Conditional Nested Pattern Matching in Interaction Net

TL;DR

This paper extends interaction nets with nested pattern matching capabilities, maintaining their core properties and providing a translation to non-nested forms, thereby enhancing expressiveness without sacrificing fundamental benefits.

Contribution

It introduces nested pattern matching to interaction nets, along with a translation method and new notation, preserving confluence and parallelism.

Findings

Nested pattern matching is compatible with interaction nets' properties.

A translation to non-nested matching is developed.

The extension is conservative in rewriting.

Abstract

Interaction nets are a form of restricted graph rewrite system that can serve as a graphical or textual programming language. As such, benefits include one-step confluence, ease of parallelism and explicit garbage collection. However, some of these restrictions burden the programmer, so they have been extended in several ways, notably to include data types and conditional rules. This paper introduces a further extension to allow nested pattern matching and to do so in a way that preserves these benefits and fundamental properties of interaction nets. We also show that by introducing a translation to non-nested matching, this extension is conservative in rewriting. In addition, we propose a new notation to express this pattern matching.