[Haskell-cafe] List comparisons and permutation group code

[Mikael Johansson]

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.

-- 
Mikael Johansson                 | To see the world in a grain of sand
mikael at johanssons.org            |  And heaven in a wild flower
http://www.mikael.johanssons.org | To hold infinity in the palm of your hand
                                  |  And eternity for an hour