This question led to a series of related blog posts by the author:
- The Algebra of Algebraic Data Types
- The Algebra of Algebraic Data Types, Part 2
- The Algebra of Algebraic Data Types, Part 3
Culminating in the awesome reveal that a zipper is nothing but the differentiation of its associated ADT.
The standard paper on ADT derivatives is Conor McBride’s The Derivative of a Regular Type is its Type of One-Hole Contexts