Learn You a Haskell for Great Good! by Lipovača

Sunday April 11, 2021

Here's a good book you can read for free. Like it says on the back, "Maps, Monads, Monoids, and More!" It does a great job explaining things in ways that are helpful. The humble list can be a functor, an applicative functor, a monoid, and a monad.

There's a joke: "A monad is just a monoid in the category of endofunctors, what's the problem?" This is like saying "the median is just a medoid on the field of reals."

In both cases, if you don't know what the first term is, you likely don't know what the others are. It's not a good way to explain.

In both cases, the explanatory terms are needlessly obscure: "endo" is likely gratuitous; "field of reals" is probably not better than "numbers".

Also in both cases, the explanation isn't complete; it describes without defining. For the median, the L1 norm has to be specified. For monads, the monoid function has to be join. See also Crockett's explanation and my pictures showing how map and join give you bind.

I'm not giving a complete explanation here either. Read the book! It has zippers too!

Forcing non-pure stuff into do blocks, as seems common in Haskell, is very reminiscent of the functional core, imperative shell pattern.

Haskell's pattern-matching (often instead of conditionals) is pretty neat. Python is getting something analogous in 3.10.

Haskell's type inference gives behavior sort of like coercion in other languages, but without the craziness. So 3 + 4.5 will work like you'd expect, but there's no chance '3' + 4.5 will turn out to be '34.5' (which is what happens in JavaScript).

Haskell has a funny quirk in some of its ranges:

ghci> [0.1, 0.3 .. 1]
[0.1,0.3,0.5,0.7,0.8999999999999999,1.0999999999999999]

It's surprising that 1.1 is in there, when 1 was the upper bound. This is because of a rule that if the value is within half the step size (for floats and things like them) then it gets included in the result. Wacky!

"Sets and maps from Data.Set and Data.map are implemented using trees, but instead of normal binary search trees, they use balanced binary search trees." (page 135)

Interesting! Usually these would be hash maps... Hmm! The closest Haskell gets to a "normal" hash map (I think this?) is implemented with hash array mapped tries. Also good for persistence (meaning re-using things in memory rather than creating everything from scratch, because we don’t mutate). Fun!

"We can read the type of putStrLn like this: putStrLn takes a string and returns an I/O action that has a result type of () (that is, the empty tuple, also known as unit)." (page 155)

The wiki for unit type is helpful for understanding why it's called that.

On page 275, he defines a pipe operator with x -: f = f x. Pretty neat!

"While similar to a normal list, a difference list is actually a function that takes a list and prepends another list to it. For example, the difference list equivalent of a list like [1,2,3] is the function \xs -> [1,2,3] ++ xs. A normal empty list is [], whereas an empty difference list is the function \xs -> [] ++ xs." (page 307)

And so we get efficient appending to linked lists!

"the function monad is also called the reader monad." (page 312)

"For instance, if we have Just (Just 9), can we make that into Just 9? It turns out that any nested monadic value can be flattened and that this is actually a property unique to monads." (page 326)

This makes it sound fancier than it is, I think because the author talks about bind more than join and doesn't talk about the relationship between them.

"We don't usually set out to make a monad with the sole purpose of making a monad. Rather, we make a type whose purpose is to model an aspect of some problem, and then later on, if we see that the type represents a value with a context and can act like a monad, we give it a Monad instance." (page 336)