hn-classics/_stories/2006/13263038.md

created_at	title	url	author	points	story_text	comment_text	num_comments	story_id	story_title	story_url	parent_id	created_at_i	_tags	objectID	year
2016-12-27T13:36:08.000Z	Finger Trees: A Simple General-Purpose Data Structure (2006)	http://www.staff.city.ac.uk/~ross/papers/FingerTree.html	tosh	267			75					1482845768	story author_tosh story_13263038	13263038	2006

Finger Trees: A Simple General-purpose Data Structure

Ralf Hinze and Ross Paterson, Journal of Functional Programming 16(2):197–217, 2006. doi:10.1017/S0956796805005769

Summary

We present 2-3 finger trees, a functional representation of persistent sequences supporting access to the ends in amortized constant time, and concatenation and splitting in time logarithmic in the size of the smaller piece. Representations achieving these bounds have appeared previously, but 2-3 finger trees are much simpler, as are the operations on them. Further, by defining the split operation in a general form, we obtain a general purpose data structure that can serve as a sequence, priority queue, search tree, priority search queue and more.

The basic structure is expressed as a non-regular (or nested) type:

data FingerTree a = Empty
                  | Single a
                  | Deep (Digit a) (FingerTree (Node a)) (Digit a)

data Digit a = One a | Two a a | Three a a a | Four a a a a
data Node a = Node2 a a | Node3 a a a

This produces trees of 2-3 trees, with favoured access (fingers) at the ends, like

(more examples) and also supports efficient concatenation. To support splitting and searching, we annotate the internal nodes of the tree with values drawn from an application-specific monoid.

• PDF, gzipped PostScript, BibTeX.
• A sequence implementation based on the application discussed in section 4.2 is included as a module Data.Sequence in the Glasgow Haskell Compiler and other Haskell implementations. Note: The class Reduce in the paper is replaced by the class Foldable.
• The fingertree package is a generic finger tree structure, for use as a base for various container types.