Nesting forward-mode AD in a functional framework

Siskind , Jeffrey Mark and Pearlmutter, Barak A. (2008) Nesting forward-mode AD in a functional framework. Advances in Automatic Differentiation. ISSN 1439-7358

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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
Keywords: Automatic differentiation; Applicative (functional) languages; Referential transparency; Multiple transformation; Hamilton Institute.
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1731
Depositing User: Hamilton Editor
Date Deposited: 10 Dec 2009 15:11
Journal or Publication Title: Advances in Automatic Differentiation
Publisher: Springer
Refereed: Yes

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