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Systematic Efficient Parallelization of Scan and Other List Homomorphisms
 In Annual European Conference on Parallel Processing, LNCS 1124
, 1996
"... Homomorphisms are functions which can be parallelized by the divideandconquer paradigm. A class of distributable homomorphisms (DH) is introduced and an efficient parallel implementation schema for all functions of the class is derived by transformations in the BirdMeertens formalism. The schema ..."
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Cited by 33 (7 self)
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Homomorphisms are functions which can be parallelized by the divideandconquer paradigm. A class of distributable homomorphisms (DH) is introduced and an efficient parallel implementation schema for all functions of the class is derived by transformations in the BirdMeertens formalism. The schema can be directly mapped on the hypercube with an unlimited or an arbitrary fixed number of processors, providing provable correctness and predictable performance. The popular scanfunction (parallel prefix) illustrates the presentation: the systematically derived implementation for scan coincides with the practically used "folklore" algorithm for distributedmemory machines.
The Third Homomorphism Theorem
, 1995
"... The Third Homomorphism Theorem is a folk theorem of the constructive algorithmics community. It states that a function on lists that can be computed both from left to right and from right to left is necessarily a list homomorphismit can be computed according to any parenthesization of the list. ..."
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Cited by 27 (3 self)
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The Third Homomorphism Theorem is a folk theorem of the constructive algorithmics community. It states that a function on lists that can be computed both from left to right and from right to left is necessarily a list homomorphismit can be computed according to any parenthesization of the list. We formalize and prove the theorem, and use it to improveanO#n 2 # sorting algorithm to O#n log n#. 1Introduction List homomorphisms are those functions on #nite lists that promote through list concatenationthat is, functions h for which there exists a binary operator # such that, for all #nite lists x and y , h #x ++ y# = hx#hy where `++' denotes list concatenation. Such functions are ubiquitous in functional programming. Some examples of list homomorphisms are: # the identity function id ; # the map function map f , which applies a given function f to every elementof a list; # the function concat , which concatenates a list of lists into a single long list; # the function ...
A library of constructive skeletons for sequential style of parallel programming
 In InfoScale ’06: Proceedings of the 1st international conference on Scalable information systems, volume 152 of ACM International Conference Proceeding Series
, 2006
"... With the increasing popularity of parallel programming environments such as PC clusters, more and more sequential programmers, with little knowledge about parallel architectures and parallel programming, are hoping to write parallel programs. Numerous attempts have been made to develop highlevel pa ..."
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Cited by 27 (8 self)
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With the increasing popularity of parallel programming environments such as PC clusters, more and more sequential programmers, with little knowledge about parallel architectures and parallel programming, are hoping to write parallel programs. Numerous attempts have been made to develop highlevel parallel programming libraries that use abstraction to hide lowlevel concerns and reduce difficulties in parallel programming. Among them, libraries of parallel skeletons have emerged as a promising way towards this direction. Unfortunately, these libraries are not well accepted by sequential programmers, because of incomplete elimination of lowerlevel details, adhoc selection of library functions, unsatisfactory performance, or lack of convincing application examples. This paper addresses principle of designing skeleton libraries of parallel programming and reports implementation details and practical applications of a skeleton library SkeTo. The SkeTo library is unique in its feature that it has a solid theoretical foundation based on the theory of Constructive Algorithmics, and is practical to be used to describe various parallel computations in a sequential manner. 1.
Extracting and Implementing List Homomorphisms in Parallel Program Development
 Science of Computer Programming
, 1997
"... this paper, we study functions called list homomorphisms, which represent a particular pattern of parallelism. ..."
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Cited by 14 (0 self)
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this paper, we study functions called list homomorphisms, which represent a particular pattern of parallelism.
Parallelizing Functional Programs by Generalization
 Journal of Functional Programming
, 1997
"... List homomorphisms are functions that are parallelizable using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential ..."
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Cited by 10 (1 self)
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List homomorphisms are functions that are parallelizable using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons and snoclists, respectively, there is also a representation as a homomorphism. Our contribution is a mechanizable method to extract the homomorphism representation from a pair of sequential representations. The method is decomposed to a generalization problem and an inductive claim, both solvable by term rewriting techniques. To solve the former we present a sound generalization procedure which yields the required representation, and terminates under reasonable assumptions. We illustrate the method and the procedure by the parallelization of the scanfunction (parallel prefix). The inductive claim is provable automatically.
Construction of List Homomorphisms by Tupling and Fusion
, 1996
"... List homomorphisms are functions which can be efficiently computed in parallel since they ideally suit the divideandconquer paradigm. However, some interesting functions, e.g., the maximum segment sum problem, are not list homomorphisms. In this paper, we propose a systematic way of embedding them ..."
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Cited by 5 (4 self)
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List homomorphisms are functions which can be efficiently computed in parallel since they ideally suit the divideandconquer paradigm. However, some interesting functions, e.g., the maximum segment sum problem, are not list homomorphisms. In this paper, we propose a systematic way of embedding them into list homomorphisms so that parallel programs are derived. We show, with an example, how a simple, and "obviously" correct, but possibly inefficient solution to the problem can be successfully turned into a semantically equivalent almost homomorphism by means of two transformations: tupling and fusion.
Parallelizing Functional Programs by Term Rewriting
, 1997
"... List homomorphisms are functions that can be computed in parallel using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward se ..."
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Cited by 2 (2 self)
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List homomorphisms are functions that can be computed in parallel using the divideandconquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the BirdMeertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons and snoclists, respectively, there is also a representation as a homomorphism. Our contribution is a mechanizable method to extract the homomorphism representation from a pair of sequential representations. The method is decomposed to a generalization problem and an inductive claim, both solvable by term rewriting techniques. To solve the former we present a sound generalization procedure which yields the required representation, and terminates under reasonable assumptions. We illustrate the method and the procedure by the parallelization of the scanfunction (parallel prefix). The inductive claim is provable automatically. Keywords: P...
A Calculational Framework for Parallelization of Sequential Programs
 In International Symposium on Information Systems and Technologies for Network Society
, 1997
"... this paper, we propose ..."
List Homomorphism with Accumulation
 In Proceedings of Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD
, 2003
"... This paper introduces accumulation into list homomorphisms for systematic development of both efficient and correct parallel programs. New parallelizable recursive pattern called is given, and transformations from sequential patterns in the form into (H)homomorphism are shown. We illustrate ..."
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Cited by 1 (0 self)
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This paper introduces accumulation into list homomorphisms for systematic development of both efficient and correct parallel programs. New parallelizable recursive pattern called is given, and transformations from sequential patterns in the form into (H)homomorphism are shown. We illustrate the power of our formalization by developing a novel and general parallel program for a class of interesting and challenging problems, known as maximum marking problems. 1.