Derivatives of containers

Authors:
Michael Abbott;Thorsten Altenkirch;Neil Ghani;Conor McBride
Affiliations:
Department of Mathematics and Computer Science, University of Leicester;School of Computer Science and Information Technology, Nottingham University;Department of Mathematics and Computer Science, University of Leicester;Department of Computer Science, University of Durham
Venue:
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Year:
2003

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Abstract

We are investigating McBride's idea that the type of one-hole contexts are the formal derivative of a functor from a categorical perspective. Exploiting our recent work on containers we are able to characterise 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 differentiable containers include those generated by polynomials and least fixpoints. Finally, we discuss abstract containers (i.e. quotients of containers) -- this includes a container which plays the role of ex in calculus by being its own derivative.