lens

I will write this answer in the flavor of your average Haskell library, as read by somebody who has learned the core language very well but not that library: you <*$%^> everyone %%<#>%% experience Are you really going to tell me you have never looked at code written with a package you haven't learned and initially found it to be unintelligible? If not, then I would guess that you are simply well-suited to Haskell. Again, I'm not saying Haskell is bad, but that it does have attributes that make it daunting to many people. The top-rated comment on here even talks about how easy Haskell is now that he's "over the hump." Even compared to a relatively esoteric language like Clojure, Haskell's hump is pretty big. I believe the canonical example of a weird math-based library that makes beginners cry is Control.Arrow. Reading arrow-based code

Indeed, it's not the whole story. Infinite types and recursive types will come along in part 2! As to the practical advantage - does there have to be one? Isn't the fact that it's intellectually gratifying enough? If you insist, though - I sometimes see the kind of laws I presented used in actual Haskell code. For example, in the Data.Lens package[0] you can consider a lens on a a structure of type a to be composed of a getter and a setter of values of type b data Lens a b = Lens (a -> b, a -> b -> a) which is refactored, using the law (a -> b, a -> c) == a -> (b,c), to look like data Lens a b = Lens (a -> (b, b -> a)) which allows for a more efficient 'modify' operation. It also allows you to notice that lenses are related to the 'Store' comonad[1]: data Store b a = Store (b, b -> a) data Lens a b = Lens (a -> Store b a