On Mon, Jun 27, 2011 at 4:25 PM, Twan van Laarhoven
On 2011-06-27 13:51, Steffen Schuldenzucker wrote:
Could you specify what exactly the function is supposed to do? I am pretty sure that a function like
seqPeriod :: (Eq a) => [a] -> Maybe Integer -- Nothing iff non-periodic
cannot be written.
What about sequences that can be specified in terms of 'iterate':
This is beginning to be reminiscent of the recent paper by Max Bolingbroke, "termination combinators forever" (great paper). http://www.cl.cam.ac.uk/~mb566/papers/termination-combinators-hs11.pdf
import Control.Arrow (first)
-- Return the non-repeating part of a sequence followed by the repeating part. -- -- > iterate f x0 == in a ++ cycle b -- > where (a,b) = findCycle f x0 -- -- see http://en.wikipedia.org/wiki/**Cycle_detectionhttp://en.wikipedia.org/wiki/Cycle_detection findCycle :: Eq a => (a -> a) -> a -> ([a],[a]) findCycle f x0 = go1 (f x0) (f (f x0)) where go1 x y | x == y = go2 x0 x | otherwise = go1 (f x) (f (f y)) go2 x y | x == y = ([], x : go3 x (f x)) | otherwise = first (x:) (go2 (f x) (f y)) go3 x y | x == y = [] | otherwise = y : go3 x (f y)
-- diverges if not periodic seqPeriod :: Eq a => (a -> a) -> a -> Integer seqPeriod f x0 = length . snd $ findCycle f x0
Twan
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