From Differential Linear Logic to Coherent Differentiation

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.