On Thu, 19 Oct 2006, Mikael Johansson wrote:
On Thu, 19 Oct 2006, Mikael Johansson wrote:
Comparing the code for permutationgropus at http://www.polyomino.f2s.com/david/haskell/codeindex.html with my own thoughts on the matter, I discover the one line to figure out whether a specific list represents the identity:
isIdentity (PL xs) = all (\(i,j) -> i==j) (zip [1..] xs)
Is there any sort of benefit to be won by using this construction instead of
isIdentity (PL xs) = xs == [1..(length xs)]
and if so, what?
At some point in the future, I'll learn to think more before I post. Say
isIdentity xs = all (\(i,j) -> i==j) (zip [1..] xs) isIdentity' xs = xs == [1..(length xs)]
Then isIdentity 1:3:2:[4..100000] finishes in an instant, whereas isIdentity' 1:3:2:[4..100000] takes noticable time before completing.
So it's a question of getting laziness to work for you.
Indeed. The first version works also for infinite lists. That is, if the infinite list does not represent the identity, the function will eventually return False, otherwise it runs forever. Btw. you can simplify this version to: isIdentity (PL xs) = and (zipWith (==) [1..] xs)