Article

Functional automatic differentiation with dirac impulses

Author:

Henrik NilssonAuthors Info & Claims

ICFP '03: Proceedings of the eighth ACM SIGPLAN international conference on Functional programming

Pages 153 - 164

https://doi.org/10.1145/944705.944720

Published: 25 August 2003 Publication History

Abstract

Functional Reactive Programming (FRP) is a framework for reactive programming in a functional setting. FRP has been applied to a number of domains, such as graphical animation, graphical user interfaces, robotics, and computer vision. Recently, we have been interested in applying FRP-like principles to hybrid modeling and simulation of physical systems. As a step in that direction, we have extended an existing FRP implementation, Yampa, in two new ways that make it possible to express certain models in a very natural way, and reduces the amount of work needed to put modeling equations into a suitable form for simulation. First, we have added Dirac impulses that allow certain types of discontinuities to be handled in an easy yet rigorous manner. Second, we have adapted automatic differentiation to the setting of Yampa, and generalized it to work correctly with Dirac impulses. This allows derivatives of piecewise continuous signals to be well-defined at all points. This paper reviews the basic ideas behind automatic differentiation, in particular Jerzy Karczmarczuk's elegant version for a lazy functional language with overloading, and then considers the integration with Yampa and the addition of Dirac impulses.

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Cited By

Apopei BDodd T(2011)FPGA automatic re-synchronisation for pipelined, floating point control systems applicationsDesign Automation for Embedded Systems10.1007/s10617-011-9077-315:3-4(247-288)Online publication date: 1-Dec-2011
https://dl.acm.org/doi/10.1007/s10617-011-9077-3
Elliott C(2009)Beautiful differentiationACM SIGPLAN Notices10.1145/1631687.159657944:9(191-202)Online publication date: 31-Aug-2009
https://dl.acm.org/doi/10.1145/1631687.1596579
Elliott CHutton GTolmach A(2009)Beautiful differentiationProceedings of the 14th ACM SIGPLAN international conference on Functional programming10.1145/1596550.1596579(191-202)Online publication date: 31-Aug-2009
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Index Terms

Functional automatic differentiation with dirac impulses
1. Computing methodologies
  1. Modeling and simulation
    1. Simulation support systems
      1. Simulation languages
    2. Simulation types and techniques
      1. Continuous simulation
      2. Discrete-event simulation
2. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Data flow languages
        Functional languages

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cover image ACM Conferences

ICFP '03: Proceedings of the eighth ACM SIGPLAN international conference on Functional programming

August 2003

310 pages

ISBN:1581137567

DOI:10.1145/944705

General Chair:
Colin Runciman
University of York, UK
,
Program Chair:
Olin Shivers
Georgia Institute of Technology, USA

ACM SIGPLAN Notices Volume 38, Issue 9
September 2003
289 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/944746
Issue’s Table of Contents

Copyright © 2003 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 25 August 2003

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Cited By

Apopei BDodd T(2011)FPGA automatic re-synchronisation for pipelined, floating point control systems applicationsDesign Automation for Embedded Systems10.1007/s10617-011-9077-315:3-4(247-288)Online publication date: 1-Dec-2011
https://dl.acm.org/doi/10.1007/s10617-011-9077-3
Elliott C(2009)Beautiful differentiationACM SIGPLAN Notices10.1145/1631687.159657944:9(191-202)Online publication date: 31-Aug-2009
https://dl.acm.org/doi/10.1145/1631687.1596579
Elliott CHutton GTolmach A(2009)Beautiful differentiationProceedings of the 14th ACM SIGPLAN international conference on Functional programming10.1145/1596550.1596579(191-202)Online publication date: 31-Aug-2009
https://dl.acm.org/doi/10.1145/1596550.1596579
Siskind JPearlmutter B(2008)Nesting forward-mode AD in a functional frameworkHigher-Order and Symbolic Computation10.1007/s10990-008-9037-121:4(361-376)Online publication date: 1-Dec-2008
https://dl.acm.org/doi/10.1007/s10990-008-9037-1
Pang AStewart DSeefried SChakravarty MNilsson H(2004)Plugging Haskell inProceedings of the 2004 ACM SIGPLAN workshop on Haskell10.1145/1017472.1017478(10-21)Online publication date: 22-Sep-2004
https://dl.acm.org/doi/10.1145/1017472.1017478
Courtney ANilsson HPeterson JJeuring J(2003)The Yampa arcadeProceedings of the 2003 ACM SIGPLAN workshop on Haskell10.1145/871895.871897(7-18)Online publication date: 28-Aug-2003
https://dl.acm.org/doi/10.1145/871895.871897
Clift JMurfet D(2020)Cofree coalgebras and differential linear logicMathematical Structures in Computer Science10.1017/S096012952000013430:4(416-457)Online publication date: 10-Jun-2020
https://doi.org/10.1017/S0960129520000134
Damala ARuthven IHornecker E(2019)The MUSETECH ModelJournal on Computing and Cultural Heritage 10.1145/329771712:1(1-22)Online publication date: 20-Feb-2019
https://dl.acm.org/doi/10.1145/3297717
Gomes CThule CBroman DLarsen PVangheluwe H(2018)Co-SimulationACM Computing Surveys10.1145/317999351:3(1-33)Online publication date: 23-May-2018
https://dl.acm.org/doi/10.1145/3179993
Radu VTong CBhattacharya SLane NMascolo CMarina MKawsar F(2018)Multimodal Deep Learning for Activity and Context RecognitionProceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies10.1145/31611741:4(1-27)Online publication date: 8-Jan-2018
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