This repo contains code for examples presented in my talk Monads Are Not About Sequencing (Functional Scala 2023, video, slides).

Examples:

• Monads in the category <:< (Scala's subtype relationship)
  • are closure operators on the partial order of Scala types
  • example given: type Result[+A] = Error | A
  • no sequencing because there's no execution or effects
• Monads in the category <= (opposite category to =>)
  • are comonads from =>
  • example given: Id
  • executes in reverse order, i.e. not the sequence given in code
• Writer monad (in =>) type Writer[A] = (List[String], A) with flipped concatenation (as, bs) => bs ++ as
  • constituent logs appear in reverse order, i.e. not the sequence given in code
• Concurrent, nondeterministic Writer monad in -⚬, the category of Libretto functions
  • with concurrent merge as the monoid operation to combine logs
  • non-deterministic order of messages in the result log