Difference between revisions of "Zipper monad"
DavidHouse (talk | contribs) m (fix up code/hask mismatches) |
(Added ref to the generic zipper.) |
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+ | The Zipper 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 [[Zipper|The Zipper]] but in fact there is no requirement to use such an idiom. |
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+ | At the moment there are two specific libraries that use the Travel monad: [[Zipper_monad/TravelTree|TravelTree]] for navigating around binary trees, and [[Zipper_monad/TravelBTree|TravelBTree]] for navigating around "B-Trees", trees where each node has an arbitrary number of branches. Please see below for an alternative zipper implementation that works for any data structure whatsoever. |
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− | The TravelTree Monad is a monad proposed and designed by Paolo Martini (xerox), and coded by David House (davidhouse). It is based on the State monad and is used for navigating around in binary trees, using the concept of [[TheZipper]]. |
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+ | You can [http://haskell.org/sitewiki/images/b/b7/Zipper.tar.gz download] the library in its entirety. To run the tests: |
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− | == Definition == |
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− | <haskell> |
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− | newtype Travel t a = Travel { unT :: State t a } |
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− | deriving (Functor, Monad, MonadState t) |
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− | type TravelTree a = Travel (Loc a) (Tree a) |
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− | </haskell> |
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+ | tar xzf Zipper.tar.gz |
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− | Computations in <hask>TravelTree</hask> are stateful. <hask>Loc a</hask> and <hask>Tree a</hask> are defined as follows: |
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+ | cd Zipper |
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+ | ghc -o test --make Main.hs |
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+ | ./test |
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+ | == Definition == |
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<haskell> |
<haskell> |
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− | data |
+ | data Loc c a = Loc { struct :: a, |
+ | cxt :: c } |
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− | |||
+ | deriving (Show, Eq) |
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− | data Cxt a = Top |
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− | | L (Cxt a) (Tree a) |
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− | | R (Tree a) (Cxt a) |
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− | deriving (Show) |
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+ | newtype Travel loc a = Travel { unT :: State loc a } |
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− | type Loc a = (Tree a, Cxt a) |
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+ | deriving (Functor, Monad, MonadState loc, Eq) |
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</haskell> |
</haskell> |
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+ | Computations in <hask>Travel</hask> are stateful. <hask>Loc c a</hask> is a type for storing the location within a structure. <hask>struct</hask> should be the substructure that the <hask>Loc</hask> is refering to, and <hask>cxt</hask> the "context" of the substructure; i.e. the rest of the structure. <hask>Loc</hask> is designed to hold a [[Zipper]] (although it doesn't have to; for example if you wanted to traverse a list it would probably be more natural to hold the entire structure and an index). Indeed, both of the libraries provided with the generic <hask>Travel</hask> monad use a zipper. |
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− | See [[TheZipper]] for an explanation of the <hask>Cxt</hask> and <hask>Loc</hask> concepts. |
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== Functions == |
== Functions == |
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− | === Moving around === |
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− | There are four main functions for stringing together <hask>TravelTree</hask> computations: |
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+ | === Movement === |
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− | <haskell> |
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+ | 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 [[Zipper_monad/TravelTree|TravelTree]] (binary trees) or [[Zipper_monad/TravelBTree|TravelBTree]] (B-Trees; trees where each node has an arbitrary number of branches). |
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− | left, -- moves down a level, through the left branch |
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− | right, -- moves down a level, through the right branch |
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− | up, -- moves to the node's parent |
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− | top -- moves to the top node |
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− | :: TravelTree a |
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− | </haskell> |
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− | |||
− | All four return the subtree at the new location. |
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=== Mutation === |
=== Mutation === |
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− | There are |
+ | There are three generic functions available for changing the structure: |
<haskell> |
<haskell> |
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− | + | getStruct :: Travel (Loc c a) a |
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− | + | putStruct :: a -> Travel (Loc c a) a |
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− | + | modifyStruct :: (a -> a) -> Travel (Loc c a) a |
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</haskell> |
</haskell> |
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− | These are direct front-doors for State's <hask>get</hask>, <hask>put</hask> and <hask>modify</hask>, and all three return the |
+ | These are direct front-doors for State's <hask>get</hask>, <hask>put</hask> and <hask>modify</hask>, and all three return the substructure after any applicable modifications. |
=== Exit points === |
=== Exit points === |
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<haskell> |
<haskell> |
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− | traverse :: |
+ | traverse :: Loc c a -- starting location (initial state) |
+ | -> Travel (Loc c a) a -- locational computation to use |
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+ | -> a -- resulting substructure |
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</haskell> |
</haskell> |
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− | Again, this is just a front-door for <hask>evalState</hask> |
+ | Again, this is just a front-door for <hask>evalState</hask>. Note that you have to give a <hask>Loc</hask> as a starting state. Both the libraries provided supply a <hask>getTop</hask> function, which takes a tree and returns the <hask>Loc</hask> corresponding to the top of the tree. Thus a typical call to <hask>traverse</hask> might look like: |
− | |||
− | == Examples == |
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− | The following examples use as the example tree: |
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<haskell> |
<haskell> |
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− | t = Branch ( |
+ | let t = Branch (Leaf 1) (Branch (Leaf 2) (Leaf 3)) |
+ | in (getTop t) `traverse` (left >> swap >> right) |
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− | (Leaf 3)) |
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− | (Branch (Leaf 4) |
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− | (Leaf 5)) |
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</haskell> |
</haskell> |
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+ | == Examples == |
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− | [[Image:Tree.png|frame|right|The example tree]] |
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+ | |||
+ | <hask>Travel</hask> is too general to be used in itself, so there are examples given on the documentation pages for the libraries. Here are the links again: |
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+ | |||
+ | * [[Zipper_monad/TravelTree|TravelTree]] for binary trees. |
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+ | * [[Zipper_monad/TravelBTree|TravelBTree]] for B-Trees; trees where each node has an arbitrary number of branches. |
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== Code == |
== Code == |
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+ | |||
+ | Here's the base Zipper monad in full ([http://haskell.org/sitewiki/images/3/36/Zipper.hs download] or download the [http://haskell.org/sitewiki/images/b/b7/Zipper.tar.gz entire library]): |
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<haskell> |
<haskell> |
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+ | {-# OPTIONS_GHC -fglasgow-exts #-} |
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− | data Cxt a = Top |
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+ | module Zipper where |
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− | | L (Cxt a) (Tree a) |
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− | | R (Tree a) (Cxt a) |
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− | deriving (Show) |
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+ | -- A monad implementing for traversing data structures |
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− | type Loc a = (Tree a, Cxt a) |
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+ | -- http://haskell.org/haskellwiki/Zipper_monad |
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+ | -------------------------------------------------------------------------------- |
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+ | import Control.Monad.State |
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− | newtype Travel t a = Travel { unT :: State t a } |
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− | deriving (Functor, Monad, MonadState t) |
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− | type TravelTree a = Travel (Loc a) (Tree a) |
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+ | data Loc c a = Loc { struct :: a, |
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− | t = Branch (Branch (Branch (Leaf 1) (Leaf 2)) |
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− | + | cxt :: c } |
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− | + | deriving (Show, Eq) |
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− | (Leaf 5)) |
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+ | newtype Travel loc a = Travel { unT :: State loc a } |
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− | left :: TravelTree a |
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+ | deriving (Functor, Monad, MonadState loc, Eq) |
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− | left = modify left' >> liftM fst get where |
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− | left' (Branch l r, c) = (l, L c r) |
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+ | -- Exit Points |
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− | right :: TravelTree a |
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+ | -- |
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− | right = modify right' >> liftM fst get where |
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− | right' (Branch l r, c) = (r, R l c) |
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+ | -- get out of the monad |
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− | up :: TravelTree a |
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+ | traverse :: Loc c a -- starting location (initial state) |
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− | up = modify up' >> liftM fst get where |
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− | + | -> Travel (Loc c a) a -- locational computation to use |
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+ | -> a -- resulting substructure |
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− | up' (t, R l c) = (Branch l t, c) |
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+ | traverse start tt = evalState (unT tt) start |
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+ | -- Mutation |
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− | top :: TravelTree a |
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+ | -- |
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− | top = modify (second $ const Top) >> liftM fst get |
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+ | -- modify the substructure at the current node |
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− | modifyTree :: (Tree a -> Tree a) -> TravelTree a |
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+ | modifyStruct :: (a -> a) -> Travel (Loc c a) a |
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− | modifyTree f = modify (first f) >> liftM fst get |
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+ | modifyStruct f = modify editStruct >> liftM struct get where |
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+ | editStruct (Loc s c) = Loc (f s) c |
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+ | -- put a new substructure at the current node |
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− | putTree :: Tree a -> TravelTree a |
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+ | putStruct :: a -> Travel (Loc c a) a |
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− | putTree t = modifyTree $ const t |
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+ | putStruct t = modifyStruct $ const t |
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+ | -- get the current substructure |
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− | getTree :: TravelTree a |
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+ | getStruct :: Travel (Loc c a) a |
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− | getTree = modifyTree id -- works because modifyTree returns the 'new' tree |
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+ | getStruct = modifyStruct id -- works because modifyTree returns the 'new' tree |
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+ | </haskell> |
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+ | == Alternative implementation == |
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− | traverse :: Tree a -> TravelTree a -> Tree a |
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− | traverse t tt = evalState (unT tt) (t, Top) |
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+ | An alternative implementation, which is polymorphic over data structures |
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− | leftLeftRight :: TravelTree a |
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+ | and so can be written once and for all, is available at |
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− | leftLeftRight = do left |
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+ | [http://pobox.com/~oleg/ftp/Computation/Continuations.html#zipper Generic Zipper and its applications] |
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− | left |
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+ | The code on that page served as the basis for a Zipper-based file system. |
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− | right |
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+ | [[Category:Idioms]] |
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− | revTreeZipper :: Tree a -> Tree a |
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+ | [[Category:Monad]] |
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− | revTreeZipper t = t `traverse` revTreeZipper' where |
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− | revTreeZipper' :: TravelTree a |
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− | revTreeZipper' = do t <- getTree |
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− | case t of |
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− | Branch _ _ -> do left |
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− | l' <- revTreeZipper' |
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− | up |
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− | right |
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− | r' <- revTreeZipper' |
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− | up |
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− | putTree $ Branch r' l' |
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− | Leaf x -> return $ Leaf x |
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− | </haskell> |
Latest revision as of 01:00, 9 October 2006
The Zipper 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. Please see below for an alternative zipper implementation that works for any data structure whatsoever.
You can download the library in its entirety. To run the tests:
tar xzf Zipper.tar.gz cd Zipper ghc -o test --make Main.hs ./test
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)
Computations in Travel
are stateful. Loc c a
is a type for storing the location within a structure. struct
should be the substructure that the Loc
is refering to, and cxt
the "context" of the substructure; i.e. the rest of the structure. Loc
is designed to hold a Zipper (although it doesn't have to; for example if you wanted to traverse a list it would probably be more natural to hold the entire structure and an index). Indeed, both of the libraries provided with the generic Travel
monad use a zipper.
Functions
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).
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
These are direct front-doors for State's get
, put
and modify
, and all three return the substructure after any applicable modifications.
Exit points
To get out of the monad, use traverse
:
traverse :: Loc c a -- starting location (initial state)
-> Travel (Loc c a) a -- locational computation to use
-> a -- resulting substructure
Again, this is just a front-door for evalState
. Note that you have to give a Loc
as a starting state. Both the libraries provided supply a getTop
function, which takes a tree and returns the Loc
corresponding to the top of the tree. Thus a typical call to traverse
might look like:
let t = Branch (Leaf 1) (Branch (Leaf 2) (Leaf 3))
in (getTop t) `traverse` (left >> swap >> right)
Examples
Travel
is too general to be used in itself, so there are examples given on the documentation pages for the libraries. Here are the links again:
- TravelTree for binary trees.
- TravelBTree for B-Trees; trees where each node has an arbitrary number of branches.
Code
Here's the base Zipper monad in full (download or download the entire library):
{-# 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
Alternative implementation
An alternative implementation, which is polymorphic over data structures and so can be written once and for all, is available at Generic Zipper and its applications The code on that page served as the basis for a Zipper-based file system.