P. G. Harrison, "Function inversion," in [9], pp. 153--166.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for inverse computation in TSG, we show how inverse computation can be performed in MP. Inverse computation in MP is achieved via the standard MP TSG interpreter (Sec. 9) 10.1. The Universal Resolving Algorithm: an Inversion Modifier There exist di#erent methods for inverse computation [16, 28, 50]. The universal resolving algorithm outlined in this section uses methods from supercompilation, in particular driving [51] The idea for this algorithm appeared in the early seventies [50] and since then several variants were implemented for functional languages [3, 5, 41, 42] Our algorithm ....

....exists for equivalence transformation modifiers, not much work has been done regarding inversion modifiers. Experiments [40, 53] show that specializing an interpreter for inverse computation can invert programs. Only a very small number of publications studies the problem of program inversion [27, 28, 41, 42, 54]. The modifier projections suggest a new way of constructing program inverters, namely by transforming an inverse interpreter. Inserting an interpreter between a source program and a program transformer can achieve certain powerful transformations [34, 49, 53] Our use of the interpretive ....

P. G. Harrison, "Function inversion," in [9], pp. 153--166.

....since the inverses of these functions were statically included into the interpreter. An example with arbitrary functions would be power (b; 0) 1 power (b; 2 n) square (power (b; n) power (b; n 1) b power (b; n) A second application is in the area of implementing abstract data types [5, 6]. Let A be an abstract data type and I its implementation with abstraction ff : I A. Let f be an abstract operation and g its implementation. Then the following diagram commutes: A f Gamma A ff ff I g Gamma I Thus, g may be obtained as g = ff Gamma1 ffi f ffi ff. The ....

....is similar to unfold fold; function calls are symbolically driven , i.e. unfolded. The configurational analysis is related to reordering. A graph of configurations is created and variables are annotated as known or unknown. Then the graph is rearranged according to some rules. Harrison s method [6] is radically different from ours. He uses a variable free FP like language and applies algebraic laws, e.g. f ffi g) Gamma1 = g Gamma1 ffi f Gamma1 , to derive inverses. In his paper, he demonstrates his method with the example of inverse append, i.e. the problem app (x ; y ) z. ....

Harrison, P.G.: Function inversion, In: Bjrner, D., Ershov, A.P., Jones, N.D., Ed.: Partial Evaluation and Mixed Computation, (Elsevier, North Holland, Amsterdam, 1988) 153-166

....1972 by performing subtraction by inverse computation of binary addition [80] In 1973 S.A. Romanenko and later S.M. Abramov implemented an algorithm, Universal Resolving Algorithm (URA) in which driving was combined with a mechanical extraction of answers [1, 65] For program inversion see also [39, 41, 66, 93, 60]. In logic programming, one defines a predicate by a program P x y and solves the inversion problem for Z = True . Theorem proving and program transformation are indistinguishable in the approach outlined above; they are two applications of the same equivalence transformation. The definition ....

P.G. Harrison. Function inversion. In Bjørner et al. [8], pp. 153--166.

....P may be formulated as an algorithm checking the linguistic object x. The inversion of programs is a fundamental problem, and a large branch of computer science has been based on solutions emerging from logic and proof theory [3,4] Direct methods for inverting algorithms have been developed [5 7]. By varying the metaevaluator Mc and the method for solving the inverse problem different linguistic models can be generated by MST formulas involving composition and inversion. 3.3 Problem of Program Specialization Automatic inversion by metacomputation is a hard problem, and hence it is ....

P. G. Harrison, "Function inversion", D. Bjørner, A. P. Ershov and N. D. Jones (ed.), Partial Evaluation and Mixed Computation, 153-166, North-Holland (1988).

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P.G. Harrison, Function Inversion, in: [17], pp. 153-166

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P.G. Harrison. Function inversion. In D. Bjørner et al., editors. Partial Evaluation and Mixed Computation. 153--166 (North-Holland, 1988).

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