`foldr` 和 `foldl` 的定义中使用了哪些类型的递归？

Question

foldr   ::  (a  ->  b   ->  b)  ->  b   ->  [a] ->  b
foldr   f   v   [] =    v
foldr   f   v   (x:xs)  =   f   x   (foldr  f   v   xs)

and和

foldl   ::  (a  ->  b   ->  a)  ->  a   ->  [b] ->  a
foldl   f   v   [] =    v
foldl   f   v   (x:xs)  =   foldl   f   (f  v   x)  xs

seem to use different kinds of recursions.似乎使用不同种类的递归。

What kinds of recursions are used in the definitions of foldr and foldl ? foldr和foldl的定义中使用了哪些递归？

Thanks.谢谢。

Answer 1

foldl uses tail recursion. foldl使用尾递归。

foldr uses guarded recursion , the recursion being guarded by f 's laziness (if any). foldr使用受保护的递归，递归由f的懒惰（如果有）保护。