# Difference between revisions of "User:WillNess"

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− | I am a newbie, interested in Haskell. |
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+ | I like ''[http://ideone.com/qpnqe this one-liner]'': |
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− | I like ''this'': |
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<haskell> |
<haskell> |
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+ | -- infinite folding due to Richard Bird |
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+ | -- double staged primes production due to Melissa O'Neill |
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+ | -- tree folding idea Heinrich Apfelmus / Dave Bayer |
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+ | _Y g = g (_Y g) -- multistage production via Y combinator |
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+ | |||

+ | gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c, |
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+ | | k < c = k : gaps (k+2) s -- fused for better performance |
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+ | | otherwise = gaps (k+2) t -- k==c |
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</haskell> |
</haskell> |
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− | <code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]]. |
+ | <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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+ | The constructive definition of primes is the Sieve of Eratosthenes: |
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+ | ::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{p\,q:q \in \mathbb{N}_{p}\}</math> |
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+ | using standard definition |
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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 is: |
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+ | ::::<math>\textstyle\mathbb{T} = \{n \in \mathbb{N}_{2}: (\forall p \in \mathbb{T})(2\leq p\leq \sqrt{n}\, \Rightarrow \neg{(p \mid n)})\}</math> |
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+ | 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>, but even ancient Greeks knew better. |

## 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.