# User:WillNess

### From HaskellWiki

(Difference between revisions)

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− | A perpetual Haskell newbie. I like ''[http://ideone.com/qpnqe this semi-one-liner]'': |
+ | A perpetual Haskell newbie. I like ''[http://ideone.com/qpnqe this one-liner]'': |

<haskell> |
<haskell> |
||

− | -- inifinte folding idea due to Richard Bird |
+ | -- infinite folding idea due to Richard Bird |

-- double staged production idea due to Melissa O'Neill |
-- double staged production idea due to Melissa O'Neill |
||

− | -- tree folding idea Dave Bayer / simplified formulation Will Ness |
+ | -- tree folding idea Dave Bayer / improved tree structure |

− | primes = 2 : g (fix g) |
+ | -- Heinrich Apfelmus / simplified formulation Will Ness |

− | where |
+ | primes = 2 : _Y ((3:) . gaps 5 |

− | g xs = 3 : gaps 5 (foldi (\(c:cs) -> (c:) . union cs) [] |
+ | . foldi (\(x:xs) -> (x:) . union xs) [] |

− | [[x*x, x*x+2*x..] | x <- xs]) |
+ | . map (\p-> [p*p, p*p+2*p..])) |

− | fix g = xs where xs = g xs -- global defn to avoid space leak |
+ | _Y g = g (_Y g) -- multistage production |

− | gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c, |
+ | gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c, |

− | | k < c = k : gaps (k+2) s -- fused to avoid a space leak |
+ | | k < c = k : gaps (k+2) s -- fused for better performance |

− | | True = gaps (k+2) t |
+ | | otherwise = gaps (k+2) t -- k==c |

</haskell> |
</haskell> |
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## Latest revision as of 09:30, 6 August 2013

A perpetual Haskell newbie. I like *this one-liner*:

-- infinite folding idea due to Richard Bird -- double staged production idea due to Melissa O'Neill -- tree folding idea Dave Bayer / improved tree structure -- Heinrich Apfelmus / simplified formulation Will Ness 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 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.