Encoding left reduction in the λ-calculus with interaction nets

Encoding Left Reduction in the Lambda-Calculus with Interaction Nets

Pi-nets: interaction nets for pi-calculus

π-calculus is a framework that aims to describe concurrent calculations through a formal definition of processes. Originally, π-calculus is defined by a formal language and a set of reduction rules, much in the spirit of λ-calculus. Our aim is to provide a graphical representation of π-calculus using multi-wired interaction nets, in the spirit this time of proof-nets of linear logic. 1 π-calcul...

Encoding Iterators in Interaction Nets

We propose a method for encoding iterators (recursion operators) using interaction nets. The method can be used to obtain a visual notation for functional programs, and also to extend with recursion the many translations of the λ-calculus into interaction nets, which have been proposed as efficient implementation mechanisms. We exemplify the method with a number of list-processing examples that...

Proof nets and the call-by-value λ-calculus

This paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize an isomorphism between the two systems: every single rewriting step on the calculus maps to a single step on proof nets, and viceversa. In this way, we obtain an algebraic reformulation of proof nets...

A Calculus for Interaction Nets

Interaction nets are graphical rewriting systems which can be used as either a high-level programming paradigm or a low-level implementation language. However, an operational semantics together with notions of strategy and normal form which are essential to reason about implementations, are not easy to formalize in this graphical framework. The purpose of this paper is to study a textual calcul...