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31
Shortcut Deforestation in Calculational Form
 In Proc. Conference on Functional Programming Languages and Computer Architecture
, 1995
"... In functional programming, intermediate data structures are often used to "glue" together small programs. Deforestation is a program transformation to remove these intermediate data structures automatically. We present a simple algorithm for deforestation based on two fusion rules for hylomorphism, ..."
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Cited by 91 (3 self)
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In functional programming, intermediate data structures are often used to "glue" together small programs. Deforestation is a program transformation to remove these intermediate data structures automatically. We present a simple algorithm for deforestation based on two fusion rules for hylomorphism, an expressive recursion pattern. A generic notation for hylomorphisms is introduced, where natural transformations are explicitly factored out, and it is used to represent programs. Our method successfully eliminates intermediate data structures of any algebraic type from a much larger class of compositional functional programs than previous techniques. 1 Introduction In functional programming, programs are often constructed by "gluing" together small components, using intermediate data structures to convey information between them. Such data are constructed in one component and later consumed in another component, but never appear in the result of the whole program. The compositional styl...
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.
Fusion of Recursive Programs with Computational Effects
 Theor. Comp. Sci
, 2000
"... Fusion laws permit to eliminate various of the intermediate data structures that are created in function compositions. The fusion laws associated with the traditional recursive operators on datatypes cannot in general be used to transform recursive programs with effects. Motivated by this fact, t ..."
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Cited by 14 (4 self)
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Fusion laws permit to eliminate various of the intermediate data structures that are created in function compositions. The fusion laws associated with the traditional recursive operators on datatypes cannot in general be used to transform recursive programs with effects. Motivated by this fact, this paper addresses the definition of two recursive operators on datatypes that capture functional programs with effects. Effects are assumed to be modeled by monads. The main goal is thus the derivation of fusion laws for the new operators. One of the new operators is called monadic unfold. It captures programs (with effects) that generate a data structure in a standard way. The other operator is called monadic hylomorphism, and corresponds to programs formed by the composition of a monadic unfold followed by a function defined by structural induction on the data structure that the monadic unfold generates. 1 Introduction A common approach to program design in functional programmin...
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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Cited by 12 (8 self)
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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.
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 12 (1 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.
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 12 (7 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.
Promotional Transformation on Monadic Programs
, 1995
"... this paper, we propose a new theory on monadic catamorphism bymoving Fokkinga's assumption on the monad to the condition of a map between monadic algebras so that our theory is valid for arbitrary monads including, for example, the state monad that is not allowed in Fokkinga's theory. Our theory cov ..."
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Cited by 9 (0 self)
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this paper, we propose a new theory on monadic catamorphism bymoving Fokkinga's assumption on the monad to the condition of a map between monadic algebras so that our theory is valid for arbitrary monads including, for example, the state monad that is not allowed in Fokkinga's theory. Our theory covers Fokkinga's as a special case. Moreover, Meijer and Jeuring's informal transformation rules of monadic programs in their case study is actually an instance of our general promotion theorem.
Bottomup Grammar Analysis  A Functional Formulation
 Proceedings Programming Languages and SystemsESOP '94
, 1994
"... This paper discusses bottomup grammar analysis problems such as the Empty problem and the First problem. It defines a general class of bottom up grammar analysis problems, and from this definition it derives a functional program for performing bottomup grammar analysis. The derivation is purely ..."
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Cited by 7 (3 self)
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This paper discusses bottomup grammar analysis problems such as the Empty problem and the First problem. It defines a general class of bottom up grammar analysis problems, and from this definition it derives a functional program for performing bottomup grammar analysis. The derivation is purely calculational, using theorems from lattice theory, the BirdMeertens calculus, and laws for listcomprehensions. Sufficient conditions guaranteeing the existence of a solution emerge as a byproduct of the calculation. The resulting program is used to construct programs for the Empty problem and the First problem. 1 Introduction Grammar analysis is performed in many different situations: Yacc tests whether or not its input grammar is LALR(1), parser generators contain functions for determining whether or not a nonterminal can derive the empty string (Empty) as part of determining the set of all symbols that can appear as the first symbol of a derived string (First), and for determining the ...
Constructing Functional Programs for Grammar Analysis Problems
 In Conference Record of FPCA '95, SIGPLANSIGARCHWG2.8 Conference on Functional Programming Languages and Computer Architecture
, 1995
"... This paper discusses the derivation of functional programs for grammar analysis problems, such as the Empty problem and the Reachable problem. Grammar analysis problems can be divided into two classes: topdown problems such as Follow and Reachable, which are described in terms of the contexts of n ..."
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Cited by 7 (3 self)
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This paper discusses the derivation of functional programs for grammar analysis problems, such as the Empty problem and the Reachable problem. Grammar analysis problems can be divided into two classes: topdown problems such as Follow and Reachable, which are described in terms of the contexts of nonterminals, and bottomup problems such as Empty and First, which do not refer to contexts. In a previous paper we derive a program for bottomup grammar analysis problems. In this paper we derive a program for topdown grammar analysis problems by transforming the specification of an arbitrary topdown problem into a program. The existence of a solution is guaranteed provided some natural conditions are satisfied. Furthermore, we describe a general transformation that applies to both classes of grammar analysis problems. The result of this transformation is a program that avoids unnecessary computations in the computation of a fixed point. Constructor classes, which are used to abstract fr...
Monadic Corecursion  Definition, Fusion Laws, and Applications
 Electronic Notes in Theoretical Computer Science
, 1998
"... This paper investigates corecursive definitions which are at the same time monadic. This corresponds to functions that generate a data structure following a corecursive process, while producing a computational effect modeled by a monad. We introduce a functional, called monadic anamorphism, that cap ..."
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Cited by 5 (1 self)
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This paper investigates corecursive definitions which are at the same time monadic. This corresponds to functions that generate a data structure following a corecursive process, while producing a computational effect modeled by a monad. We introduce a functional, called monadic anamorphism, that captures definitions of this kind. We also explore another class of monadic recursive functions, corresponding to the composition of a monadic anamorphism followed by (the lifting of) a function defined by structural recursion on the data structure that the monadic anamorphism generates. Such kind of functions are captured by socalled monadic hylomorphism. We present transformation laws for these monadic functionals. Two nontrivial applications are also described.