As an aside on an aside, there is also the related classic: Conor McBride, The Derivative of a Regular Type is its Type of One-Hole Contexts http://strictlypo

As an aside on an aside, there is also the related classic: Conor McBride, The Derivative of a Regular Type is its Type of One-Hole Contexts http://strictlypositive.org/diff.pdf http://strictlypositive.org/diff.pdf related to Huet's Zipper and Hinze, Paterson Finger Trees, with a huge of follow-on literature: https://personal.cis.strath.ac.uk/conor.mcbride/Holes.pdf https://personal.cis.strath.ac.uk/conor.mcbride/Holes.pdf https://conal.net/blog/posts/differentiation-of-higher-order-types https://conal.net/blog/posts/differentiation-of-higher-order... and numerous old posts by sigfpe (Dan Piponi), e.g. http://blog.sigfpe.com/2008/06/blessed-mans-formula-for-holey.html http://blog.sigfpe.com/2008/06/blessed-mans-formula-for-hole...