让我们稍微简化一下这个例子,看看会发生什么。您只需考虑惰性求值和图形缩减就可以解决大部分问题,而无需进行任何更低级别的操作。ourLast (mkList 3)
让我们看一下这段代码的简化简化:
ourLast :: [a] -> a
ourLast [] = error "ourLast []"
ourLast (x:[]) = x
ourLast (_:xs) = ourLast xs
mkList :: Int -> [Int]
mkList 0 = []
mkList n = let rest = mkList (n-1) in n : rest
?foo
意思是“我们还没有看过的值”。我们用“let”创建这些。
foo@bar
意思是“我们已经计算bar
出的?foo
值是”foo@bar
foo := bar
foo
bar
-- We start here by creating some value and giving it to ourLast to
-- look at.
let ?list3 = mkList 3
ourLast ?list3
-- At this point ourLast examines its argument to figure out whether
-- it's of the form (_:_) or []
-- mkList sees that 3 /= 0, so it can pick the second case, and it
-- computes the value for ?list3.
-- (I'll skip the arithmetic reductions and other boring things.)
let ?list2 = mkList 2
list3 := 3 : ?list2 -- we don't need to compute ?list2 yet, so
-- (mkList 3) is done and we can go back to ourLast
ourLast list3@(3 : ?list2)
-- ourLast needs to examine ?list2 to find out whether it's [] or not,
-- so mkList does the same thing again
let ?list1 = mkList 1
list2 := 2 : ?list1
ourLast list3@(3 : list2@(2 : ?list1))
-- Now ourLast has enough information to continue;
-- ourLast (_ : xs@(_ : _)) = ourLast xs
-- Notice how we don't need to compute list2 a second time; we save its
-- value the first time we compute it. This is what lazy evaluation is.
ourLast list2@(2 : ?list1)
-- at this point, there are no references to `list3` anywhere, so it
-- can be GCed.
-- Repeat (ourLast examines ?list1, mkList sees that 1 /= 0).
let ?list0 = mkList 0
list1 := 1 : ?list0
ourLast list2@(2 : list1@(1 : ?list0))
ourLast list1@(1 : ?list0)
-- Can GC list2.
-- Now mkList is being called with 0, so it just returns an empty list.
list0 := []
ourLast list1@(1 : list0@[])
1
-- We're done! (And we can GC list1.)
请注意,在任何给定时间,我们只需要实际分配几个 thunk,其余的要么尚未计算,要么可以进行 GC。当我们评估时,评估在和ourLast list3
之间来回跳转(有点像协程)。ourLast
mkList
如果您想更准确地了解 Haskell 编译器的工作原理,在“分配何时以及如何发生”的级别上,以下内容很有帮助:
仅从图形简化的角度来大致了解惰性求值的工作原理——例如这篇文章——是有用的。