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arXiv · 2401.14834

From Differential Linear Logic to Coherent Differentiation

Thomas Ehrhard
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Abstract

In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are compatible with determinism. Indeed, due to the Leibniz rule of the differential calculus, differential linear logic and the differential lambda-calculus feature an operation of addition of proofs or terms operationally interpreted as a strong form of nondeterminism. The main idea of coherent differentiation is that these sums can be controlled and kept in the realm of determinism by means of a notion of summability, upon enforcing summability restrictions on the derivatives which can be written in the models and in the syntax.

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Thomas Ehrhard. 2024-01-26. From Differential Linear Logic to Coherent Differentiation. https://arxiv.org/abs/2401.14834

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