Derivatives of Containers
Michael Abbott, Thorsten Altenkirch, Neil Ghani, Conor Thomas McBride · 2002
Abstract. We are investigating McBride's idea that the type of onehole contexts are the formal derivative of a functor from a categorical perspective. Exploiting our recent work on containers we are able to characterize derivatives by a universal property and show that the laws of calculus including a rule for initial algebras as presented by McBride hold -- hence the dierentiable containers include those generated by polynomials and least xpoints. Finally, we discuss abstract containers (i.e. quotients of containers) -- this includes a container which plays the role of e^x in calculus by being its own derivative.