Graph rewrites, from graphic lambda calculus, to chemlambda, to directed interaction combinators

TL;DR

This paper explores the connections and modifications among graphic lambda calculus, chemlambda, and directed interaction combinators, contributing to the understanding of their relationships within artificial chemistry and lambda calculus frameworks.

Contribution

It introduces modifications and relations between these formalisms, advancing the study of artificial chemistry models and their connection to lambda calculus and interaction combinators.

Findings

Established links between graphic lambda calculus and chemlambda

Demonstrated modifications improving formal relationships

Explored applications within artificial chemistry

Abstract

Here I report about the modifications of and relations between graphic lambda calculus, various formalisms which appeared under the name chemlambda and a version of directed interaction combinators. This is part of the study and experiments with the artificial chemistry chemlambda and the relations with lambda calculus or interaction combinators, as described in arXiv:2003.14332 and available from the entry page at https://chemlambda.github.io/index.html