On graphic lambda calculus and the dual of the graphic beta move

TL;DR

This paper explores a duality in graphic lambda calculus related to knot diagrams, introducing a dual graphic beta move that connects lambda calculus and emergent algebra sectors.

Contribution

It introduces the dual of the graphic beta move, highlighting a duality between lambda calculus and emergent algebra within graphic lambda calculus.

Findings

Dual graphic beta move relates to emergent algebras

Knot diagram duality reveals new structural insights

Enhanced understanding of lambda calculus and emergent algebra connection

Abstract

This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move. While the graphic beta move corresponds to beta reduction in untyped lambda calculus, the dual graphic beta move appears in relation to emergent algebras.