Nested Term Graphs (Work In Progress)

TL;DR

This work introduces nested term graphs to formalize higher-order terms with recursion, providing a structural and functional framework that can be faithfully implemented by first-order term graphs.

Contribution

It defines nested term graphs with a novel partitioned signature and demonstrates their faithful implementation via first-order term graphs.

Findings

Nested term graphs formalize higher-order terms with recursion.

Definitions induce bisimulation notions for nested term graphs.

Main result shows faithful implementation by first-order term graphs.

Abstract

We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent the nested scope structure of a higher-order term by a nested structure of term graphs. Based on a signature that is partitioned into atomic and nested function symbols, we define nested term graphs both in a functional representation, as tree-like recursive graph specifications that associate nested symbols with usual term graphs, and in a structural representation, as enriched term graph structures. These definitions induce corresponding notions of bisimulation between nested term graphs. Our main result states that nested term graphs can be implemented faithfully by first-order term graphs. keywords: higher-order term graphs, context-free grammars, cyclic lambda-terms, higher-order rewrite systems