http://stackoverflow.com/questions/3380347/common-recursion-pattern/16632211#16632211

gistfile1.txt

it's kind of a [paramorphism][2]. Encoded via `foldr + tails`,

    import Data.List (tails)

    foo :: (a -> b -> b) -> (a -> b) -> [a] -> b
    foo g k = foldr (\xs r -> case xs of [x] -> k x; (x:_) -> g x r) undefined
                . init . tails

Richard Bird in his 2010 book "Pearls of Functional Algorithm Design" gives it a 
special name, [`foldrn`][1], with a direct implementation which follows the usual
`foldr` implementation very closely. (I'm not copying it here because it's part of 
a copyrighted book).

 [1]: http://books.google.co.il/books?id=ZQJnYoAmw6gC&pg=PA42&lpg=PA42&dq=foldrn&source=bl&ots=7zcGAESrzM&sig=OFQVpR_-M4mOmKYnOBUXfEB4xAo&hl=en&sa=X&ei=A3aYUbKVDsLQOaqjgIAP&redir_esc=y#v=onepage&q=foldrn&f=false
 [2]: http://stackoverflow.com/questions/13317242/what-are-paramorphisms/13317563#13317563