# User:WillNess

### From HaskellWiki

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

<haskell> | <haskell> | ||

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

− | -- double staged production | + | -- double staged primes production due to Melissa O'Neill |

− | -- tree folding idea Dave Bayer | + | -- tree folding idea Heinrich Apfelmus / Dave Bayer |

− | primes = 2 : | + | 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) | + | 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> | ||

Line 23: | Line 22: | ||

::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{p\,q:q \in \mathbb{N}_{p}\}</math> | ::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{p\,q:q \in \mathbb{N}_{p}\}</math> | ||

using standard definition | using standard definition | ||

− | ::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math>   . . . or,  <math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math> | + | ::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math>   . . . or,  <math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math> . |

Trial division sieve is: | Trial division sieve is: |

## Latest revision as of 11:45, 8 April 2015

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.