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Adaptive Functional Programming
 IN PROCEEDINGS OF THE 29TH ANNUAL ACM SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 2001
"... An adaptive computation maintains the relationship between its input and output as the input changes. Although various techniques for adaptive computing have been proposed, they remain limited in their scope of applicability. We propose a general mechanism for adaptive computing that enables one to ..."
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Cited by 64 (23 self)
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An adaptive computation maintains the relationship between its input and output as the input changes. Although various techniques for adaptive computing have been proposed, they remain limited in their scope of applicability. We propose a general mechanism for adaptive computing that enables one to make any purelyfunctional program adaptive. We show
Marked Ancestor Problems
, 1998
"... Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the wellknown predecessor problem, where the tree is a path. ..."
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Cited by 52 (7 self)
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Consider a rooted tree whose nodes can be marked or unmarked. Given a node, we want to find its nearest marked ancestor. This generalises the wellknown predecessor problem, where the tree is a path.
Dynamizing static algorithms with applications to dynamic trees and history independence
 In ACMSIAM Symposium on Discrete Algorithms (SODA
, 2004
"... We describe a machine model for automatically dynamizing static algorithms and apply it to historyindependent data structures. Static programs expressed in this model are dynamized automatically by keeping track of dependences between code and data in the form of a dynamic dependence graph. To study ..."
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Cited by 43 (26 self)
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We describe a machine model for automatically dynamizing static algorithms and apply it to historyindependent data structures. Static programs expressed in this model are dynamized automatically by keeping track of dependences between code and data in the form of a dynamic dependence graph. To study the performance of such automatically dynamized algorithms we present an analysis technique based on trace stability. As an example of the use of the model, we dynamize the Parallel Tree Contraction Algorithm of Miller and Reif to obtain a historyindependent data structure for the dynamic trees problem of Sleator and Tarjan. 1
Functional Programming with Graphs
 2ND ACM SIGPLAN INT. CONF. ON FUNCTIONAL PROGRAMMING
, 1997
"... Graph algorithms expressed in functional languages often suffer from their inherited imperative, statebased style. In particular, this impedes formal program manipulation. We show how to model persistent graphs in functional languages by graph constructors. This provides a decompositional view of g ..."
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Cited by 29 (10 self)
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Graph algorithms expressed in functional languages often suffer from their inherited imperative, statebased style. In particular, this impedes formal program manipulation. We show how to model persistent graphs in functional languages by graph constructors. This provides a decompositional view of graphs which is very close to that of data types and leads to a "more functional" formulation of graph algorithms. Graph constructors enable the definition of general fold operations for graphs. We present a promotion theorem for one of these folds that allows program fusion and the elimination of intermediate results. Fusion is not restricted to the elimination of treelike structures, and we prove another theorem that facilitates the elimination of intermediate graphs. We describe an MLimplementation of persistent graphs which efficiently supports the presented fold operators. For example, depthfirstsearch expressed by a fold over a functional graph has the same complexity as the corresp...
Purely Functional RandomAccess Lists
 In Functional Programming Languages and Computer Architecture
, 1995
"... We present a new data structure, called a randomaccess list, that supports array lookup and update operations in O(log n) time, while simultaneously providing O(1) time list operations (cons, head, tail). A closer analysis of the array operations improves the bound to O(minfi; log ng) in the wor ..."
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Cited by 17 (2 self)
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We present a new data structure, called a randomaccess list, that supports array lookup and update operations in O(log n) time, while simultaneously providing O(1) time list operations (cons, head, tail). A closer analysis of the array operations improves the bound to O(minfi; log ng) in the worst case and O(log i) in the expected case, where i is the index of the desired element. Empirical evidence suggests that this data structure should be quite efficient in practice. 1 Introduction Lists are the primary data structure in every functional programmer 's toolbox. They are simple, convenient, and usually quite efficient. The main drawback of lists is that accessing the ith element requires O(i) time. In such situations, functional programmers often find themselves longing for the efficient random access of arrays. Unfortunately, arrays can be quite awkward to implement in a functional setting, where previous versions of the array must be available even after an update. Since arra...
Purely Functional Representations of Catenable Sorted Lists.
 In Proceedings of the 28th Annual ACM Symposium on Theory of Computing
, 1996
"... The power of purely functional programming in the construction of data structures has received much attention, not only because functional languages have many desirable properties, but because structures built purely functionally are automatically fully persistent: any and all versions of a structur ..."
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Cited by 16 (5 self)
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The power of purely functional programming in the construction of data structures has received much attention, not only because functional languages have many desirable properties, but because structures built purely functionally are automatically fully persistent: any and all versions of a structure can coexist indefinitely. Recent results illustrate the surprising power of pure functionality. One such result was the development of a representation of doubleended queues with catenation that supports all operations, including catenation, in worstcase constant time [19].
Inductive Graphs and Functional Graph Algorithms
, 2001
"... We propose a new style of writing graph algorithms in functional languages which is based on an alternative view of graphs as inductively defined data types. We show how this graph model can be implemented efficiently, and then we demonstrate how graph algorithms can be succinctly given by recursive ..."
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Cited by 16 (2 self)
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We propose a new style of writing graph algorithms in functional languages which is based on an alternative view of graphs as inductively defined data types. We show how this graph model can be implemented efficiently, and then we demonstrate how graph algorithms can be succinctly given by recursive function definitions based on the inductive graph view. We also regard this as a contribution to the teaching of algorithms and data structures in functional languages since we can use the functionalstyle graph algorithms instead of the imperative algorithms that are dominant today. Keywords: Graphs in Functional Languages, Recursive Graph Algorithms, Teaching Graph Algorithms in Functional Languages
Purely Functional, RealTime Deques with Catenation
 Journal of the ACM
, 1999
"... We describe an efficient, purely functional implementation of deques with catenation. In addition to being an intriguing problem in its own right, finding a purely functional implementation of catenable deques is required to add certain sophisticated programming constructs to functional programming ..."
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Cited by 13 (2 self)
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We describe an efficient, purely functional implementation of deques with catenation. In addition to being an intriguing problem in its own right, finding a purely functional implementation of catenable deques is required to add certain sophisticated programming constructs to functional programming languages. Our solution has a worstcase running time of O(1) for each push, pop, inject, eject and catenation. The best previously known solution has an O(log k) time bound for the k deque operation. Our solution is not only faster but simpler. A key idea used in our result is an algorithmic technique related to the redundant digital representations used to avoid carry propagation in binary counting.
Simple Confluently Persistent Catenable Lists
 SIAM JOURNAL ON COMPUTING
, 1998
"... We consider the problem of maintaining persistent lists subject to concatenation and to insertions and deletions at both ends. Updates to a persistent data structure are nondestructive  each operation produces a new list incorporating the change, while keeping intact the list or lists to which it a ..."
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Cited by 11 (2 self)
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We consider the problem of maintaining persistent lists subject to concatenation and to insertions and deletions at both ends. Updates to a persistent data structure are nondestructive  each operation produces a new list incorporating the change, while keeping intact the list or lists to which it applies. Although general techniques exist for making data structures persistent, these techniques fail for structures that are subject to operations, such as catenation, that combine two or more versions. In this paper we develop a simple implementation of persistent doubleended queues with catenation that supports all deque operations in constant amortized time. Our implementation is functional if we allow memoization.
Making Data Structures Confluently Persistent
, 2001
"... We address a longstanding open problem of [10, 9], and present a general transformation that transforms any pointer based data structure to be confluently persistent. Such transformations for fully persistent data structures are given in [10], greatly improving the performance compared to the naive ..."
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Cited by 10 (0 self)
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We address a longstanding open problem of [10, 9], and present a general transformation that transforms any pointer based data structure to be confluently persistent. Such transformations for fully persistent data structures are given in [10], greatly improving the performance compared to the naive scheme of simply copying the inputs. Unlike fully persistent data structures, where both the naive scheme and the fully persistent scheme of [10] are feasible, we show that the naive scheme for confluently persistent data structures is itself infeasible (requires exponential space and time). Thus, prior to this paper there was no feasible method for implementing confluently persistent data structures at all. Our methods give an exponential reduction in space and time compared to the naive method, placing confluently persistent data structures in the realm of possibility.