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<haskell>
 
<haskell>
primes = 2 : g (fix g) -- double staged production idea due to M. O'Neill
+
-- inifinte folding idea due to Richard Bird
where
+
-- double staged production idea due to Melissa O'Neill
g xs = 3 : (gaps 5 $ foldi (\(q:qs) -> (q:) . union qs)
+
-- tree folding idea Dave Bayer / simplified formulation Will Ness
[[p*p, p*p+2*p..] | p <- xs])
+
primes = 2 : g (fix g)
gaps k s@(x:xs)
+
where
| k < x = k : gaps (k+2) s -- | k<=x = minus [k,k+2..] xs
+
g ps = 3 : gaps 5 (foldi (\(q:qs) -> (q:) . union qs)
| True = gaps (k+2) xs -- inlined to avoid a space leak
+
[[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
 
fix g = xs where xs = g xs -- global defn to avoid space leak
 
</haskell>
 
</haskell>
   
<code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]]. More at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]].
+
<code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]] page. More at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]].

Revision as of 15:25, 7 August 2011

I am a newbie, 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. More at Prime numbers.