Z. Hu, H. Iwasaki, and M. Takeichi. Calculating Accumulations. Technical Report METR 96-03, Faculty of Engineering, University of Tokyo, March 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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. 1 Introduction often called accumulators [20, 5, 15]. In functional programming, the notion of accumulation is usually associated with the so called accumulation technique [8, 4, 18, 3] which transforms recursive definitions by the introduction of additional arguments over which intermediate results are computed. The accumulation technique is ....

.... X A) Examples of the use of these laws can be found in [29] 4 Accumulations Accumulations are recursive functions that keep intermediate results in additional parameters, known as accumulating parameters or accumulators, which are eventually used in later stages of the computation (see e.g. [4, 20, 5, 15]) In this section we define a generic operator that permits us to represent structural recursive accumulations on inductive types. The operator is obtained by a small modification in the definition of pfold. Let us start with an example of an accumulation. Consider the function that computes the ....

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Z. Hu, H. Iwasaki, and M. Takeichi. Calculating Accumulations. Technical Report METR 96-03, Faculty of Engineering, University of Tokyo, March 1996.

.... prune = pfold BA (T(alg s) That is, prune(empty; 0 prune(node(t; a; t 0 ) if a 2 then 0 else 1 count(t; count(t 0 ; 2 5 Accumulations Accumulations are functions that use an extra parameter to keep intermediate results to be used during the computation (see e.g. [4, 13, 14, 18]) In this section we build up a comonadic operator for a kind of downwards accumulations by adding some ingredients to the definition of pfold. For defining accumulations we can follow, essentially, the same two alternatives discussed before for functions with parameters. One is to define ....

....of downwards accumulations by adding some ingredients to the definition of pfold. For defining accumulations we can follow, essentially, the same two alternatives discussed before for functions with parameters. One is to define accumulations by higher order folds. This is the approach adopted in [18] and [5] As before, this alternative requires to work in a cartesian closed category. As an example, consider the function asums that computes the list of accumulated sums of a list of natural numbers. The curried version is of type list(N) N list(N) asums [ e = e] asums (n : e = e ....

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Z. Hu, H. Iwasaki, and M. Takeichi. Calculating Accumulations. Technical Report METR 96-03, Faculty of Engineering, University of Tokyo, March 1996.

....an extension is not hard to be formulated. However, the interesting part seems to be the study of their calculational properties (We guess that their definition as unique arrows in CX will be helpful in this case as well) Finally, another direction of interest concerns the study of accumulations [Gib93, HIT96], a class of recursive functionals on inductive types that use extra parameters to accumulate intermediate results. For example, in [HIT96] they are presented as higher order catamorphisms. Our approach is to see accumulations as functionals that take extra parameters whose value may change ....

....definition as unique arrows in CX will be helpful in this case as well) Finally, another direction of interest concerns the study of accumulations [Gib93, HIT96] a class of recursive functionals on inductive types that use extra parameters to accumulate intermediate results. For example, in [HIT96] they are presented as higher order catamorphisms. Our approach is to see accumulations as functionals that take extra parameters whose value may change during computation. Assuming that the signature of datatypes is given by strong functors, preliminary investigations have shown that a ....

Z. Hu, H. Iwasaki, and M. Takeichi. Calculating Accumulations. Technical Report METR 96-03, Faculty of Engineering, University of Tokyo, March 1996.

....multiple data structures [HIT96d] mutual recursions, and etc. in order to enable more fusion. In a near future, we are going to extend HYLO to be a general automatic program calculation system, which can optimize functional programs not only by fusion but also by tupling [HIT96b] accumulating[HIT96a] as well as other optimization tactics. ACKNOWLEDGEMENT This paper owes much to the thoughtful and helpful discussions with Akihiko Takano, Fer Jan de Vries and other CACA members. Thanks are also to Oege de Moor for reading the manuscript and making a number of helpful suggestions, and to the ....

Z. Hu, H. Iwasaki, and M. Takeichi. Caculating accumulations. Technical Report METR 96--03, Faculty of Engineering, University of Tokyo, March 1996.

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Hu, Z., Iwasaki, H. & Takeichi, M. (1996a), Caculating accumulations, Technical Report METR 96--03, Faculty of Engineering, University of Tokyo.

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