CHAD: Combinatory Homomorphic Automatic Differentiation

نویسندگان

چکیده

We introduce Combinatory Homomorphic Automatic Differentiation (CHAD), a principled, pure, provably correct define-then-run method for performing forward and reverse mode automatic differentiation (AD) on programming languages with expressive features. It implements AD as compositional, type-respecting source-code transformation that generates purely functional code. This code is principled in the sense it unique homomorphic (structure preserving) extension to of Elliott’s well-known unambiguous definitions first-order language. Correctness follows by (compositional) logical relations argument shows semantics syntactic derivative usual calculus original program. In their most elegant formulation, transformations generate linear types. However, can be implemented standard language lacking types: While correctness proof requires tracking linearity, actual do not. fact, even language, we get all type-safety types give us: implement used type abstract using basic module system. this article, detail when applied simple higher-order manipulating statically sized arrays. explain how methodology applies, more generally, other Finally, discuss scope CHAD extends beyond applications dynamic program analyses accumulate data commutative monoid.

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ژورنال

عنوان ژورنال: ACM Transactions on Programming Languages and Systems

سال: 2022

ISSN: ['1558-4593', '0164-0925']

DOI: https://doi.org/10.1145/3527634