Higher-Order and Symbolic Computation, 14(1)35-57
Functional Differentiation of Computer ProgramsJerzy Karczmarczuk, Department of Computer Science, University of Caen, Sciences III, Bd. Maréchal Juin, 14032 Caen, France
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Abstract: We present a purely functional implementation of the
computational differentiation tools -- the well known numeric (i.e.,
not symbolic) techniques which permit one to compute point-wise
derivatives of functions defined by computer programs economically and
exactly (with machine precision). We show how the use of lazy
evaluation permits a transparent and elegant construction of the
entire infinite tower of derivatives of higher order for any
expressions present in the program. The formalism may be useful in
various problems of scientific computing which often demand a hard and
ungracious human preprocessing before writing the final code. Some
concrete examples are given.
Keywords: Haskell, differentiation, arithmetic, lazy semantics |
This article can be downloaded [here].
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