Container Morphisms for Composable Interactive Systems

TL;DR

This paper introduces a mathematical framework using container morphisms to enable modular, type-safe client-server communication, integrating dependent types, monads, and stateful protocols within a categorical setting.

Contribution

It develops a novel categorical approach to modeling interactive systems with containers, combining dependent types and monads to ensure modularity and safety in communication protocols.

Findings

Defines monads on containers that mirror functional programming constructs

Models stateful protocols using the Kleene star within the container framework

Provides a categorical foundation for composable, type-safe client-server interactions

Abstract

This paper provides a mathematical framework for client-server communication that results in a modular and type-safe architecture. It is informed and motivated by the software engineering practice of developing server backends with a database layer and a frontend, all of which communicate with a notion of request/response. I make use of dependent types to ensure the request/response relation matches and show how this idea fits in the broader context of containers and their morphisms. Using the category of containers and their monoidal products, I define monads on containers that mimic their functional programming counterparts, and using the Kleene star, I describe stateful protocols in the same system.