在haskell中的二叉树上应用FOLD

Question

I have a small haskell code which implement binary tree. I want to apply a fold function on the tree. Here is the code-

data Btree a = Tip a | Bin (Btree a) (Btree a) deriving Show

foldbtree :: (a->a->a) -> Btree a-> a
foldbtree f (Tip x) = x
foldbtree f (Bin t1 t2) = (foldbtree f t1) f (foldbtree f t2)

But I am getting compilation error -

 Occurs check: cannot construct the infinite type:
      t2 = t0 -> t1 -> t2
    In the return type of a call of `foldbtree'
    Probable cause: `foldbtree' is applied to too many arguments
    In the expression: (foldbtree f t1) f (foldbtree f t2)
    In an equation for `foldbtree':
        foldbtree f (Bin t1 t2) = (foldbtree f t1) f (foldbtree f t2)

bird_exercise.hs:206:47:
    Occurs check: cannot construct the infinite type:
      t1 = t0 -> t1 -> t2
    In the return type of a call of `foldbtree'
    Probable cause: `foldbtree' is applied to too few arguments
    In the fourth argument of `foldbtree', namely `(foldbtree f t2)'
    In the expression: (foldbtree f t1) f (foldbtree f t2)

Please help me regarding this. Thank you.

Answer 1

在最后一种情况下你需要的是：

foldbtree f (Bin t1 t2) = f (foldbtree f t1) (foldbtree f t2)

Answer 2

In fact, you should probably "cheat" and let GHC derive the Foldable instance of your datatype for you automatically, using the DeriveFoldable extension:

{-# LANGUAGE DeriveFoldable #-}

module XXX where

import Data.Foldable (Foldable, foldMap)
import Data.Monoid (Sum(..))

data Btree a = Tip a | Bin (Btree a) (Btree a) deriving (Show, Foldable)

sumTips :: Btree Int -> Int
sumTips = getSum . foldMap Sum

(The relevant bits are the {-# LANGUAGE DeriveFoldable #-} pragma at the top of your .hs file and the deriving (..., Foldable, ...) clause in your datatype definition.) The fold , foldMap , etc. that come from the compiler-derived Btree instance of Foldable are almost certainly the ones you want anyway. While you're at it, you might also want to derive Functor and Traversable instances, which is done exactly as for Foldable . If you prefer, you can pass the DeriveXXX pragmas via cabal or the command line, although I like the specificity of per-file pragmas.