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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 (\(q:qs)-> (q:) . union qs)
+
     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 = k : gaps (k+2) s    -- | k<=x = minus [k,k+2..] xs
 +
      | True  =    gaps (k+2) xs    -- inlined to avoid a space leak
  
fix g = xs where xs = g xs
+
fix g = xs where xs = g xs           -- global defn to avoid space leak
 
+
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 13:38, 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])
    gaps k s@(x:xs)                
       | k < x = k : gaps (k+2) s     -- | k<=x = minus [k,k+2..] xs
       | True  =     gaps (k+2) xs    -- inlined to avoid a space leak
 
fix g = xs where xs = g xs            -- global defn to avoid space leak

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