Needed Computations Shortcutting Needed Steps

TL;DR

This paper introduces a compilation scheme for constructor-based graph rewriting systems that shortcuts needed steps, reducing memory and time consumption while maintaining normalization under an innermost strategy.

Contribution

It presents a novel compilation method that shortcuts needed steps in graph rewriting systems, enabling efficient implementation and execution.

Findings

Reduces memory consumption in rewriting computations

Decreases execution time compared to ordinary rewriting

Maintains normalization for the original system under innermost strategy

Abstract

We define a compilation scheme for a constructor-based, strongly-sequential, graph rewriting system which shortcuts some needed steps. The object code is another constructor-based graph rewriting system. This system is normalizing for the original system when using an innermost strategy. Consequently, the object code can be easily implemented by eager functions in a variety of programming languages. We modify this object code in a way that avoids total or partial construction of the contracta of some needed steps of a computation. When computing normal forms in this way, both memory consumption and execution time are reduced compared to ordinary rewriting computations in the original system.