Local and global moves on locally planar trivalent graphs, lambda calculus and $\lambda$-Scale

TL;DR

This paper explores local and global transformations on locally planar trivalent graphs, revealing that lambda calculus and its beta reduction can be represented through graph transformations, offering a novel graphical perspective.

Contribution

It introduces a graph-based framework for lambda calculus, showing that beta reduction corresponds to a local graph transformation, bridging graph theory and lambda calculus.

Findings

Lambda calculus is embedded in locally planar trivalent graphs.

Beta reduction corresponds to a local graph sewing transformation.

The framework unifies graph transformations with lambda calculus operations.

Abstract

We give a description of local and global moves on a class of locally planar trivalent graphs and we show that it contains $\lambda$-Scale calculus, therefore in particular untyped lambda calculus. Surprisingly, the beta reduction rule comes from a local "sewing" transformation of trivalent locally planar graphs.