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Tech Talk: Conor McBride

Data-with-a-hole-in-it: differential operators on data structures

Thursday June 3 from 9.30 am

This talk is a tutorial on the differential calculus, applied to the algebraic structure of data. Container-like data types can be seen as generalised polynomials over their element types. Differential operators act on those polynomials to give notions of “focus” or “cursor”, splitting whole structures into substructure and context.
Moreover, differentiation uniformly induces comonad structure on data, with the counit asking “what is here?” and the comultiplication asking “where else could I go?”. I’ll investigate the consequences of these observations for rationalising traditional (but tricky) techniques for manipulating data in place.

Video of the talk:



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