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A cost calculus for parallel functional programming
 Journal of Parallel and Distributed Computing
, 1995
"... Abstract 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 programmin ..."
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Cited by 58 (6 self)
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Abstract 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.
Parallel Programming using Functional Languages
, 1991
"... I am greatly indebted to Simon Peyton Jones, my supervisor, for his encouragement and technical assistance. His overwhelming enthusiasm was of great support to me. I particularly want to thank Simon and Geoff Burn for commenting on earlier drafts of this thesis. Through his excellent lecturing Cohn ..."
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Cited by 48 (3 self)
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I am greatly indebted to Simon Peyton Jones, my supervisor, for his encouragement and technical assistance. His overwhelming enthusiasm was of great support to me. I particularly want to thank Simon and Geoff Burn for commenting on earlier drafts of this thesis. Through his excellent lecturing Cohn Runciman initiated my interest in functional programming. I am grateful to Phil Trinder for his simulator, on which mine is based, and Will Partain for his help with LaTex and graphs. I would like to thank the Science and Engineering Research Council of Great Britain for their financial support. Finally, I would like to thank Michelle, whose culinary skills supported me whilst I was writingup.The Imagination the only nation worth defending a nation without alienation a nation whose flag is invisible and whose borders are forever beyond the horizon a nation whose motto is why have one or the other when you can have one the other and both
Arrows, Robots, and Functional Reactive Programming
 Advanced Functional Programming, 4th International School, volume 2638 of LNCS
, 2002
"... Functional reactive programming, or FRP, is a paradigm for programming hybrid systems  i.e., systems containing a combination of both continuous and discrete components  in a highlevel, declarative way. The key ideas in FRP are its notions of continuous, timevarying values, and timeordere ..."
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Cited by 47 (10 self)
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Functional reactive programming, or FRP, is a paradigm for programming hybrid systems  i.e., systems containing a combination of both continuous and discrete components  in a highlevel, declarative way. The key ideas in FRP are its notions of continuous, timevarying values, and timeordered sequences of discrete events.
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 41 (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 ...
Elements of a Relational Theory of Datatypes
 Formal Program Development, volume 755 of Lecture Notes in Computer Science
, 1993
"... The "Boom hierarchy" is a hierarchy of types that begins at the level of trees and includes lists, bags and sets. This hierarchy forms the basis for the calculus of total functions developed by Bird and Meertens, and which has become known as the "BirdMeertens formalism". This paper describes a hie ..."
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Cited by 35 (0 self)
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The "Boom hierarchy" is a hierarchy of types that begins at the level of trees and includes lists, bags and sets. This hierarchy forms the basis for the calculus of total functions developed by Bird and Meertens, and which has become known as the "BirdMeertens formalism". This paper describes a hierarchy of types that logically precedes the Boom hierarchy. We show how the basic operators of the BirdMeertens formalism (map, reduce and filter) can be introduced in a logical sequence by beginning with a very simple structure and successively refining that structure. The context of this work is a relational theory of datatypes, rather than a calculus of total functions. Elements of the theory necessary to the later discussion are summarised at the beginning of the paper. 1 Introduction This paper reports on an experiment into the design of a programming algebra. The algebra is an algebra of datatypes oriented towards the calculation of polymorphic functions and relations. Its design d...
An Exploration of the BirdMeertens Formalism
 In STOP Summer School on Constructive Algorithmics, Abeland
, 1989
"... Two formalisms that have been used extensively in the last few years for the calculation of programs are the Eindhoven quantifier notation and the formalism developed by Bird and Meertens. Although the former has always been applied with ultimate goal the derivation of imperative programs and th ..."
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Cited by 32 (3 self)
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Two formalisms that have been used extensively in the last few years for the calculation of programs are the Eindhoven quantifier notation and the formalism developed by Bird and Meertens. Although the former has always been applied with ultimate goal the derivation of imperative programs and the latter with ultimate goal the derivation of functional programs there is a remarkable similarity in the formal games that are played. This paper explores the BirdMeertens formalism by expressing and deriving within it the basic rules applicable in the Eindhoven quantifier notation. 1 Calculation was an endless delight to Moorish scholars. They loved problems, they enjoyed finding ingenious methods to solve them, and sometimes they turned their methods into mechanical devices. (J. Bronowski, The Ascent of Man. Book Club Associates: London (1977).) 1 Introduction Our ability to calculate  whether it be sums, products, differentials, integrals, or whatever  would be woefull...
Foundations for a Practical Theory of Program Refinement and Transformation
, 1994
"... A wide spectrum language is presented, which is designed to facilitate the proof of the correctness of refinements and transformations. Two different proof methods are introduced and used to prove some fundamental transformations, including a general induction rule (Lemma 3.9) which enables transfor ..."
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Cited by 21 (14 self)
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A wide spectrum language is presented, which is designed to facilitate the proof of the correctness of refinements and transformations. Two different proof methods are introduced and used to prove some fundamental transformations, including a general induction rule (Lemma 3.9) which enables transformations of recursive and iterative programs to be proved by induction on their finite truncations. A theorem for proving the correctness of recursive implementations is presented (Theorem 3.21), which provides a method for introducing a loop, without requiring the user to provide a loop invariant. A powerful, general purpose, transformation for removing or introducing recursion is described and used in a case study (Section 5) in which we take a small, but highly complex, program and apply formal transformations in order to uncover an abstract specification of the behaviour of the program. The transformation theory supports a transformation system, called FermaT, in which the applicability conditions of each transformation (and hence the correctness of the result) are mechanically verified. These results together considerably simplify the construction of viable program transformation tools; practical consequences are briefly discussed.
Program Calculation Properties of Continuous Algebras
, 1991
"... Defining data types as initial algebras, or dually as final coalgebras, is beneficial, if not indispensible, for an algebraic calculus for program construction, in view of the nice equational properties that then become available. It is not hard to render finite lists as an initial algebra and, ..."
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Cited by 19 (0 self)
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Defining data types as initial algebras, or dually as final coalgebras, is beneficial, if not indispensible, for an algebraic calculus for program construction, in view of the nice equational properties that then become available. It is not hard to render finite lists as an initial algebra and, dually, infinite lists as a final coalgebra. However, this would mean that there are two distinct data types for lists, and then a program that is applicable to both finite and infinite lists is not possible, and arbitrary recursive definitions are not allowed. We prove the existence of algebras that are both initial in one category of algebras and final in the closely related category of coalgebras, and for which arbitrary (continuous) fixed point definitions ("recursion") do have a solution. Thus there is a single data type that comprises both the finite and the infinite lists. The price to be paid, however, is that partiality (of functions and values) is unavoidable.
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...
Basic theorems about security
 Journal of Computer Security
, 1992
"... We build a mathematical structure in which we can ask questions about the methods for achieving security properties, such as confidentiality and integrity, and functionality properties, such as safety and liveness. The structure allows us to consider many different choices for the meaning of “confid ..."
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Cited by 14 (1 self)
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We build a mathematical structure in which we can ask questions about the methods for achieving security properties, such as confidentiality and integrity, and functionality properties, such as safety and liveness. The structure allows us to consider many different choices for the meaning of “confidentiality” and “integrity ” and so on, and to compare and contrast security properties with functionality properties.