[2101.10491v1] Categorical semantics of a simple differential programming language
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Mathematics > Category Theory

arXiv:2101.10491v1 (math)
[Submitted on 26 Jan 2021]

Title:Categorical semantics of a simple differential programming language

Authors:Geoffrey Cruttwell, Jonathan Gallagher, Dorette Pronk
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Abstract:With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support for this types of structure. One approach, due to Abadi and Plotkin, provides a simple differential programming language. Another approach is the notion of a reverse differential category. In the present paper we bring these two approaches together. In particular, we show how an extension of reverse derivative categories models Abadi and Plotkin's language, and describe how this categorical model allows one to consider potential improvements to the operational semantics of the language.
Comments: In Proceedings ACT 2020, arXiv:2101.07888
Subjects: Category Theory (math.CT); Programming Languages (cs.PL)
ACM classes: D.3.1
Cite as: arXiv:2101.10491 [math.CT]
  (or arXiv:2101.10491v1 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2101.10491
Journal reference: EPTCS 333, 2021, pp. 289-310
Related DOI: https://doi.org/10.4204/EPTCS.333.20

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 26 Jan 2021 00:08:48 UTC (44 KB)
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