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26
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 26 (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.
Generic Downwards Accumulations
 Science of Computer Programming
, 2000
"... . A downwards accumulation is a higherorder operation that distributes information downwards through a data structure, from the root towards the leaves. The concept was originally introduced in an ad hoc way for just a couple of kinds of tree. We generalize the concept to an arbitrary regular d ..."
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Cited by 19 (3 self)
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. A downwards accumulation is a higherorder operation that distributes information downwards through a data structure, from the root towards the leaves. The concept was originally introduced in an ad hoc way for just a couple of kinds of tree. We generalize the concept to an arbitrary regular datatype; the resulting denition is coinductive. 1 Introduction The notion of scans or accumulations on lists is well known, and has proved very fruitful for expressing and calculating with programs involving lists [4]. Gibbons [7, 8] generalizes the notion of accumulation to various kinds of tree; that generalization too has proved fruitful, underlying the derivations of a number of tree algorithms, such as the parallel prex algorithm for prex sums [15, 8], Reingold and Tilford's algorithm for drawing trees tidily [21, 9], and algorithms for query evaluation in structured text [16, 23]. There are two varieties of accumulation on lists: leftwards and rightwards. Leftwards accumulation ...
Efficient Parallel Algorithms for Tree Accumulations
 Science of Computer Programming
, 1994
"... Accumulations are higherorder operations on structured objects; they leave the shape of an object unchanged, but replace elements of that object with accumulated information about other elements. Upwards and downwards accumulations on trees are two such operations; they form the basis of many tree ..."
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Cited by 18 (7 self)
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Accumulations are higherorder operations on structured objects; they leave the shape of an object unchanged, but replace elements of that object with accumulated information about other elements. Upwards and downwards accumulations on trees are two such operations; they form the basis of many tree algorithms. We present two Erew Pram algorithms for computing accumulations on trees taking O(log n) time on O(n= log n) processors, which is optimal.
Calculating Accumulations
, 1999
"... this paper, we shall formulate accumulations as higher order catamorphisms , and propose several general transformation rules for calculating accumulations (i.e., finding and manipulating accumulations) by calculationbased (rather than a searchbased) program transformation methods. Some examples ..."
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Cited by 16 (6 self)
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this paper, we shall formulate accumulations as higher order catamorphisms , and propose several general transformation rules for calculating accumulations (i.e., finding and manipulating accumulations) by calculationbased (rather than a searchbased) program transformation methods. Some examples are given for illustration.
Systematic Extraction and Implementation of DivideandConquer Parallelism
 Programming languages: Implementation, Logics and Programs, Lecture Notes in Computer Science 1140
, 1996
"... Homomorphisms are functions that match the divideandconquer paradigm and thus can be computed in parallel. Two problems are studied for homomorphisms on lists: (1) parallelism extraction: finding a homomorphic representation of a given function; (2) parallelism implementation: deriving an efficien ..."
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Cited by 16 (5 self)
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Homomorphisms are functions that match the divideandconquer paradigm and thus can be computed in parallel. Two problems are studied for homomorphisms on lists: (1) parallelism extraction: finding a homomorphic representation of a given function; (2) parallelism implementation: deriving an efficient parallel program that computes the function. A systematic approach to parallelism extraction proceeds by generalization of two sequential representations based on traditional cons lists and dual snoc lists. For some nonhomomorphic functions, e.g., the maximum segment sum problem, our method provides an embedding into a homomorphism. The implementation is addressed by introducing a subclass of distributable homomorphisms and deriving for them a parallel program schema, which is time optimal on the hypercube architecture. The derivation is based on equational reasoning in the BirdMeertens formalism, which guarantees the correctness of the parallel target program. The approach is illustrated with function...
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 12 (0 self)
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this paper, we study functions called list homomorphisms, which represent a particular pattern of parallelism.
Generic Accumulations
, 2002
"... which are eventually used in later stages of the computation. We present a generic definition of accumulations, achieved by the introduction of a new recursive operator on inductive types. We also show that the notion of downwards accumulation developed by Gibbons is subsumed by our notion of acc ..."
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Cited by 10 (0 self)
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which are eventually used in later stages of the computation. We present a generic definition of accumulations, achieved by the introduction of a new recursive operator on inductive types. We also show that the notion of downwards accumulation developed by Gibbons is subsumed by our notion of accumulation.
Computing Downwards Accumulations on Trees Quickly
, 1995
"... Downwards passes on binary trees are essentially functions which pass information down a tree, from the root towards the leaves. Under certain conditions, a downwards pass is both `efficient' (computable in a functional style in parallel time proportional to the depth of the tree) and `manipulable' ..."
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Cited by 9 (3 self)
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Downwards passes on binary trees are essentially functions which pass information down a tree, from the root towards the leaves. Under certain conditions, a downwards pass is both `efficient' (computable in a functional style in parallel time proportional to the depth of the tree) and `manipulable' (enjoying a number of distributivity properties useful in program construction); we call a downwards pass satisfying these conditions a downwards accumulation. In this paper, we show that these conditions do in fact yield a stronger conclusion: the accumulation can be computed in parallel time proportional to the logarithm of the depth of the tree, on a Crew Pram machine.
Towards Merging Recursion and Comonads
, 2000
"... Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold op ..."
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Cited by 9 (2 self)
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Comonads are mathematical structures that account naturally for effects that derive from the context in which a program is executed. This paper reports ongoing work on the interaction between recursion and comonads. Two applications are shown that naturally lead to versions of a comonadic fold operator on the product comonad. Both versions capture functions that require extra arguments for their computation and are related with the notion of strong datatype. 1 Introduction One of the main features of recursive operators derivable from datatype definitions is that they impose a structure upon programs which can be exploited for program transformation. Recursive operators structure functional programs according to the data structures they traverse or generate and come equipped with a battery of algebraic laws, also derivable from type definitions, which are used in program calculations [24, 11, 5, 15]. Some of these laws, the socalled fusion laws, are particularly interesting in p...
Diffusion: Calculating Efficient Parallel Programs
 IN 1999 ACM SIGPLAN WORKSHOP ON PARTIAL EVALUATION AND SEMANTICSBASED PROGRAM MANIPULATION (PEPM ’99
, 1999
"... Parallel primitives (skeletons) intend to encourage programmers to build a parallel program from readymade components for which efficient implementations are known to exist, making the parallelization process easier. However, programmers often suffer from the difficulty to choose a combination of p ..."
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Cited by 9 (7 self)
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Parallel primitives (skeletons) intend to encourage programmers to build a parallel program from readymade components for which efficient implementations are known to exist, making the parallelization process easier. However, programmers often suffer from the difficulty to choose a combination of proper parallel primitives so as to construct efficient parallel programs. To overcome this difficulty, we shall propose a new transformation, called diffusion, which can efficiently decompose a recursive definition into several functions such that each function can be described by some parallel primitive. This allows programmers to describe algorithms in a more natural recursive form. We demonstrate our idea with several interesting examples. Our diffusion transformation should be significant not only in development of new parallel algorithms, but also in construction of parallelizing compilers.