Some things I played around with to understand them better. Fun stuff!

• monads:

  Simple implementation of the Reader monad, followed by a monad instance for functions

• epsilon:

  A seemingly impossible program: It checks whether total predicates on infinite lists of Bools are

  • satisfiable (returning an example)
  • a tautology
  • equal to another predicate

  despite there being uncountably many of these lists.

  Thanks to Ingo Blechschmidt for exposing me to the idea! Extensive information can be found in this blog post by Martín Escardó.

• catamorphisms (also called generic eliminators or recursion schemes):

  Catamorphisms deconstruct a data structure and are a generalization of the concept of a fold. Instead of writing a recursive function on the data structure manually, you just pass the respective algebra (functions that describe how to deconstruct each constructor) to a generic eliminator.

  Thanks to Andor Pénzes for exposing me to the idea! More information can be found on the Haskell Wiki.

• free-monads

  An interesting way to decouple describing programs from executing them.