Fingertree头复杂度

Question

我刚刚第二次阅读Apfelmus' excellent introduction to Finger Trees，开始怀疑他对head的实现：

import Prelude hiding (head)

data Tree v a = Leaf   v a
              | Branch v (Tree v a) (Tree v a)

toList :: Tree v a -> [a]
toList (Leaf _ a)     = [a]
toList (Branch _ x y) = toList x ++ toList y

head :: Tree v a -> a
head (Leaf _ a)     = a
head (Branch _ x _) = head x

由于相互实现功能是一种非常好的重用代码的方式，这让我开始思考下面的实现是否会像他的原始实现一样高效（复杂性）：

import Prelude -- not needed, just for making it obvious
data Tree v a = Leaf   v a
              | Branch v (Tree v a) (Tree v a) deriving Show

toList :: Tree v a -> [a]
toList (Leaf _ a)     = [a]
toList (Branch _ x y) = toList x ++ toList y

head' :: Tree v a -> a
head' = head . toList

惰性求值是否与原始实现一样高效？

Answer 1

是的，head 和 head' 如果交给 GHC 应该具有相同的时间复杂度。我预计 head 会出现小的常数因子差异（对此可能有 60% 的信心——列表融合优化的东西在起作用时非常疯狂）。