# Zipper monad

### From HaskellWiki

The Travel Monad is a generic monad for navigating around arbitrary data structures. It supports movement, mutation and classification of nodes (is this node the top node or a child node?, etc). It was proposed and designed by Paolo Martini (xerox), and coded by David House (davidhouse). It's designed for use with The Zipper but in fact there is no requirement to use such an idiom.

At the moment there are two specific libraries that use the Travel monad: TravelTree for navigating around binary trees, and TravelBTree for navigating around "B-Trees", trees where each node has an arbitrary number of branches.

## Contents |

## 1 Definition

data Loc c a = Loc { struct :: a, cxt :: c } deriving (Show, Eq) newtype Travel loc a = Travel { unT :: State loc a } deriving (Functor, Monad, MonadState loc, Eq)

## 2 Functions

### 2.1 Movement

At the moment, movement is specific to the structure you are traversing and as such, the movement functions are provided by libraries implementing specific structures. Try the documentation for TravelTree (binary trees) or TravelBTree (B-Trees; trees where each node has an arbitrary number of branches).

### 2.2 Mutation

There are three generic functions available for changing the structure:

getStruct :: Travel (Loc c a) a putStruct :: a -> Travel (Loc c a) a modifyStruct :: (a -> a) -> Travel (Loc c a) a

### 2.3 Exit points

To get out of the monad, usetraverse :: Loc c a -- starting location (initial state) -> Travel (Loc c a) a -- locational computation to use -> a -- resulting substructure

let t = Branch (Leaf 1) (Branch (Leaf 2) (Leaf 3)) in (getTop t) `traverse` (left >> swap >> right)

## 3 Examples

- TravelTree for binary trees.
- TravelBTree for B-Trees; trees where each node has an arbitrary number of branches.

## 4 Code

Here's the base Zipper monad in full (download):

{-# OPTIONS_GHC -fglasgow-exts #-} module Zipper where -- A monad implementing for traversing data structures -- http://haskell.org/haskellwiki/Zipper_monad -------------------------------------------------------------------------------- import Control.Monad.State data Loc c a = Loc { struct :: a, cxt :: c } deriving (Show, Eq) newtype Travel loc a = Travel { unT :: State loc a } deriving (Functor, Monad, MonadState loc, Eq) -- Exit Points -- -- get out of the monad traverse :: Loc c a -- starting location (initial state) -> Travel (Loc c a) a -- locational computation to use -> a -- resulting substructure traverse start tt = evalState (unT tt) start -- Mutation -- -- modify the substructure at the current node modifyStruct :: (a -> a) -> Travel (Loc c a) a modifyStruct f = modify editStruct >> liftM struct get where editStruct (Loc s c) = Loc (f s) c -- put a new substructure at the current node putStruct :: a -> Travel (Loc c a) a putStruct t = modifyStruct $ const t -- get the current substructure getStruct :: Travel (Loc c a) a getStruct = modifyStruct id -- works because modifyTree returns the 'new' tree