Well, THIS is interesting. By compiling programs to categories it is
possible to do things like computing program derivatives. Watch
the video.
http://media.podcasts.ox.ac.uk/comlab/comsci/2017-09-04-ICFP2017/2017-09-04-ICFP2017-day2-pm-08.mp4

and the website:
http://conal.net/papers/compiling-to-categories/

This introduces an interesting wrinkle in computer algebra.

Tim

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