User:WillNess
Jump to navigation
Jump to search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
Monad is composable computation descriptions.
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, P = N2\N2*N2 = N2\P*N2 :
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 , as the ancient Greeks might or mightn't have done, as well.