Derivatives of Containers | Zendy

Michael Abbott | Zendy; Thorsten Altenkirch | Zendy; Neil Ghani | Zendy; Conor McBride | Zendy

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Derivatives of Containers

Author(s) -

Michael Abbott,

Thorsten Altenkirch,

Neil Ghani,

Conor McBride

Publication year - 2003

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-40332-9

DOI - 10.1007/3-540-44904-3_2

Subject(s) - functor , differentiable function , container (type theory) , computer science , derivative (finance) , categorical variable , perspective (graphical) , quotient , property (philosophy) , calculus (dental) , type (biology) , algebra over a field , mathematics , pure mathematics , artificial intelligence , philosophy , epistemology , mechanical engineering , medicine , ecology , dentistry , engineering , biology , machine learning , financial economics , economics

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 e x in calculus by being its own derivative.

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