Siskind, Jeffrey Mark and Pearlmutter, Barak A. (2008) Nesting forward-mode AD in a functional framework. Higher Order and Symbolic Computation, 21. pp. 361-376. ISSN 1388-3690

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Abstract

We discuss the augmentation of a functional-programming language with a derivative-taking operator implemented with forward-mode automatic differentiation (AD). The primary technical difficulty in doing so lies in ensuring correctness in the face of nested invocation of that operator, due to the need to distinguish perturbations introduced by distinct invocations. We exhibit a series of implementations of areferentially-transparent forward-mode-AD derivative-taking operator, each of which uses a different non-referentially-transparent mechanism to distinguish perturbations. Even though the forward-mode-AD derivative-taking operator is itself referentially transparent, we hypothesize that one cannot correctly formulate this operator as a function definition in current pure dialects of Haskell.

Item Type:	Article
Additional Information:	This is the postprint version of the published article, which is available at https://doi.org/10.1007/s10990-008-9037-1 Cite as: Siskind, J.M. & Pearlmutter, B.A. Higher-Order Symb Comput (2008) 21: 361. https://doi.org/10.1007/s10990-008-9037-1
Keywords:	Automatic differentiation; Applicative (functional) languages; Referential transparency; Multiple transformation; Hamilton Institute.
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	1731
Identification Number:	https://doi.org/10.1007/s10990-008-9037-1
Depositing User:	Hamilton Editor
Date Deposited:	10 Dec 2009 15:11
Journal or Publication Title:	Higher Order and Symbolic Computation
Publisher:	Springer
Refereed:	Yes
Funders:	National Science Foundation, US (NSF), Science Foundation Ireland (SFI), Higher Education Authority (HEA)
URI:	https://link.springer.com
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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