-Directed Negation Elimination

In the modal mu-calculus, a formula is well-formed if each recursive variable occurs underneath an even number of negations. By means of De Morgan's laws, it is easy to transform any well-formed formula into an equivalent formula without negations -- its negation normal form. Moreover, if the formula is of size n, its negation normal form of is of the same size O(n). The full modal mu-calculus and the negation normal form fragment are thus equally expressive and concise. In this paper we extend this result to the higher-order modal fixed point logic (HFL), an extension of the modal mu-calculus with higher-order recursive predicate transformers. We present a procedure that converts a formula into an equivalent formula without negations of quadratic size in the worst case and of linear size when the number of variables of the formula is fixed.Comment: In Proceedings FICS 2015, arXiv:1509.0282

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

A lightweight abstract machine for interaction nets

We present a new abstract machine for interaction nets and demonstrate that an implementation based on the ideas is significantly more efficient than existing interaction net evaluators. The machine, which is founded on a chemical abstract machine formulation of interaction nets, is a simplification of a previous abstract machine for interaction nets. This machine, together with an implementation, is at the heart of current work on using interaction nets as a new foundation as an intermediate language for compiler technology

Aggregation of student answers in a classroom setting

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 51-52).In a typical class, an instructor does not have enough time to poll all students for answers to questions, although it would be the best method for discovering students' misconceptions. The aggregator module of a system called Classroom Learning Partner provides a solution to this problem by collecting answers students wirelessly submit on tablet PCs and placing them in clusters, which then are displayed to the instructor in histogram form. The student answers are compared, via syntactic parsing and similarity measures, to each other and to instructor-provided example answers to form clusters, which represent student misconceptions. In tests, the aggregator module consistently created relevant clusters, very similar to those created by humans working with the same data. Classroom Learning Partner, including the aggregator module, has been deployed successfully in an MIT introductory computer science class.by Amanda C. Smith.M.Eng

Token-passing nets for functional languages

Proceedings of the 7th International Workshop on Reduction Strategies in Rewriting and Programming (WRS 2007)Token-passing nets were proposed by Sinot as a simple mechanism for encoding evaluation strategies for the λ-calculus in interaction nets. This work extends token-passing nets to cover a typed functional language equipped with structured types and unrestricted recursion. The resulting interaction system is derived systematically from the chosen big-step operational semantics. Along the way, we actually characterize and discuss several design decisions of token-passing nets and extend them in order to achieve simpler interaction net systems with a higher degree of embedded parallelism.Fundação para a Ciência e a Tecnologia (FCT