Haskell 哈斯凯尔树上的地图

我如何定义一个像map一样工作但在树上工作的函数？新功能的打字签名为：

data Tree a = Empty | Node a (Tree a) (Tree a)

map :: (a -> b) -> [a] -> [b]

---

甚至可以为map创建一个通用的typeclass吗？

该typeclass已经存在于Prelude:

要实现它，您可以使用语言扩展，这样GHC就可以通过

派生

子句为您实现它：

class Functor f where
    fmap :: (a -> b) -> f a -> f b

或者，您也可以手动实现它：

{-# LANGUAGE DeriveFunctor #-}

data Tree a = Empty | Node a (Tree a) (Tree a) deriving (Functor)

mapTree :: (a -> b) -> Tree a -> Tree b
mapTree = fmap

{-# LANGUAGE DeriveFunctor #-}

data Tree a = Empty | Node a (Tree a) (Tree a) deriving (Functor)

mapTree :: (a -> b) -> Tree a -> Tree b
mapTree = fmap

data Tree a = Empty | Node a (Tree a) (Tree a)

mapTree :: (a -> b) -> Tree a -> Tree b
mapTree _ Empty = Empty
mapTree f (Node x l r) = Node (f x) (mapTree f l) (mapTree f r)

instance Functor Tree where
    fmap = mapTree