Difference between revisions of "User:WillNess"
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g xs = 3 : gaps 5 (foldi (\(c:cs) > (c:) . union cs) [] 
g xs = 3 : gaps 5 (foldi (\(c:cs) > (c:) . union cs) [] 

[[x*x, x*x+2*x..]  x < xs]) 
[[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 
+  fix g = xs where xs = g xs  global defn to avoid space leak 
</haskell> 
</haskell> 

Revision as of 06:57, 26 October 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:
If you're put off by selfreferentiality, just replace or on the righthand side of equations with .