# Coherent differentiation

Thomas Ehrhard
IRIF, Université de Paris
https://www.irif.fr/~ehrhard/

Date(s) : 09/09/2021   iCal
11 h 00 min - 12 h 30 min

The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential linear logic are concerned, these models feature finite non-determinism and indeed these languages are essentially non-deterministic.

We introduce a categorical framework for differentiation which does not require additivity and is compatible with deterministic models such as coherence spaces and probabilistic models such as probabilistic coherence spaces. Based on this semantics we sketch the syntax of a deterministic differential PCF.

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