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SUMMARY:Coherent differentiation makes the differential lambda-calculus de
 terministic - Thomas Ehrhard\, University of Paris
DTSTART:20221028T130000Z
DTEND:20221028T140000Z
UID:TALK184934@talks.cam.ac.uk
CONTACT:Jamie Vicary
DESCRIPTION:Categorical models of differentiation are either additive cate
 gories\,\nthat is categories enriched over commutative monoids\, or left-a
 dditive\ncategories. This is due to the fact that the differentiation of a
 \nfunction depending on a tuple of arguments requires a summation of\npart
 ial derivatives. From a computational point of view this means that\na mod
 el of a programming language where programs can be differentiated\n(in the
  sense of the differential lambda-calculus) features a strong\nform of non
 -determinism. The recently introduced coherent\ndifferentiation shows that
  this is not a fatality\, proposing a new\nsetting where morphisms can be 
 differentiated - in a completely standard\nway - in categories which are n
 ot necessarily additive. As an outcome we\nintroduce a differential versio
 n of the functional language PCF equipped\nwith a fully deterministic oper
 ational semantics. This new approach is\nbased on a functorial axiomatizat
 ion of the concept of summability.
LOCATION:SS03
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