# User:WillNess

### From HaskellWiki

(Difference between revisions)

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primes = 2 : g (fix g) |
primes = 2 : g (fix g) |
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where |
where |
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− | g ps = 3 : gaps 5 (foldi (\(q:qs) -> (q:) . union qs) |
+ | g xs = 3 : gaps 5 (foldi (\(c:cs) -> (c:) . union cs) |

− | [[p*p, p*p+2*p..] | p <- ps]) |
+ | [[x*x, x*x+2*x..] | x <- xs]) |

− | gaps k s@(c:t) |
+ | gaps k s@(c:t) |

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

| True = gaps (k+2) t -- fused to avoid a space leak |
| True = gaps (k+2) t -- fused to avoid a space leak |
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<code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]] page. <code>union</code> and more at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]]. |
<code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]] page. <code>union</code> and more at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]]. |
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− | Also, the math formula for Sieve of Eratosthenes, |
+ | The math formula for Sieve of Eratosthenes, |

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

## Revision as of 10:06, 29 August 2011

I'm interested in Haskell.

I like *this*:

-- inifinte folding idea due to Richard Bird -- double staged production idea due to Melissa O'Neill -- tree folding idea Dave Bayer / simplified formulation Will Ness primes = 2 : g (fix g) where g xs = 3 : gaps 5 (foldi (\(c:cs) -> (c:) . union cs) [[x*x, x*x+2*x..] | x <- xs]) gaps k s@(c:t) | k < c = k : gaps (k+2) s -- minus [k,k+2..] (c:t), k<=c | True = gaps (k+2) t -- fused to avoid a space leak fix g = xs where xs = g xs -- global defn to avoid space leak

`foldi`

is on Tree-like folds page. `union`

and more at Prime numbers.

The math formula for Sieve of Eratosthenes,

where

- . . . or, :) :) .

Trial division sieve: