Abstract

Power series and stream processing were made for each other. Stream algorithms for power series are short, sweet, and compositional. Their neatness shines through in Haskell, thanks to pattern-matching, lazy lists, and operator overloading. In a short compass one can build working code from ground zero (scalar operations) up to exact calculation of generating functions and solutions of di#erential equations. I opened the serious here and beat them easy. --- Ring Lardner, You know me Al 1 Introduction Pitching baseballs for the White Sox, Ring Lardner's unlettered hero, Jack Keefe, mastered the Cubs in the opening game of the Chicago series. Pitching heads and tails, I intend here to master power series by opening them one term at a time. A power series, like that for cos x, 1 - x 2 /2! + x 4 /4! - x 6 /6! + · · · , is characterized by an infinite sequence of coe#cients, in this case 1, 0, -1/2, 0, 1/24, 0, -1/720, . . . . It is ideal for implementing as a data stream...

Citations