An abstract view on syntax with sharing

TL;DR

This paper presents an abstract framework for understanding term graphs, extending the concept of inductively generated syntax to include sharing and discarding of subterms, with applications beyond traditional set-based contexts.

Contribution

It introduces an abstract expression for term graphs analogous to initial algebras for syntax, broadening the theoretical foundation and applications of term graphs.

Findings

Develops an abstract categorical framework for term graphs.

Extends the theory of inductively generated syntax to include sharing.

Discusses applications beyond set-based syntax.

Abstract

The notion of term graph encodes a refinement of inductively generated syntax in which regard is paid to the the sharing and discard of subterms. Inductively generated syntax has an abstract expression in terms of initial algebras for certain endofunctors on the category of sets, which permits one to go beyond the set-based case, and speak of inductively generated syntax in other settings. In this paper we give a similar abstract expression to the notion of term graph. Aspects of the concrete theory are redeveloped in this setting, and applications beyond the realm of sets discussed.