``Computer science''

Why do they call it computer science?
It's not about computers and it's not a science.

>>34

No, not everything is really a monad

Of course it's not, that's why we always carefully check the fulfillment of monad laws before calling something a monad.
Oh, and trying to find monads everywhere is the right thing to do because it opens up a whole slew of library functions (that are monad-agnostic thanks to higher-kind polymorphism), and even more if you find a MonadPlus or some other typeclass.

Don't get me wrong, monads are great, and being able to treat a new thing as a monad can simplify code a lot, like applying any abstraction. But I don't think it's useful to think of imperative programs as really being inside of the state monad. An object orienteer sees everything as objects, and Paul Graham thinks that everything really is a list, but I think you'd object to both of those notions. As humans, once we start recognizing a pattern we tend to see it everywhere, and there's a risk that we mistake the abstract idea to be the underlying reality. There are infinite axioms to choose from and theorems to derive. Who's to say which set of ideas are the right ones?

No, types aren't really algebraic

I don't even know what you're complaining here. Go read about datatypes a la carte.

I wasn't referring to the expression problem. I also don't think it's a big deal. And don't worry, Pierce's brick wall book is on my shelf.

What I'm getting at here is that I think that it's useful to talk about e.g. arrays as such. You could of course see them as algebraic types, i.e. homogeneous tuples. It's just that your pattern matches become infinitely big to handle all sizes. You might want to forget about them (who needs them anyway) and restrict them to being just a way to implement tuples or records, or a special case of lists (that happen to be cdr-coded). But I think it's stupid to restrict your thinking this way. It's even worse to insist that the patterns you use to describe problems is the right one.

Of course, you wouldn't think this way, and I'm not putting words in your mouth. But some do, and I find them irritating.