# User:WillNess

### From HaskellWiki

(Difference between revisions)

Line 1: | Line 1: | ||

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

<haskell> | <haskell> | ||

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

− | | k < c = k : gaps (k+2) s -- fused | + | | k < c = k : gaps (k+2) s -- fused for better performance |

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

</haskell> | </haskell> | ||

## 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.