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No tutorial, I swear...

After grinding through much of the "20 Intermediate Exercises" and just about all of the Monad Challenges, Monads make much more sense to me.

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…

Flipping out

I came across the excellent Monad Challenges, a collection of exercises designed to take you through what have become some of the standard example monads and take you through the process that motivates monads as a way to handle these seemingly diverse data structures. Both the Monad Challenges and the 20 Intermediate Exercises are well worth your time. Doing them both is helping me a lot.

That said, they don't quite match up. 20IE's banana is flip bind and apple is flip ap. (This isn't unique; the also excellent Learning Haskell from first principles has as an exercise writing bind in terms of fmap and join, but the declaration it gives has the type of flip bind. The authors do point this out.) As a result, I find myself with something that there's got to be some way to simplify, of the form

foo = flip $ (flip mumble) . (flip frotz)

I'd like to think there's some sort of distributive-like law to be found and used here... watch this space.

Trust in Schönfinkel

I'm working through the "20 Intermediate Exercises" that give Functors and Monads and such cute, non-threatening names and ask you to implement them. I've gotten most of the way through, with three or four that I'm stuck on--that's under the assumption that the inductive step from banana to banana2 will make the rest of the banana<n> obvious. (If you have sausage, it's easy to implement moppy, and vice versa, but avoiding circularity is the issue.)

So... I did a Bad Thing and looked at solutions a couple of people have posted, saying to myself, "OK, I'll look at those I've already done with an eye to more elegant expression, and look at the ones I'm having issues with and make sure I understand"... and came face to face with a question about composition.

<andy_rooney>Didja ever notice that the examples of composition you see are what we think of as functions with one argument?</andy_rooney> Well, one of the solution…

Careful with that infinite list, Eugene...

Warning: this will give away one way to solve a certain low-numbered Project Euler problem.

Any Haskell book, blog, or tutorials you come across has a good chance of including the très élégant Haskell one-liner for an infinite list containing the Fibonacci sequence:

fibs = 0 : 1 : (zipWith (+) fibs (tail fibs))

Thanks to laziness, it will only evaluate out to the last term we actually request... that was, long ago, my downfall. I wanted the terms no bigger than four million, so

filter (<= 4000000) fibs

right? Wrong. You and I know that the Fibonacci sequence is monotonically increasing, but filter doesn't, and it doesn't even notice the particular function we're filtering with to realize it could terminate thanks to monotonicity. So instead,

takeWhile (<= 4000000) fibs

is the way to go.

The particular problem has an additional constraint, because it only wants the even terms of the sequence no bigger than four million. Easy enough to do, just feed it through

filter even