In John Hughes' paper [1], Programming with Arrows, p. 20, "The truly interesting arrow types are those which do not correspond to a monad, because it is here that arrows give us real extra generality. Since we know that stream functions cannot be represented as a monad, then they are one of these "interesting" arrow types. So are the arrows used for functional reactive programming, for building GUIs, and the arrows for discrete event simulation we present in Section 5. And since these arrows cannot be represented by a monad, we know that they cannot support a sensible definition of app either." He described a few things that "cannot" be represented as a monad, they are: 1. Stream 2. FRP 3. GUI (request/response?) 4. Event Driven System (like circuits, robots?) My first question is: Are they "absolutely" outside of the realm of function + monad, therefore, arrows are indispensable? Or it is simply because the haskell program would be very cumbersome without arrows in these areas? (I mean without utilizing FFI to rescue.) The second question is: Other than the 4 areas above, are there more? Just want to get a sense of how useful arrows are. Not really a theoretical question. Thanks, Steve [1] http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf