Haskell—with its powerful type system—has a great support for type-level programming and it has gotten much better in the recent times with the new releases of the GHC compiler. But type-level programming remains a daunting topic even with seasoned haskellers. Thinking with Types: Type-level Programming in Haskell by Sandy Maguire is a book which attempts to fix that. I’ve taken some notes to summarize my understanding of the same.
Binary tree is the simplest of tree data structures. It is a tree in which each node has at most two children. A tree traversal is a process of visiting each node in the tree, exactly once. There are multiple ways of traversing a binary tree in depth-first fashion with each traversal resulting in a different enumeration of the tree elements. These tree traversals are defined as simple recursive functions. But what if we want to write Java-style iterators for them? Is there a way to mechanically derive these iterators from the traversal functions? Let’s find out.