This project arose from my attempt to solve some of the Project Euler problems using Mathematica. I found it frustrating that I had to guess how many prime numbers or how many Fibonacci numbers I'd have to scan in order to satisfy the "primes under 2 million" or "Fibonacci numbers under 4 million".
I knew how I'd solve the problem in C# or Python (chaining a bunch of IEnumerables or generators, respectively), and wanted to see how close I could get to that style in Mathematica, so I posed the question on the fledgling Mathematica Stack Exchange site.
A helpful user named WReach wrote up a great rough implementation, citing his experience with the Haskell programming language as his major source of inspiration.
I cleaned up his implementation, put it in a package, and made it look a little more native (First, Rest instead of Head, Tail). I've added a few more functions (TakeWhile, FoldList, Most, Last).
Finally, I added a helper called Lazy that lets you trivially turn many built-ins (Fibonacci and Prime, in fact) into lazy sources that you can pump for as many items as you need without going to too much effort.
I'm providing this code under an MIT-style license in the hopes that others find it useful. If anyone ends up adding any new features, especially by providing Stream upvalues for more built-ins, please send me a pull request.
Project Euler #1: Find the sum of all the multiples of 3 or 5 below 1000.
Total[Lazy[Integers]~TakeWhile~((# < 1000) &) ~Select~((Mod[#, 3] == 0 || Mod[#, 5] == 0) &)]
Project Euler #12: What is the value of the first triangle number to have over five hundred divisors?
(* First, a non-lazy helper *) divisorsLength[n_] := Apply[Times, #[] + 1 & /@ FactorInteger[n]]; (* Then a lazy definition of the (infinite) list of all Triangular numbers. *) triangles = FoldList[Plus, 0, Lazy[Integers]]; (* Filter that list down to just the ones with more than 500 divisors and take the first element. *) triangles ~Select~ (divisorsLength[#] > 500 &) // First