# Foundations of Total Functional Data-Flow Programming

arXiv: https://arxiv.org/abs/1406.2063 · HTML: https://mlsanity.com/paper/1406.2063/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2014.

## Built on by (most cited first, 1 of 1)

- [Towards a unified framework for programming paradigms: A systematic review of classification formalisms and methodological foundations](https://mlsanity.com/paper/2508.00534/) (2025)

## Abstract (arXiv)

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.