Data.FDList

Haskell98

http://okmij.org/ftp/Algorithms.html#pure-cyclic-list

Pure functional, mutation-free, constant-time-access double-linked lists

Note that insertions, deletions, lookups have a worst-case complexity of O(min(n,W)), where W is either 32 or 64 (depending on the paltform). That means the access time is bounded by a small constant (32 or 64).

Pure functional, mutation-free, efficient double-linked lists

It is always an interesting challenge to write a pure functional and efficient implementation of an imperative algorithm destructively operating a data structure. The functional implementation has a significant benefit of equational reasoning and modularity. We can comprehend the algorithm without keeping the implicit global state in mind. The mutation-free, functional realization has practical benefits: the ease of adding checkpointing, undo and redo. The absence of mutations makes the code multi-threading-safe and helps in porting to distributed or non-shared-memory parallel architectures. On the other hand, an imperative implementation has the advantage of optimality: mutating a component in a complex data structure is a constant-time operation, at least on conventional architectures. Imperative code makes sharing explicit, and so permits efficient implementation of cyclic data structures.

We show a simple example of achieving all the benefits of an imperative data structure -- including sharing and the efficiency of updates -- in a pure functional program. Our data structure is a doubly-linked, possibly cyclic list, with the standard operations of adding, deleting and updating elements; traversing the list in both directions; iterating over the list, with cycle detection. The code:

 uniformly handles both cyclic and terminated lists;  does not rebuild the whole list on updates;  updates the value in the current node in time bound by a small constant;  does not use or mention any monads;  does not use any IORef, STRef, TVars, or any other destructive updates;  permits the logging, undoing and redoing of updates, checkpointing;  easily generalizes to two-dimensional meshes.

The algorithm is essentially imperative, thus permitting identity checking and in-place updates, but implemented purely functionally. Although the code uses many local, type safe heaps, there is emphatically no global heap and no global state.

Version: The current version is 1.2, Jan 7, 2009.

References

Haskell-Cafe discussion ``Updating doubly linked lists''. January 2009

Documentation

type Ref = Int

Representation of the double-linked list

data Node a

Constructors

Node

Fields

node_val :: a

node_left :: Ref

node_right :: Ref

data DList a

Because DList contains the pointer to the current element, DList is also a Zipper

Constructors

DList

Fields

dl_counter :: Ref

dl_current :: Ref

dl_mem :: IntMap (Node a)

empty :: DList a

Operations on the DList a

well_formed :: DList a -> Bool

In a well-formed list, dl_current must point to a valid node All operations below preserve well-formedness

is_empty :: DList a -> Bool

get_curr_node :: DList a -> Node a

auxiliary function

insert_right :: a -> DList a -> DList a

The insert operation below makes a cyclic list The other operations don't care Insert to the right of the current element, if any Return the DL where the inserted node is the current one

delete :: DList a -> DList a

Delete the current element from a non-empty list We can handle both cyclic and terminated lists The right node becomes the current node. If the right node does not exists, the left node becomes current

get_curr :: DList a -> a

move_right :: DList a -> Maybe (DList a)

move_right' :: DList a -> DList a

If no right, just stay inplace

move_left :: DList a -> Maybe (DList a)

move_left' :: DList a -> DList a

If no left, just stay inplace

fromList :: [a] -> DList a

takeDL :: Int -> DList a -> [a]

The following does not anticipate cycles (deliberately)

takeDLrev :: Int -> DList a -> [a]

Reverse taking: we move left

update :: a -> DList a -> DList a

Update the current node inplace

toList :: DList a -> [a]

This one watches for a cycle and terminates when it detects one