Foundations of Total Functional Data-Flow Programming

TL;DR

This paper introduces a mathematically grounded framework that unifies data-flow graph and functional reactive programming styles for stream programming, emphasizing compositional semantics and set theory.

Contribution

It presents a new foundational framework based on set theory and coalgebraic principles that unifies data-flow and functional reactive programming paradigms.

Findings

Framework based on set theory and coalgebraic coinduction

Symmetrical reduction of paradigms to a low-level core

Full core of a novel stream programming language

Abstract

The field of declarative stream programming (discrete time, clocked synchronous, modular, data-centric) is divided between the data-flow graph paradigm favored by domain experts, and the functional reactive paradigm favored by academics. In this paper, we describe the foundations of a framework for unifying functional and data-flow styles that differs from FRP proper in significant ways: It is based on set theory to match the expectations of domain experts, and the two paradigms are reduced symmetrically to a low-level middle ground, with strongly compositional semantics. The design of the framework is derived from mathematical first principles, in particular coalgebraic coinduction and a standard relational model of stateful computation. The abstract syntax and semantics introduced here constitute the full core of a novel stream programming language.