# Difference between revisions of "User:WillNess"

From HaskellWiki

(if you're put off by self-referentiality) |
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Trial division sieve: |
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} |
+ | ::::<math>\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\not\exists p \in \mathbb{T}) (p\leq \sqrt{n}\,, p\mid n)\}</math> |

If you're put off by self-referentiality, just replace <math>\mathbb{S}</math> or <math>\mathbb{T}</math> on the right-hand side of equations with <math>\mathbb{N}_{2}</math>. |
If you're put off by self-referentiality, just replace <math>\mathbb{S}</math> or <math>\mathbb{T}</math> on the right-hand side of equations with <math>\mathbb{N}_{2}</math>. |

## Revision as of 16:40, 5 September 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:

If you're put off by self-referentiality, just replace or on the right-hand side of equations with .