On Jan 20, 2025, at 8:54 AM, Douglas McIlroy <douglas.mcilroy@dartmouth.edu> wrote:

> catalanNumbers :: Num a => [a]
> catalanNumbers =
>   let xs = 1 : PowerSeries.mul xs xs
>   in  xs

This example of a generating function come to life as a program deserves to be better known. Bill Burge presented it 50 years ago in "Recursive Programming Techniques", Addison-Wesley, 1975. I revisited it in "Power series, power serious", JFP 9 (1999) 323-335, where, with overloadied arithmetic, it became

      ts = 1 : ts^2

The technique is laid bare in ten one-liners at https://www.cs.dartmouth.edu/~doug/powser.html.

Doug

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