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copied!<p><a href="http://www.haskell.org/ghc/docs/6.12-latest/html/libraries/containers-0.3.0.0/src/Data-Sequence.html#applicativeTree" rel="nofollow noreferrer"><code>applicativeTree</code></a> is quite fancy, but mainly in a way which has to do with FingerTrees in particular, which are quite a fancy data structure themselves. We had some discussion of the intricacies <a href="https://cstheory.stackexchange.com/q/5356">over at cstheory</a>. Note that <code>applicativeTree</code> is written to work over <em>any</em> Applicative. It just so happens that when it is specialized to <code>Id</code> then it can share nodes in a manner that it otherwise couldn't. You can work through the specialization yourself by inlining the <code>Id</code> methods and seeing what happens. Note that this specialization is used in only one place -- the O(log n) <code>replicate</code> function. The fact that the more general function specializes neatly to the constant case is a very clever bit of code reuse, but that's really all.</p> <p>In general, <code>Sequence</code> teaches more about designing persistent data structures than about all the tricks for eeking out performance, I think. Dons' suggestions are of course excellent. I'd also just browse through the source of the <em>really</em> canonical and tuned libs -- <code>Map</code>, <code>IntMap</code>, <code>Set</code>, and <code>IntSet</code> in particular. Along with those, its worth taking a look at Milan's <a href="http://fox.ucw.cz/papers/containers/containers.pdf" rel="nofollow noreferrer">paper on his improvements to containers</a>.</p>

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