User:WillNess

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Monad is composable computation descriptions.


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, P  =  N2\N2*N2  =  N2\P*N2 :

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 , as the ancient Greeks might or mightn't have done, as well.