User:WillNess
From HaskellWiki
I like this one-liner:
-- infinite folding due to Richard Bird
-- double staged primes production due to Melissa O'Neill
-- tree folding idea Heinrich Apfelmus / Dave Bayer
primes = 2 : _Y ((3:) . gaps 5
. foldi (\(x:xs) -> (x:) . union xs) []
. map (\p-> [p*p, p*p+2*p..]))
_Y g = g (_Y g) -- multistage production via Y combinator
gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c,
| k < c = k : gaps (k+2) s -- fused for better performance
| otherwise = gaps (k+2) t -- k==c
foldi
is on Tree-like folds page. union
and more at Prime numbers.
The constructive definition of primes is the Sieve of Eratosthenes:
using standard definition
. . . or,
.
Trial division sieve is:
If you're put off by self-referentiality, just replace or
on the right-hand side of equations with
, but even ancient Greeks knew better.