如何在Haskell中实现B +树？

这是(不可变/"可变" - 重构/可拉伸)ADT表示(涉及不可变向量)的想法:

module Data.BTree.Internal where

import Data.Vector

type Values v = Vector v

type Keys k = Vector k

data Leaf k v
  = Leaf
    { _leafKeys   :: !(Keys k)
    , _leafValues :: !(Values v)
    , _leafNext   :: !(Maybe (Leaf k v)) -- @Maybe@ is lazy in @Just@, so this strict mark
                                         -- is ok for tying-the-knot stuff.
    -- , _leafPrev   :: !(Maybe (Leaf k v))
    -- ^ for doubly-linked lists of leaves
    }

type Childs k v = Vector (BTree k v)

data Node k v
  = Node
    { _nodeKeys   :: !(Keys k)
    , _nodeChilds :: !(Childs k v)
    }

data BTree k v
  = BTreeNode !(Node k v)
  | BTreeLeaf !(Leaf k v)

newtype BTreeRoot k v
  = BTreeRoot (BTree k v)

这应该是内部的,因此不正确使用原始构造函数,访问器或模式匹配不会破坏树.

Keys,Values,Childs长度控制可以添加(与运行时检查或可能与GADTs并且这样的).

对于一个界面:

module Data.BTree ( {- appropriate exports -} ) where

import Data.Vector
import Data.BTree.Internal

-- * Building trees: "good" constructors.

keys :: [k] -> Keys k
keys = fromList

values :: [v] -> Values v
values = fromList

leaves :: [Leaf k v] -> Childs k v
leaves = fromList . fmap BTreeLeaf

leaf :: Keys k -> Values v -> Maybe (Leaf k v) -> Leaf k v
-- or
-- leaf :: Keys k -> Values v -> Maybe (Leaf k v) -> Maybe (Leaf k v) -> Leaf k v
-- for doubly-linked lists of leaves
leaf = Leaf

node :: Keys k -> Childs k v -> BTree k v
node ks = BTreeNode . Node ks

-- ...

-- * "Good" accessors.

-- ...

-- * Basic functions: insert, lookup, etc.

-- ...

那么这种树:

可以建成

test :: BTree Int ByteString
test = let
  root  = node (keys [3, 5]) (leaves [leaf1, leaf2, leaf3])
  leaf1 = leaf (keys [1, 2]) (values ["d1", "d2"]) (Just leaf2)
  leaf2 = leaf (keys [3, 4]) (values ["d3", "d4"]) (Just leaf3)
  leaf3 = leaf (keys [5, 6, 7]) (values ["d5", "d6", "d7"]) Nothing
  in root

这种技术被称为"打结".叶子可循环使用:

  leaf1 = leaf (keys [1, 2]) (values ["d1", "d2"]) (Just leaf2)
  leaf2 = leaf (keys [3, 4]) (values ["d3", "d4"]) (Just leaf3)
  leaf3 = leaf (keys [5, 6, 7]) (values ["d5", "d6", "d7"]) (Just leaf1)

或双重链接(假设_leafPrev和相应的leaf功能):

  leaf1 = leaf (keys [1, 2]) (values ["d1", "d2"]) (Just leaf2) (Just leaf3)
  leaf2 = leaf (keys [3, 4]) (values ["d3", "d4"]) (Just leaf3) (Just leaf1)
  leaf3 = leaf (keys [5, 6, 7]) (values ["d5", "d6", "d7"]) (Just leaf1) (Just leaf2)

使用可变载体和可变引用也可以完全可变的表示:

type Values v = IOVector v

type Keys k = IOVector k

type Childs k v = IOVector (BTree k v)

    , _leafNext   :: !(IORef (Maybe (Leaf k v)))

等等,基本相同,但使用IORef和IOVector,在IOmonad 工作.