Difference between revisions of "User:WillNess"
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− | + | I like ''[http://ideone.com/qpnqe this one-liner]'': |
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<haskell> |
<haskell> |
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− | -- infinite folding |
+ | -- infinite folding due to Richard Bird |
− | -- double staged |
+ | -- double staged primes production due to Melissa O'Neill |
− | -- tree folding idea |
+ | -- tree folding idea Heinrich Apfelmus / Dave Bayer |
− | -- Heinrich Apfelmus / simplified formulation Will Ness |
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primes = 2 : _Y ((3:) . gaps 5 |
primes = 2 : _Y ((3:) . gaps 5 |
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. foldi (\(x:xs) -> (x:) . union xs) [] |
. foldi (\(x:xs) -> (x:) . union xs) [] |
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. map (\p-> [p*p, p*p+2*p..])) |
. map (\p-> [p*p, p*p+2*p..])) |
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− | _Y g = g (_Y g) -- multistage production |
+ | _Y g = g (_Y g) -- multistage production via Y combinator |
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, |
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::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{p\,q:q \in \mathbb{N}_{p}\}</math> |
::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{p\,q:q \in \mathbb{N}_{p}\}</math> |
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using standard definition |
using standard definition |
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− | ::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math>   . . . or,  <math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math> |
+ | ::::<math>\textstyle\mathbb{N}_{k} = \{ n \in \mathbb{N} : n \geq k \}</math>   . . . or,  <math>\textstyle\mathbb{N}_{k} = \{k\} \bigcup \mathbb{N}_{k+1}</math> . |
Trial division sieve is: |
Trial division sieve is: |
Revision as of 11:45, 8 April 2015
I like this one-liner:
-- infinite folding due to Richard Bird
-- double staged primes production due to Melissa O'Neill
-- tree folding idea Heinrich Apfelmus / Dave Bayer
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 via Y combinator
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.