On 1/31/07, Andrew Wagner
So, a couple of questions to ponder about this: Is this unique to Haskell, or could the same be said about any functional language? How can we teach this better to newbies? Most of what I see in the tutorials is "Higher order functions accept as parameters and/or return other functions. Here's some examples: <explanation of map>, <explanation of foldr>. Moving on, ..." But clearly, this is something important, and I think we can do a better job of teaching it. Suggestions?
The first time I really thought about this much was after reading Meijer, Fokkinga and Patterson's "Functional Programming with Bananas, Lenses and Barbed Wire," which makes the comparison between arbitrary recursion and goto early on, and develops four replacement operators (cata-, ana-, hylo-, and paramorphisms). At the time, I was involved in teaching an introduction FP class in which we frequently discovered that students would latch onto primitive recursion early in the course and never stop using it, even as their functions became more convoluted and using maps and filters correspondingly easier. My natural thought was to wonder if the beginning of the course could be rewritten without primitive recursion, only introducing it later after the students were already comfortable with the higher-order combinators. Sadly, that never went anywhere. I'd be interested in hearing if anybody else got farther in attempting that teaching technique. /g -- It is myself I have never met, whose face is pasted on the underside of my mind.