Therefore, I will follow the excellent advice of Stephen Diehl, and will not write a monad-analogy tutorial. Instead, I will say: do the 20 Intermediate Exercises, and take the Monad Challenges. To paraphrase Euclid, there is no royal road to Monads; the exercises and challenges take you down that road at whose end you'll see at least part of why Monads are so useful.
If you were trying to learn group theory and people were standing around you saying "groups are like the integers", "groups are like Rubik's Cube", "groups are like m x n matrices", "groups are like baryons and mesons", your situation would be much like the student of Haskell amidst all the monad analogy tutorials. In a sense they're backwards. All those things are groups, just as burritos et al. can at least be thought…
I assure you there will be no further allusions to Korean earworms. That said, on to the subject at hand...
Remember the exercise in the online Haskell course that had several tests to filter out weak passwords, all of which had to pass for the fictitious system to allow a String value to be used as a password? I wanted to make it easy to change, so I wanted to take a [String -> Bool] and get a [Bool] I could apply and to for the final thumbs up/thumbs down decision.
The first step: roll my own, which has a pleasing symmetry with map if you write it as a list comprehension:
If I don't already have the Haskell subreddit link over on the right, I'll add it ASAP.
This evening a Haskell beginner posted about some trouble he was having writing code to generate a particular sequence. I didn't catch on to the sequence he was going for, but I should have from a comment in his code:
Someone did catch on, though, and asked "Are you trying to make a look and say sequence?" The poster said yes... and off to Wikipedia I went.
Said sequence starts 1, 11, 21, 1211, 111221, ... and the way you get the next term is to take the current one and sort of run-length encode it. The first term would be "one one", i.e. a run of ones of length one, so the second term is 11. That in turn would be described as "two ones", hence the third term is 21, or "one two, one one", giving 1211, and so on.
If each digit were on its own line, you could get the next term of …