Functors, applicatives, and monads in pictures

I think that many monad tutorials, including this one, fall into the same trap. They explain monads without giving any motivation, or when they do, it seems like monads only exist to get around problems caused by being pure. When you program in normal languages, you have the ability to perform effects all of the time. You can always read/write to/from files, you can always raise exceptions or otherwise change the control flow. There's nothing you can't do. Haskell is…

I would complement it with: - Scott Wlaschin's Railway Oriented Programming (ROP): https://fsharpforfunandprofit.com/rop/ and https://fsharpforfunandprofit.com/posts/recipe-part2/ - Scott Wlaschin's The "Map and Bind and Apply, Oh my!" series at https://fsharpforfunandprofit.com/series/map-and-bind-and-ap... and its concept of an "elevated world". - And for Elixir Programmers, Zohaib Rauf's "Railway Oriented Programming in Elixir" at https://zohaib.me/railway-programming-pattern-in-elixir/ based on Scott Wlaschin…

Nice pictures, but I just don't get it. Sure, it's very easy for me to understand monads mathematically, what kind of structure are they. I don't need any pictures for that, the definition suffices for me. But that doesn't tell me what are they good for. We invent things for a reason, and I don't see the reason. Now I know the reason, it's been told to me many times (some way to wrap I/O while preserving functional purity), but…

Goofy, but this is the best explanation I've ever seen.