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Parallelization via Context Preservation
 In IEEE Intl Conference on Computer Languages
, 1998
"... Abstract program schemes, such as scan or homomorphism, can capture a wide range of data parallel programs. While versatile, these schemes are of limited practical use on their own. A key problem is that the more natural sequential specifications may not have associative combine operators required b ..."
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Cited by 18 (16 self)
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Abstract program schemes, such as scan or homomorphism, can capture a wide range of data parallel programs. While versatile, these schemes are of limited practical use on their own. A key problem is that the more natural sequential specifications may not have associative combine operators required by these schemes. As a result, they often fail to be immediately identified. To resolve this problem, we propose a method to systematically derive parallel programs from sequential definitions. This method is special in that it can automatically invent auxiliary functions needed by associative combine operators. Apart from a formalisation, we also provide new theorems, based on the notion of context preservation, to guarantee parallelization for a precise class of sequential programs. 1 Introduction It is wellrecognised that a key problem of parallel computing remains the development of efficient and correct parallel software. This task is further complicated by the variety of parallel arc...
When is a function a fold or an unfold
 Coalgebraic Methods in Computer Science, number 44.1 in Electronic Notes in Theoretical Computer Science
, 2001
"... We give a necessary and sufficient condition for when a settheoretic function can be written using the recursion operator fold, and a dual condition for the recursion operator unfold. The conditions are simple, practically useful, and generic in the underlying datatype. 1 ..."
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Cited by 9 (3 self)
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We give a necessary and sufficient condition for when a settheoretic function can be written using the recursion operator fold, and a dual condition for the recursion operator unfold. The conditions are simple, practically useful, and generic in the underlying datatype. 1
An Analytical Method For Parallelization Of Recursive Functions
, 2001
"... Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult ..."
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Cited by 7 (0 self)
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Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult tasks. In this paper, we propose an analytical approach to transforming recursive functions on general recursive data structures into compositions of parallel skeletons. Using static slicing, we have defined a classification of subexpressions based on their dataparallelism. Then, skeletonbased parallel programs are generated from the classification. To extend the scope of parallelization, we have adopted more general parallel skeletons which do not require the associativity of argument functions. In this way, our analytical method can parallelize recursive functions with complex data flows. Keywords: data parallelism, parallelization, functional languages, parallel skeletons, data flow analysis, static slice 1.
An Algebra of Scans
 In Mathematics of Program Construction
, 2004
"... A parallel prefix circuit takes n inputs x1 , x2 , . . . , xn and produces the n outputs x1 , x1 x2 , . . . , x1 x2 xn , where `#' is an arbitrary associative binary operation. Parallel prefix circuits and their counterparts in software, parallel prefix computations or scans, have numerous app ..."
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Cited by 7 (0 self)
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A parallel prefix circuit takes n inputs x1 , x2 , . . . , xn and produces the n outputs x1 , x1 x2 , . . . , x1 x2 xn , where `#' is an arbitrary associative binary operation. Parallel prefix circuits and their counterparts in software, parallel prefix computations or scans, have numerous applications ranging from fast integer addition over parallel sorting to convex hull problems. A parallel prefix circuit can be implemented in a variety of ways taking into account constraints on size, depth, or fanout. Traditionally, implementations are either defined graphically or by enumerating the underlying graph. Both approaches have their pros and cons. A figure if well drawn conveys the possibly recursive structure of the scan but it is not amenable to formal manipulation. A description in form of a graph while rigorous obscures the structure of a scan and is equally hard to manipulate. In this paper we show that parallel prefix circuits enjoy a very pleasant algebra. Using only two basic building blocks and four combinators all standard designs can be described succinctly and rigorously. The rules of the algebra allow us to prove the circuits correct and to derive circuit designs in a systematic manner. lord darlington. . . . [Sees a fan lying on the table.] And what a wonderful fan! May I look at it? lady windermere. Do. Pretty, isn't it! It's got my name on it, and everything. I have only just seen it myself. It's my husband's birthday present to me. You know today is my birthday?  Oscar Wilde, Lady Windermere's Fan 1
A Transformational Approach which Combines Size Inference and Program Optimization
 Semantics, Applications, and Implementation of Program Generation (SAIG’01), Lecture Notes in Computer Science 2196
, 2001
"... If functional programs are to be used for highperformance computing, efficient data representations and operations must be provided. Our contribution is a calculus for the analysis of the lengths of (nested) lists and a transformation into a form which is liberated from the chain of consoperations ..."
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Cited by 5 (0 self)
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If functional programs are to be used for highperformance computing, efficient data representations and operations must be provided. Our contribution is a calculus for the analysis of the lengths of (nested) lists and a transformation into a form which is liberated from the chain of consoperations and which sometimes permits array implementations even if the length depends on runtime values. A major advantage of functional programs vs. imperative programs is that dependence analysis is much easier, due to the absence of reassignments. One severe disadvantage of functional programs as of yet is that efficient, machineoriented data structures (like the array) absolutely necessary for highperformance computing play a minor role in many language implementations since they do not harmonize with functional evaluation schemata (like graph reduction), which are at a higher level of abstraction. We propose to construct programs by composition of skeletons, i.e., functi...
The Data Field Model
 Coyne R D, Rosenman M A, Radford A D, Balachandran M and Gero J S Knowledgebased
, 2001
"... Indexed data structures are prevalent in many programming applications. Collectionoriented languages provide means to operate directly on these structures, rather than having to loop or recurse through them. This style of programming will often yield clear and succinct programs. However, these prog ..."
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Cited by 3 (2 self)
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Indexed data structures are prevalent in many programming applications. Collectionoriented languages provide means to operate directly on these structures, rather than having to loop or recurse through them. This style of programming will often yield clear and succinct programs. However, these programming languages will often provide only a limited choice of indexed data types and primitives, and the exact semantics of these primitives will sometimes vary with the data type and language. In this paper we develop a unifying semantical model for indexed data structures. The purpose is to support the construction of abstract data types and language features for such structures from first principles, such that they are largely generic over many kinds of data structures. The use of these abstract data types can make programs and their semantics less dependent of the actual data structure. This makes programs more portable across different architectures and facilitates the early design phase. The model is a generalisation of arrays, which we call data fields: these are functions with explicit information about their domains. This information can be conventional array bounds but it could also define other shapes, for instance sparse. Data fields can be interpreted as partial functions, and we define a metalanguage for partial functions. In this language we define abstract versions of collectionoriented operations, and we show a number of identities for them. This theory is used to guide the design of data fields and their operations so they correspond closely to the more abstract notion of partial functions. We define phiabstraction, a lambdalike syntax for defining data fields in a shapeindependent manner, and prove a theorem which relates phiabstraction and lambdaabstraction semantically. We also define a small data field language whose semantics is given by formal data fields, and give examples of data field programming for parallel algorithms with arrays and sparse structures, database quering and computing, and specification of symbolic drawings.
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.
Development and Verification of Parallel Algorithms in the Data Field Model
 Proc. 2nd Int. Workshop on Constructive Methods for Parallel Programming
, 2000
"... . Data fields are partial functions provided with explicit domain information. They provide a very general, formal model for collections of data. Algorithms computing data collections can be described in this formalism at various levels of abstraction: in particular, explicit data distributions a ..."
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Cited by 1 (1 self)
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. Data fields are partial functions provided with explicit domain information. They provide a very general, formal model for collections of data. Algorithms computing data collections can be described in this formalism at various levels of abstraction: in particular, explicit data distributions are easy to model. Parallel versions of algorithms can then be formally verified against algorithm specifications in the model. Functions computing data fields can be directly programmed in the language Data Field Haskell. In this paper we give a brief introduction to the data field model. We then describe Data Field Haskell and make a small case study of how an algorithm and a parallel version of it both can be specified in the language. We then verify the correctness of the parallel version in the data field model. 1 Introduction Many computing applications require indexed data structures. In many applications the indexing capability provides an important part of the model. On the ...
An Analytical Method For Parallelization Of Recursive Functions
, 2000
"... Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult ..."
Abstract
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Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult tasks. In this paper, we propose an analytical approach to transforming recursive functions on general recursive data structures into compositions of parallel skeletons. Using static slicing, wehave defined a classification of subexpressions based on their dataparallelism. Then, skeletonbased parallel programs are generated from the classification. To extend the scope of parallelization, wehave adopted more general parallel skeletons which do not require the associativity of argument functions. In this way, our analytical method can parallelize recursive functions with complex data flows. Keywords: data parallelism, parallelization, functional languages, parallel skeletons, data flow analysis, static slice 1.