Lisp/Scheme/Clojure's map function doesn't just give you a list functor; it is also a zip-list applicative functor
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pure (+) <*> ZipList [1,2,3] <*> ZipList [4,5,6] == [5,7,9]
(map + '(1 2 3) '(4 5 6)) == '(5 7 9)
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For a language at the "top of the abstraction continuum" (Paul Graham), Lisp functions tend to be disappointingly concrete
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ie, just for this applicative map, Clojure needs an ISeq - you must define first, next, more, cons, count, empty, equiv, seq
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The category theory view provides a unifying and simplifying discipline; the hacker way yields endless special cases
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On the other way, Lisp's limited applicative probably has a much lower cognitive burden. There isn't a cottage industry of "map" tutorials
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Is "functor with arbitrary arity" such a difficult concept? Why do all the applicative tutorials come out so tortured and complicated?
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Wow, that's actually a useful way to think of it. Applicative has always been pretty magical/mysterious to me.
I guess it's probably got to do with the fact that I don't use it all to much in my day-to-day langs, in contrast to functors and monads…
Exactly! I probably need to use it more to really get my head around it.
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