In languages such as ML or Haskell, you can define data types by specifying functions you will use to construct values of any given type. In itself, that is not that interesting, but combined with a pattern matching feature of these languages, you can write very succinct functions for transforming data structures.
In my book Functional Data Structures in R (Mailund, 2017a), I describe several algorithms that depend on the transformation of various trees based on their structure. Such transformations involve figuring out the current structure of a tree—does it have ...
