Graphic lambda calculus and knot diagrams

TL;DR

This paper explores how graphic lambda calculus can be extended to represent knot diagrams, building on a formalism that unifies lambda calculus and emergent algebras.

Contribution

It introduces a sector within graphic lambda calculus specifically designed to model knot diagrams as macros, expanding its applicability.

Findings

Knot diagrams can be represented as macros in graphic lambda calculus.

The formalism unifies lambda calculus, emergent algebras, and knot theory.

Potential for new computational and topological insights.

Abstract

In arXiv:1207.0332 [cs.LO] was proposed a graphic lambda calculus formalism, which has sectors corresponding to untyped lambda calculus and emergent algebras. Here we explore the sector covering knot diagrams, which are constructed as macros over the graphic lambda calculus.