1 research outputs found
Formal Adventures in Convex and Conical Spaces
Convex sets appear in various mathematical theories, and are used to define
notions such as convex functions and hulls. As an abstraction from the usual
definition of convex sets in vector spaces, we formalize in Coq an intrinsic
axiomatization of convex sets, namely convex spaces, based on an operation
taking barycenters of points. A convex space corresponds to a specific type
that does not refer to a surrounding vector space. This simplifies the
definitions of functions on it. We show applications including the convexity of
information-theoretic functions defined over types of distributions. We also
show how convex spaces are embedded in conical spaces, which are abstract real
cones, and use the embedding as an effective device to ease calculations.Comment: to be published in CICM 202