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A cost calculus for parallel functional programming
 JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
, 1995
"... Building a cost calculus for a parallel program development environment is difficult because of the many degrees of freedom available in parallel implementations, and because of difficulties with compositionality. We present a strategy for building cost calculi for skeletonbased programming languag ..."
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Cited by 60 (6 self)
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Building a cost calculus for a parallel program development environment is difficult because of the many degrees of freedom available in parallel implementations, and because of difficulties with compositionality. We present a strategy for building cost calculi for skeletonbased programming languages which can be used for derivational software development and which deals in a pragmatic way with the difficulties of composition. The approach is illustrated for the BirdMeertens theory of lists, a parallel functional language with an associated equational transformation system. Keywords: functional programming, parallel programming, program transformation, cost calculus, equational theories, architecture independence, BirdMeertens formalism.
The BirdMeertens Formalism as a Parallel Model
 Software for Parallel Computation, volume 106 of NATO ASI Series F
, 1993
"... The expense of developing and maintaining software is the major obstacle to the routine use of parallel computation. Architecture independent programming offers a way of avoiding the problem, but the requirements for a model of parallel computation that will permit it are demanding. The BirdMeertens ..."
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Cited by 45 (0 self)
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The expense of developing and maintaining software is the major obstacle to the routine use of parallel computation. Architecture independent programming offers a way of avoiding the problem, but the requirements for a model of parallel computation that will permit it are demanding. The BirdMeertens formalism is an approach to developing and executing dataparallel programs; it encourages software development by equational transformation; it can be implemented efficiently across a wide range of architecture families; and it can be equipped with a realistic cost calculus, so that tradeoffs in software design can be explored before implementation. It makes an ideal model of parallel computation. Keywords: General purpose parallel computing, models of parallel computation, architecture independent programming, categorical data type, program transformation, code generation. 1 Properties of Models of Parallel Computation Parallel computation is still the domain of researchers and those ...
Calculating Functional Programs
 Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, volume 2297 of LNCS, chapter 5
, 2000
"... A good way of developing a correct program is to calculate it from its specification. Functional programming languages are especially suitable for this, because their referential transparency greatly helps calculation. We discuss the ideas behind program calculation, and illustrate with an examp ..."
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Cited by 31 (8 self)
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A good way of developing a correct program is to calculate it from its specification. Functional programming languages are especially suitable for this, because their referential transparency greatly helps calculation. We discuss the ideas behind program calculation, and illustrate with an example (the maximum segment sum problem). We show that calculations are driven by promotion, and that promotion properties arise from universal properties of the data types involved. 1 Context The history of computing is a story of two contrasting trends. On the one hand, the cost and cost/performance ratio of computer hardware plummets; on the other, computer software is overcomplex, unreliable and almost inevitably over budget. Clearly, we have learnt how to build computers, but not yet how to program them. It is now widely accepted that adhoc approaches to constructing software break down as projects get more ambitious. A more formal approach, based on sound mathematical foundations, i...
Parallel Programming, List Homomorphisms and the Maximum Segment Sum Problem
 Proceedings of Parco 93. Elsevier Series in Advances in Parallel Computing
, 1993
"... We review the use of the BirdMeertens Formalism as a vehicle for the construction of programs with massive implicit parallelism. We show that a simple result from the theory, concerning the expression of list homomorphisms, can help us in our search for parallel algorithms and demonstrate its appli ..."
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We review the use of the BirdMeertens Formalism as a vehicle for the construction of programs with massive implicit parallelism. We show that a simple result from the theory, concerning the expression of list homomorphisms, can help us in our search for parallel algorithms and demonstrate its application to some simple problems including the maximum segment sum problem. Our main purpose is to show that an understanding of the homomorphism lemma can be helpful in producing programs for problems which are "not quite" list homomorphisms themselves. A more general goal is to illustrate the benefits which can arise from taking a little theory with a pinch of pragmatic salt. 1 Introduction The use of bulk operations on aggregate data sets as a means of generating programs with a high degree of implicit parallelism has a long history (e.g. see [4] for a recent presentation). Although traditionally associated with an imperative programming style and SIMD machines, the approach lends itself e...
Algebra of logic programming
 International Conference on Logic Programming
, 1999
"... At present, the field of declarative programming is split into two main areas based on different formalisms; namely, functional programming, which is based on lambda calculus, and logic programming, which is based on firstorder logic. There are currently several language proposals for integrating th ..."
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At present, the field of declarative programming is split into two main areas based on different formalisms; namely, functional programming, which is based on lambda calculus, and logic programming, which is based on firstorder logic. There are currently several language proposals for integrating the expressiveness of these two models of computation. In this thesis we work towards an integration of the methodology from the two research areas. To this end, we propose an algebraic approach to reasoning about logic programs, corresponding to the approach taken in functional programming. In the first half of the thesis we develop and discuss a framework which forms the basis for our algebraic analysis and transformation methods. The framework is based on an embedding of definite logic programs into lazy functional programs in Haskell, such that both the declarative and the operational semantics of the logic programs are preserved. In spite of its conciseness and apparent simplicity, the embedding proves to have many interesting properties and it gives rise to an algebraic semantics of logic programming. It also allows us to reason about logic programs in a simple calculational style, using rewriting and the algebraic laws of combinators. In the embedding, the meaning of a logic program arises compositionally from the meaning of its constituent subprograms and the combinators that connect them. In the second half of the thesis we explore applications of the embedding to the algebraic transformation of logic programs. A series of examples covers simple program derivations, where our techniques simplify some of the current techniques. Another set of examples explores applications of the more advanced program development techniques from the Algebra of Programming by Bird and de Moor [18], where we expand the techniques currently available for logic program derivation and optimisation. To my parents, Sandor and Erzsebet. And the end of all our exploring Will be to arrive where we started And know the place for the first time.
SVP  a Model Capturing Sets, Streams, and Parallelism
 In Proceedings of the 18th VLDB Conference
, 1992
"... We describe the SVP data model. The goal of SVP is to model both set and stream data, and to model parallelism in bulk data processing. SVP also shows promise for other parallel processing applications. SVP models collections, which include sets and streams as special cases. Collections are represen ..."
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We describe the SVP data model. The goal of SVP is to model both set and stream data, and to model parallelism in bulk data processing. SVP also shows promise for other parallel processing applications. SVP models collections, which include sets and streams as special cases. Collections are represented as ordered tree structures, and divideandconquer mappings are easily defined on these structures. We show that many useful database mappings (queries) have a divideandconquer format when specified using collections, and that this specification exposes parallelism. We formalize a class of divideandconquer mappings on collections called SVPtransducers. SVPtransducers generalize aggregates, set mappings, stream transductions, and scan computations. At the same time, they have a rigorous semantics based on continuity with respect to collection orderings, and permit implicit specification of both independent and pipeline parallelism. 1 Introduction Achieving parallelism in bulk data...
A Cost Analysis for a Higherorder Parallel Programming Model
, 1996
"... Programming parallel computers remains a difficult task. An ideal programming environment should enable the user to concentrate on the problem solving activity at a convenient level of abstraction, while managing the intricate lowlevel details without sacrificing performance. This thesis investiga ..."
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Cited by 17 (1 self)
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Programming parallel computers remains a difficult task. An ideal programming environment should enable the user to concentrate on the problem solving activity at a convenient level of abstraction, while managing the intricate lowlevel details without sacrificing performance. This thesis investigates a model of parallel programming based on the BirdMeertens Formalism (BMF). This is a set of higherorder functions, many of which are implicitly parallel. Programs are expressed in terms of functions borrowed from BMF. A parallel implementation is defined for each of these functions for a particular topology, and the associated execution costs are derived. The topologies which have been considered include the hypercube, 2D torus, tree and the linear array. An analyser estimates the costs associated with different implementations of a given program and selects a costeffective one for a given topology. All the analysis is performed at compiletime which has the advantage of reducing run...
Realtime Signal Processing  Dataflow, Visual, and Functional Programming
, 1995
"... This thesis presents and justifies a framework for programming realtime signal processing systems. The framework extends the existing "blockdiagram" programming model; it has three components: a very highlevel textual language, a visual language, and the dataflow process network model o ..."
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This thesis presents and justifies a framework for programming realtime signal processing systems. The framework extends the existing "blockdiagram" programming model; it has three components: a very highlevel textual language, a visual language, and the dataflow process network model of computation. The dataflow process network model, although widelyused, lacks a formal description, and I provide a semantics for it. The formal work leads into a new form of actor. Having established the semantics of dataflow processes, the functional language Haskell is layered above this model, providing powerful featuresnotably polymorphism, higherorder functions, and algebraic program transformationabsent in blockdiagram systems. A visual equivalent notation for Haskell, Visual Haskell, ensures that this power does not exclude the "intuitive" appeal of visual interfaces; with some intelligent layout and suggestive icons, a Visual Haskell program can be made to look very like a block dia...
Make it Practical: A Generic LinearTime Algorithm for Solving MaximumWeightsum Problems
 In Proceedings of the 5th ACM SIGPLAN International Conference on Functional Programming (ICFP'00
, 2000
"... In this paper we propose a new method for deriving a practical lineartime algorithm from the specification of a maximumweight sum problem: From the elements of a data structure x, find a subset which satisfies a certain property p and whose weightsum is maximum. Previously proposed methods for aut ..."
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In this paper we propose a new method for deriving a practical lineartime algorithm from the specification of a maximumweight sum problem: From the elements of a data structure x, find a subset which satisfies a certain property p and whose weightsum is maximum. Previously proposed methods for automatically generating lineartime algorithms are theoretically appealing, but the algorithms generated are hardly useful in practice due to a huge constant factor for space and time. The key points of our approach are to express the property p by a recursive boolean function over the structure x rather than a usual logical predicate and to apply program transformation techniques to reduce the constant factor. We present an optimization theorem, give a calculational strategy for applying the theorem, and demonstrate the effectiveness of our approach through several nontrivial examples which would be difficult to deal with when using the methods previously available.
The Automated Transformation of Abstract Specifications of Numerical Algorithms into Efficient Array Processor Implementations
 Science of Computer Programming
, 1997
"... We present a set of program transformations which are applied automatically to convert abstract functional specifications of numerical algorithms into efficient implementations tailored to the AMT DAP array processor. The transformations are based upon a formal algebra of a functional array form, wh ..."
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We present a set of program transformations which are applied automatically to convert abstract functional specifications of numerical algorithms into efficient implementations tailored to the AMT DAP array processor. The transformations are based upon a formal algebra of a functional array form, which provides a functional model of the array operations supported by the DAP programming language. The transformations are shown to be complete. We present specifications and derivations of two example algorithms: an algorithm for computing eigensystems and an algorithm for solving systems of linear equations. For the former, we compare the execution performance of the implementation derived by transformation with the performance of an independent, manually constructed implementation; the efficiency of the derived implementation matches that of the manually constructed implementation.