Zipper monad/TravelBTree

< Zipper monad

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TravelBTree is a library based on the Zipper monad which is used for traversing B-trees; trees where each node has an arbitrary number of branches. Read the documentation for the Zipper monad if you haven't already.

Contents 1 Definition 2 Functions 2.1 Moving around 2.2 Mutation 2.3 Node classification 3 Examples 4 Code

1 Definition

data BTree a = Leaf a | Branch [BTree a] deriving (Show, Eq)
 
data Cxt a = Top | Child { parent :: Cxt a,     -- parent's context
                           lefts  :: [BTree a], -- siblings to the left
                           rights :: [BTree a]  -- siblings to the right
                         }
           deriving (Show, Eq)
 
type BTreeLoc    a = Loc (Cxt a) (BTree a)
type TravelBTree a = Travel (BTreeLoc a) (BTree a)

The BTree type is fairly self-explanatory. Branch must be given a list of its children. Cxt is the type used for storing the context of a subtree. A BTreeLoc represents completely a subtree, said subtrees position within the entire tree, and the entire tree itself. See Zipper for an explanation of such concepts.

2 Functions

2.1 Moving around

There are five main functions for stringing together TravelBTree computations:

-- moves down to the nth child (0-indexed)
down :: Int -> TravelBTree a
left,  -- moves left a sibling
right, -- moves right a sibling
up,    -- moves to the node's parent
top    -- moves to the top node
:: TravelTree a

All five return the subtree at the new location. Note that down uses 0-indexed children, i.e. down 0 goes down to the first child. This is consistent with the list-access operator, (!!).

2.2 Mutation

You get the three functions provided by the generic Zipper monad (modifyStruct, getStruct and putStruct), but there's also a load of TravelBTree-specific mutation functions:

insertLeft,  -- insert a tree to the left of the current node
insertRight, -- insert a tree to the right of the current node
insertDown   -- insert a tree as the last child of the current node
:: BTree a -> TravelBTree a
insertDownAt -- insert a tree as the nth child of the current node
:: BTree a -> Int -> TravelBTree a 
-- delete the current node. If we're the last node of our siblings, move left.
-- If not, move right. If we're an only child move up.
delete :: TravelBTree a

2.3 Node classification

There are four functions you can call to find out what kind of node a given location points to:

isTop,   -- is the location the top node?
isChild, -- is the location the child of some other node (i.e. not the top)?
isFirst, -- is the location the first of its siblings?
isRight  -- is the location the last of its siblings?
:: TreeLoc a -> Bool

Note that these functions are not monadic but instead take a TreeBLoc. The TreeBLoc pointing to the current node is stored as the state in a TravelBTree computation. Thus to call these functions within a do block, use liftM:

do top <- liftM isTop get
   when top $ down 3 >> return ()

3 Examples

Watch this space.

4 Code

The code of this file is quite length, so you can just download it. Alternatively, download the entire zipper library.

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