Difference between revisions of "User:WillNess"
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primes = 2 : g (fix g) 
primes = 2 : g (fix g) 

where 
where 

−  g 
+  g xs = 3 : gaps 5 (foldi (\(c:cs) > (c:) . union cs) 
−  [[ 
+  [[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 = 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#Treelike_foldsTreelike folds]] page. <code>union</code> and more at [[Prime numbers#Sieve_of_EratosthenesPrime numbers]]. 
<code>foldi</code> is on [[Fold#Treelike_foldsTreelike folds]] page. <code>union</code> and more at [[Prime numbers#Sieve_of_EratosthenesPrime numbers]]. 

−  +  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 Treelike folds page. union
and more at Prime numbers.
The math formula for Sieve of Eratosthenes,
where
 . . . or, :) :) .
Trial division sieve: