ToL: A Tensor of List-Based Unified Computation Model

TL;DR

The paper introduces ToL, a unified computation model based on Tensor of List, enabling generalized expression and concise programming of complex algorithms, supported by a formal proof and a dedicated language, ToLang.

Contribution

It proposes the ToL model with five atomic computations and a formal proof of its universality, along with the ToLang language for programming high-level algorithms.

Findings

ToL can represent any elementary computation through finite composition.

ToLang enables programming of complex big data and AI algorithms.

ToL's computation metric aligns closely with FLOPs, ensuring performance predictability.

Abstract

Previous computation models either have equivalent abilities in representing all computations but fail to provide primitive operators for programming complex algorithms or lack generalized expression ability to represent newly-added computations. This article presents a unified computation model with generalized expression ability and a concise set of primitive operators for programming high-level algorithms. We propose a unified data abstraction -- Tensor of List, and offer a unified computation model based on Tensor of List, which we call the ToL model (in short, ToL). ToL introduces five atomic computations that can represent any elementary computation by finite composition, ensured with strict formal proof. Based on ToL, we design a pure-functional language -- ToLang. ToLang provides a concise set of primitive operators that can be used to program complex big data and AI algorithms. Our evaluations show ToL has generalized expression ability and a built-in performance indicator, born with a strictly defined computation metric -- elementary operation count (EOPs), consistent with FLOPs within a small error range.