Stream programs are monoid homomorphisms with state

TL;DR

This paper introduces a class of deterministic stream functions modeled as monoid homomorphisms with state, simplifying semantic reasoning and enabling optimization of complex dataflow programs.

Contribution

It defines a new framework for stream programs as monoid homomorphisms with state, simplifying semantic laws while supporting rich reasoning for dataflow optimizations.

Findings

Homomorphism laws are simpler than previous frameworks

Supports complex dataflow constructs like joins and feedback

Enables equational reasoning for stream program optimization

Abstract

We define a broad class of deterministic stream functions and show they can be implemented as homomorphisms into a "state" monoid. The homomorphism laws are simpler than the conditions of previous semantic frameworks for stream program optimization, yet retain support for rich equational reasoning over expressive dataflow programs, including sequential composition, parallel composition, and feedback. We demonstrate this using examples of partitioned database joins, stratified negation, and a simplified model of TCP.