Introduces *applicative functors* (in Haskellese, and assuming familiarity with functors and monads), a mechanism for threading a computation through an environment—crucially, without allowing the results of one computation to influence the choice of subsequent computations (otherwise you’d have a monad). The insight for applicative functors seems to have come from observing a repeated desire to thread computations through *traversable* data structures.

Having a reasonably firm handle on monads, applicative functors seemed like the next bit of functional programming jargon to get my head around. I found the paper to be mostly easy going (though I found myself stumped when trying the exercise hinted at in “For example, the functor (→) *env* cannot in general be Traversable. To see why, take *env* = Integer and try to distribute the Maybe functor!”). They give a nice example of the crux of the difference between applicative functors and monads, however the comparison between arrows and applicative functors is a bit more opaque. Arrows are probably up next in the functional programming pantheon, so perhaps enlightenment is just around the corner.

I even mostly grokked their closing discussion on the category theoretical manifestation of applicative functors as *strong lax monoidal functors*. (How is that not an oxymoron?) I owe this understanding mostly to the foundation I acquired through Gilbert’s numerous patient explanations of abstract algebraic concepts.