W. Chin and M. Hagiya. A transformation method for dynamic-sized tabulation. Acta Informatica, 32:93--115, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....which decides for a given primitive recursive program scheme M whether there is an argument for which the call by value computation of M 0 is more efficient than the call by value computation of M . We note that the strategy called safe tupling which is proposed in [Chi93] and extended in [CK93, CH95], yields similar results. However, there the authors do not show a decision algorithm with the mentioned behaviour. Since the recursion elimination deals with the concept of computations, it is reasonable to formalize our transformation strategy on formal models for the reduction semantics of ....

....us discuss this tupling informally. The idea of the tupling is to create a new function which is a tuple of these functions with the same list of arguments, such that multiple traversals of common inputs are avoided. This idea on its own is not new, it is proposed in many other papers (cf. e.g. [PP93, CH95]) What is new is the algorithmical way in which this is done. For the created tuple function, new rules have to be defined as follows: for every input symbol oe, the right hand sides of the rules of the simple functions from which the tuple function is build, are combined by a comb symbol. For ....

W. Chin and M. Hagiya. A transformation method for dynamic-sized tabulation. Acta Informatica, 32:93--115, 1995.

....influenced by Pettorossi s work [Pet87] of using lambda abstraction in conjunction with the tupling tactic. However, the transformations in the previous work require more or less humaninsights, which are hard to be made automatic. Other related work includes memoization [Mic68, Hug85] tabulation [Bir80, Coh83, CH95] and incremental algorithms [Liu96] All transformation algorithms introduced in this paper have been implemented in a rapid prototyped way. It is completely mechanical and does not rely on heuristics. Although we have to wait for the detailed experimental results to say that this system is ....

W. Chin and M. Hagiya. A transformation method for dynamic-sized tabulation. Acta Informatica, 32:93--115, 1995.

....a source of serious inefficiency because the main parameter os is traversed multiple times by fs , resembling the case for fib function in Section 2.2. This inefficient state shall be handled by the tupling transformation. The tupling technique that we shall use is called dynamic tupling [CH95] or tabulation [Bir80] as opposed to the static tupling where we know statically the fixed number of values that should be memoized. The purpose of our dynamic tupling is to merge two recursive calls of fs together so that os can be traversed once. The difficultyinsuch tupling is to ....

W. Chin and M. Hagiya. A transformation method for dynamic-sized tabulation. Acta Informatica, 32:93--115, 1995.

....In addition, we say that our Haskell programs are pseudo in the sense that they include some additional notations for sets. 4 by using the known calculation techniques of fusion [Chi92] generalization (accumulation) Bir84, HIT99] base case lter promotion [Chi90] and tabulation [Bir80, CH95] Our derivation strategy is rather standard for program optimization and can be summarized as follows. First, we eliminate as much unnecessary intermediate data structures as possible by fusion of composition of recursive functions into a single recursion function. Then, we reuse necessary ....

....fusion, accumulation, and base case lter promotion, there still remains a source of serious ineciency because the inductive parameter os is traversed multiple times by fs 0 . We want to share some computation among all recursive calls to fs 0 , by using the tabulation calculation [Bir80, CH95] 3.4.1 Tree Structure with Invariants The purpose of our tabulation calculation is to exploit the relationship among recursive calls to fs 0 so that their computation could be shared. The diculty in such tabulation is to determine which values should be tabulated and how these values are ....

W.N. Chin and M. Hagiya. A transformation method for dynamic-sized tabulation. Acta Informatica, 32:93-115, 1995.

.... we will derive an efficient program for finding frequent sets from the specification fs os vss least = fsp vss least) subs os) by using the known calculation techniques of fusion [Chi92] generalization (accumulation) Bir84, HIT99] base case filter promotion [Chi90] and tabulation [Bir80, CH95] 5 3.1 Fusion Fusion is used to merge two passes (from nested recursive calls) into a single one, by eliminating intermediate the data structure passing between the two passes. Notice that our fs has two passes, and the intermediate data structure is huge containing all the sublists of os. We ....

....fusion, accumulation, and base case filter promotion, there still remains a source of serious inefficiency because the inductive parameter os is traversed multiple times by fs 0 . We want to share some computation among all recursive calls to fs 0 , by using the tabulation calculation [Bir80, CH95] The purpose of our tabulation calculation is to exploit the relationship among recursive calls to fs 0 so that their computation could be shared. The difficulty in such tabulation is to determine which values should be tabulated. Now, taking a close look at the derived definition for fs 0 ....

W. Chin and M. Hagiya. A transformation method for dynamic-sized tabulation. Acta Informatica, 32:93--115, 1995.

....a source of serious inefficiency because the main parameter os is traversed multiple times by fs 0 , resembling the case for fib function in Section 2.2. This inefficient state shall be handled by the tupling transformation. The tupling technique that we shall use is called dynamic tupling [CH95] or tabulation [Bir80] as opposed to the static tupling where we know statically the fixed number of values that should be memoized. The purpose of our dynamic tupling is to merge two recursive calls of fs 0 together so that os can be traversed once. The A Case Study on a Modular ....

W. Chin and M. Hagiya. A transformation method for dynamic-sized tabulation. Acta Informatica, 32:93--115, 1995.

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W.-N. Chin and M. Hagiya, A transformation method for dynamic-sized tabulation, Acta Informatica, 32, (1995), p. 93--115.

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