# Towards formalizing and extending differential programming using tangent categories

@inproceedings{Cruttwell2019TowardsFA, title={Towards formalizing and extending differential programming using tangent categories}, author={Geoff S. H. Cruttwell and Jonathan Gallagher and Benjamin MacAdam}, year={2019} }

This paper gives an interpretation of a simple differential programming language (over finite dimensional R vector spaces), into a setting derived from synthetic differential geometry (SDG). The main theorem of this paper is Theorem 5.6, where we establish that there is always an interpretation of our simple differential programming language into a category of partial maps of a well-adapted smooth topos that preserves the derivative and all the control structures of the differential programming…

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