Numl - A Strongly Typed Language for Numerical Accuracy

Matthieu Martel

2017

Abstract

It is well-known that numerical computations may sometimes lead to wrong results because of roundoff errors. We propose an ML-like type system (strong, implicit, polymorphic) for numerical computations in finite precision, in which the type of an expression carries information on its accuracy. We use dependent types and a type inference which, from the user point of view, acts like ML type inference. Basically, our type system accepts expressions for which it may ensure a certain accuracy on the result of the evaluation and it rejects expressions for which a minimal accuracy on the result of the evaluation cannot be inferred. The soundness of the type system is ensured by a subject reduction theorem and we show that our type system is able to type implementations of usual simple numerical algorithms.

Paper Citation

in Harvard Style

Martel M. (2017). Numl - A Strongly Typed Language for Numerical Accuracy.In OPPORTUNITIES AND CHALLENGES for European Projects - Volume 1: EPS Portugal 2017/2018, ISBN 978-989-758-361-2, pages 177-200. DOI: 10.5220/0008862701770200

in Bibtex Style

@conference{eps portugal 2017/201817,
author={Matthieu Martel},
title={Numl - A Strongly Typed Language for Numerical Accuracy},
booktitle={OPPORTUNITIES AND CHALLENGES for European Projects - Volume 1: EPS Portugal 2017/2018,},
year={2017},
pages={177-200},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0008862701770200},
isbn={978-989-758-361-2},
}

in EndNote Style

TY - CONF

JO - OPPORTUNITIES AND CHALLENGES for European Projects - Volume 1: EPS Portugal 2017/2018,
TI - Numl - A Strongly Typed Language for Numerical Accuracy
SN - 978-989-758-361-2
AU - Martel M.
PY - 2017
SP - 177
EP - 200
DO - 10.5220/0008862701770200