Speaker:

   Mario Alvarez Picallo (Oxford)

Title: 

   An abstract model for higher-order incremental computation.

Abstract:

   Incremental computation is a technique to reduce the cost of
   applying the same function to an input that is modified over time,
   by instead applying it to an initial input and then using an
   incremental version of the function to update the output. This
   technique is well-known in the literature, but a recent work by
   Cai, Giarrusso, Rendel and Ostermann has opened a new avenue of
   research into the denotational aspects of this technique with their
   use of derivatives.

   In this talk, I intend to give a more rigorous treatment of the
   semantics of incremental computation by introducing the notions of
   difference algebras and differentiable functions between these,
   which give rise to two Cartesian closed categories of
   incrementalizable programs. These can be further generalized to
   difference stacks and smooth functions, which again constitute a
   Cartesian closed category. My intention is to show that difference
   stacks can be used as a denotational model for higher-order
   languages equipped with an operator for automatically
   incrementalizing arbitrary expressions.