A Braided Lambda Calculus

TL;DR

This paper introduces a novel untyped linear lambda calculus featuring braids, along with its combinatory logic and semantic models based on crossed G-sets, expanding the theoretical framework of lambda calculus.

Contribution

It presents the first untyped linear lambda calculus with braids, along with its combinatory logic and semantic models, advancing the understanding of braided structures in lambda calculus.

Findings

Developed a new untyped linear lambda calculus with braids

Established the corresponding combinatory logic for the calculus

Provided semantic models using crossed G-sets

Abstract

We present an untyped linear lambda calculus with braids, the corresponding combinatory logic, and the semantic models given by crossed G-sets.