# Difference between revisions of "User:WillNess"

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

+ | ::::<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>   :) :) . |
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+ | Trial division sieve: |
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+ | |||

+ | ::::<math>\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\not\exists p \in \mathbb{T}) (p\leq \sqrt{n} \and p\mid n)\}</math> |

## Revision as of 09:43, 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 ps = 3 : gaps 5 (foldi (\(q:qs) -> (q:) . union qs)
[[p*p, p*p+2*p..] | p <- ps])
gaps k s@(c:t)
| k < c = k : gaps (k+2) s -- | k<=c = minus [k,k+2..] s
| 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.

Also, the math formula for Sieve of Eratosthenes,

where

- . . . or, :) :) .

Trial division sieve: