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27
Finite differencing of computable expressions
, 1980
"... Finite differencing is a program optimization method that generalizes strength reduction, and provides an efficient implementation for a host of program transformations including "iterator inversion." Finite differencing is formally specified in terms of more basic transformations shown to ..."
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Cited by 128 (6 self)
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Finite differencing is a program optimization method that generalizes strength reduction, and provides an efficient implementation for a host of program transformations including "iterator inversion." Finite differencing is formally specified in terms of more basic transformations shown to preserve program semantics. Estimates of the speedup that the technique yields are given. A full illustrative example of algorithm derivation ispresented.
Static caching for incremental computation
 ACM Trans. Program. Lang. Syst
, 1998
"... A systematic approach is given for deriving incremental programs that exploit caching. The cacheandprune method presented in the article consists of three stages: (I) the original program is extended to cache the results of all its intermediate subcomputations as well as the nal result, (II) the e ..."
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Cited by 52 (21 self)
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A systematic approach is given for deriving incremental programs that exploit caching. The cacheandprune method presented in the article consists of three stages: (I) the original program is extended to cache the results of all its intermediate subcomputations as well as the nal result, (II) the extended program is incrementalized so that computation on a new input can use all intermediate results on an old input, and (III) unused results cached by the extended program and maintained by the incremental program are pruned away, l e a ving a pruned extended program that caches only useful intermediate results and a pruned incremental program that uses and maintains only the useful results. All three stages utilize static analyses and semanticspreserving transformations. Stages I and III are simple, clean, and fully automatable. The overall method has a kind of optimality with respect to the techniques used in Stage II. The method can be applied straightforwardly to provide a systematic approach to program improvement via caching.
A survey and classification of some program transformation approaches and techniques
 In The IFIP TC2/WG 2.1 Working Conference on Program specification and transformation
, 1987
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Transformational design and implementation of a new efficient solution to the ready simulation problem
 Science of Computer Programming
, 1995
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Deriving incremental programs
, 1993
"... A systematic approach i s g i v en for deriving incremental programs from nonincremental programs written in a standard functional programming language. We exploit a number of program analysis and transformation techniques and domainspeci c knowledge, centered around e ective utilization of cachin ..."
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Cited by 39 (21 self)
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A systematic approach i s g i v en for deriving incremental programs from nonincremental programs written in a standard functional programming language. We exploit a number of program analysis and transformation techniques and domainspeci c knowledge, centered around e ective utilization of caching, in order to provide a degree of incrementality not otherwise achievable by a generic incremental evaluator. 1
Mechanical Translation of Set Theoretic Problem Specifications Into Efficient RAM Code  A Case Study
 Proc. EUROCAL 85
, 1985
"... This paper illustrates a fully automatic topdown approach to program development in which formal problem specifications are mechanically translated into efficient RAM code. This code is guaranteed to be totally correct and an upper bound on its worst case asymptotic running time is automatically de ..."
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Cited by 28 (8 self)
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This paper illustrates a fully automatic topdown approach to program development in which formal problem specifications are mechanically translated into efficient RAM code. This code is guaranteed to be totally correct and an upper bound on its worst case asymptotic running time is automatically determined. The user is only required to supply the system with a formal problem specification, and is relieved of all responsibilities in the rest of the program development process. These results are obtained, in part, by greatly restricting the system to handle a class of determinate, set theoretic, tractable problems. The most essential transformational techniques that are used are fixed point iteration, finite differencing, and data structure selection. Rudimentary forms of these techniques have been implemented and used effectively in the RAPTS transformational programming system. This paper explains the conceptual underpinnings of our approach by considering the problem of attribute closure for relational databases and systematically deriving a program that implements a linear time solution. 1.
Viewing a Program Transformation System at Work
 Joint 6th International Conference on Programming Language Implementation and Logic programming (PLILP) and 4th International Conference on Algebraic and Logic Programming (ALP), LNCS 844
, 1994
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Caching intermediate results for program improvement
 In Proceedings of the 1995 ACM SIGPLAN Symposium on Partial Evaluation and SemanticsBased Program Manipulation, PEPM ’95
, 1995
"... A systematic approach is given for symbolically caching intermediate results useful for deriving incremental programs from nonincremental programs. We exploit a number of program analysis and transformation techniques, centered around e ective c a c hing based on its utilization in deriving increme ..."
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Cited by 22 (6 self)
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A systematic approach is given for symbolically caching intermediate results useful for deriving incremental programs from nonincremental programs. We exploit a number of program analysis and transformation techniques, centered around e ective c a c hing based on its utilization in deriving incremental programs, in order to increase the degree of incrementality not otherwise achievable by using only the return values of programs that are of direct interest. Our method can be applied straightforwardly to provide a systematic approach to program improvement via caching. 1
Discovering auxiliary information for incremental computation
 In Symp. on Princ. of Prog. Lang
, 1996
"... This paper presents program analyses and transformations that discover a general class of auxiliary information for any incremental computation problem. Combining these techniques with previous techniques for caching intermediate results, we obtain a systematic approach that transforms nonincrementa ..."
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Cited by 22 (12 self)
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This paper presents program analyses and transformations that discover a general class of auxiliary information for any incremental computation problem. Combining these techniques with previous techniques for caching intermediate results, we obtain a systematic approach that transforms nonincremental programs into e cient incremental programs that use and maintain useful auxiliary information as well as useful intermediate results. The use of auxiliary information allows us to achieve a greater degree of incrementality than otherwise possible. Applications of the approach i nclude strength reduction in optimizing compilers and nite di erencing in transformational programming. 1
Loop optimization for aggregate array computations
"... An aggregate array computation is a loop that computes accumulated quantities over array elements. Such computations are common in programs that use arrays, and the array elements involved in such computations often overlap, especially across iterations of loops, resulting in signi cant redundancy ..."
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Cited by 15 (7 self)
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An aggregate array computation is a loop that computes accumulated quantities over array elements. Such computations are common in programs that use arrays, and the array elements involved in such computations often overlap, especially across iterations of loops, resulting in signi cant redundancy in the overall computation. This paper presents a method and algorithms that eliminate such overlapping aggregate array redundancies and shows both analytical and experimental performance improvements. The method is based on incrementalization, i.e., updating the values of aggregate array computations from iteration to iteration rather than computing them from scratch in each iteration. This involves maintaining additional information not maintained in the original program. We reduce various analysis problems to solving inequality constraints on loop variables and array subscripts, and we apply results from work on array data dependence analysis. Incrementalizing aggregate array computations produces drastic program speedup compared to previous optimizations. Previous methods for loop optimizations of arrays do not perform incrementalization, and previous techniques for loop incrementalization do not handle arrays.