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Line 5: Line 5:
 
<haskell>
 
<haskell>
 
primes = 2 : g (fix g) -- double staged production idea due to M. O'Neill
 
primes = 2 : g (fix g) -- double staged production idea due to M. O'Neill
where
+
  where
  g xs = 3 : (gaps 5 $ foldi (\x:xs -> (x:) . union xs)
+
    g xs = 3 : (gaps 5 $ foldi (\q:qs -> (q:) . union qs)
                            [[p*p, p*p+2*p..] | p <- xs])
+
                              [[p*p, p*p+2*p..] | p <- xs])
  gaps k s@(x:xs) -- | k<=x = minus [k,k+2..] xs
+
                  -- inlined to avoid a space leak
+
      = if k < x
+
          then k : gaps (k+2) s
+
          else    gaps (k+2) xs
+
  
 
fix g = xs where xs = g xs
 
fix g = xs where xs = g xs
 +
 +
gaps k s@(x:xs) = if k < x      -- | k<=x = minus [k,k+2..] xs
 +
        then k : gaps (k+2) s  -- inlined to avoid a space leak
 +
        else    gaps (k+2) xs
 
</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]]. More at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]].

Revision as of 12:58, 7 August 2011

I am a newbie, interested in Haskell.

I like this:

primes = 2 : g (fix g) -- double staged production idea due to M. O'Neill
  where
    g xs = 3 : (gaps 5 $ foldi (\q:qs -> (q:) . union qs)
                               [[p*p, p*p+2*p..] | p <- xs])
 
fix g = xs where xs = g xs
 
gaps k s@(x:xs) = if k < x      -- | k<=x = minus [k,k+2..] xs
        then k : gaps (k+2) s   -- inlined to avoid a space leak
        else     gaps (k+2) xs

foldi is on Tree-like folds. More at Prime numbers.