Analytical Differential Calculus with Integration

05/06/2021
by   Han Xu, et al.
0

Differential lambda-calculus was first introduced by Thomas Ehrhard and Laurent Regnier in 2003. Despite more than 15 years of history, little work has been done on a differential calculus with integration. In this paper, we shall propose a differential calculus with integration from programming point of view. We show its good correspondence with mathematics, which is manifested by how we construct these reduction rules and how we preserve important mathematical theorems in our calculus. Moreover, we highlight applications of the calculus in incremental computation, automatic differentiation, and computation approximation.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

01/31/2022

Differentiating and Integrating ZX Diagrams

ZX-calculus has proved to be a useful tool for quantum technology with a...
10/29/2020

Linearizing Combinators

In 2017, Bauer, Johnson, Osborne, Riehl, and Tebbe (BJORT) showed that t...
12/08/2016

Automatic Differentiation: a look through Tensor and Operational Calculus

In this paper we take a look at Automatic Differentiation through the ey...
12/11/2020

Modules over monads and operational semantics

This paper is a contribution to the search for efficient and high-level ...
10/13/2009

Fractional differentiation based image processing

There are many resources useful for processing images, most of them free...
11/13/2002

XCB, the Last of the Shortest Single Axioms for the Classical Equivalential Calculus

It has long been an open question whether the formula XCB = EpEEEpqErqr ...
07/10/2020

Algorithmic differentiation of hyperbolic flow problems

We are interested in the development of an algorithmic differentiation f...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.