Difference between revisions of "User:WillNess"
Jump to navigation
Jump to search
Line 1: | Line 1: | ||
− | A perpetual Haskell newbie. I like ''[http://ideone.com/qpnqe this |
+ | A perpetual Haskell newbie. I like ''[http://ideone.com/qpnqe this one-liner]'': |
<haskell> |
<haskell> |
||
− | -- |
+ | -- infinite folding idea due to Richard Bird |
-- double staged production idea due to Melissa O'Neill |
-- double staged production idea due to Melissa O'Neill |
||
− | -- tree folding idea Dave Bayer / |
+ | -- tree folding idea Dave Bayer / improved tree structure |
+ | -- Heinrich Apfelmus / simplified formulation Will Ness |
||
− | primes = 2 : g (fix g) |
||
− | + | primes = 2 : _Y ((3:) . gaps 5 |
|
− | + | . foldi (\(x:xs) -> (x:) . union xs) [] |
|
− | + | . map (\p-> [p*p, p*p+2*p..])) |
|
+ | _Y g = g (_Y g) -- multistage production |
||
− | fix g = xs where xs = g xs -- global defn to avoid space leak |
||
− | gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c, |
+ | gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c, |
− | | k < c = k : gaps (k+2) s -- fused |
+ | | k < c = k : gaps (k+2) s -- fused for better performance |
− | | |
+ | | otherwise = gaps (k+2) t -- k==c |
</haskell> |
</haskell> |
||
Revision as of 09:30, 6 August 2013
A perpetual Haskell newbie. I like this one-liner:
-- infinite folding idea due to Richard Bird
-- double staged production idea due to Melissa O'Neill
-- tree folding idea Dave Bayer / improved tree structure
-- Heinrich Apfelmus / simplified formulation Will Ness
primes = 2 : _Y ((3:) . gaps 5
. foldi (\(x:xs) -> (x:) . union xs) []
. map (\p-> [p*p, p*p+2*p..]))
_Y g = g (_Y g) -- multistage production
gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c,
| k < c = k : gaps (k+2) s -- fused for better performance
| otherwise = gaps (k+2) t -- k==c
foldi
is on Tree-like folds page. union
and more at Prime numbers.
The constructive definition of primes is the Sieve of Eratosthenes:
using standard definition
- . . . or, :) :) .
Trial division sieve is:
If you're put off by self-referentiality, just replace or on the right-hand side of equations with , but even ancient Greeks knew better.