Motivation: ---------- Data.List.sort is a very important functionality in Haskell. I believe that the proposed implementation is: - significantly faster than the current implementation on unsorted lists, typically 14% to 27% faster - more laziness-friendly, i.e.: take 3 $ sort l will require significantly less comparisons than the current implementation Proposed Implementation ----------------------- sort :: (Ord a) => [a] -> [a] sort = sortBy compare sortBy cmp [] = [] sortBy cmp xs = head $ until (null.tail) reduce (pair xs) where pair (x:y:t) | x `cmp` y == GT = [y, x] : pair t | otherwise = [x, y] : pair t pair [x] = [[x]] pair [] = [] reduce (v:w:x:y:t) = merge v' x' : reduce t where v' = merge v w x' = merge x y reduce (x:y:t) = merge x y : reduce t reduce xs = xs merge xs [] = xs merge [] ys = ys merge xs@(x:xs') ys@(y:ys') | x `cmp` y == GT = y : merge xs ys' | otherwise = x : merge xs' ys Effect and Interactions ----------------------- I have a stack project with a criterion test for this new implementation, available at https://github.com/greg7mdp/ghc-sort. I ran the tests on an Ubuntu 14.0.2 VM and GHC 8.0.2, and had the following results: - sorting of random lists of integers is 27% faster - sorting of random lists of strings is 14% faster - sorting of already sorted lists is significantly slower, but still much faster than sorting random lists - proposed version is more laziness friendly. For example this version of sortBy requires 11 comparisons to find the smallest element of a 15 element list, while the default Data.List.sortBy requires 15 comparisons. (see https://github.com/greg7mdp/ghc-sort/blob/master/src/sort_with_trace.hs) Test results ------------ Criterion output (descending/ascending results are for already sorted lists). I barely understand what Criterion does, and I am puzzled with the various "T" output - maybe there is a bug in my bench code: vagrant@vagrant-ubuntu-trusty-64:/vagrant$ stack exec ghc-sort benchmarking ascending ints/ghc TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTtime 160.6 ms (153.4 ms .. 167.8 ms) 0.997 R² (0.986 R² .. 1.000 R²) mean 161.7 ms (158.3 ms .. 165.9 ms) std dev 5.210 ms (3.193 ms .. 7.006 ms) variance introduced by outliers: 12% (moderately inflated) benchmarking ascending ints/greg TTTTTTTTTTTTTTTTtime 473.8 ms (398.6 ms .. 554.9 ms) 0.996 R² (0.987 R² .. 1.000 R²) mean 466.2 ms (449.0 ms .. 475.0 ms) std dev 14.94 ms (0.0 s .. 15.29 ms) variance introduced by outliers: 19% (moderately inflated) benchmarking descending ints/ghc TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTtime 165.1 ms (148.2 ms .. 178.2 ms) 0.991 R² (0.957 R² .. 1.000 R²) mean 158.7 ms (154.0 ms .. 164.3 ms) std dev 7.075 ms (4.152 ms .. 9.903 ms) variance introduced by outliers: 12% (moderately inflated) benchmarking descending ints/greg TTTTTTTTTTTTTTTTtime 471.7 ms (419.8 ms .. 508.3 ms) 0.999 R² (0.995 R² .. 1.000 R²) mean 476.0 ms (467.5 ms .. 480.0 ms) std dev 7.447 ms (67.99 as .. 7.865 ms) variance introduced by outliers: 19% (moderately inflated) benchmarking random ints/ghc TTTTTTTTTTTTTTTTtime 2.852 s (2.564 s .. 3.019 s) 0.999 R² (0.997 R² .. 1.000 R²) mean 2.812 s (2.785 s .. 2.838 s) std dev 44.06 ms (543.9 as .. 44.97 ms) variance introduced by outliers: 19% (moderately inflated) benchmarking random ints/greg TTTTTTTTTTTTTTTTtime 2.032 s (1.993 s .. 2.076 s) 1.000 R² (1.000 R² .. 1.000 R²) mean 2.028 s (2.019 s .. 2.033 s) std dev 7.832 ms (0.0 s .. 8.178 ms) variance introduced by outliers: 19% (moderately inflated) benchmarking shakespeare/ghc TTTTTTTTTTTTTTTTtime 6.504 s (6.391 s .. 6.694 s) 1.000 R² (1.000 R² .. 1.000 R²) mean 6.499 s (6.468 s .. 6.518 s) std dev 28.85 ms (0.0 s .. 32.62 ms) variance introduced by outliers: 19% (moderately inflated) benchmarking shakespeare/greg TTTTTTTTTTTTTTTTtime 5.560 s (5.307 s .. 5.763 s) 1.000 R² (0.999 R² .. 1.000 R²) mean 5.582 s (5.537 s .. 5.607 s) std dev 39.30 ms (0.0 s .. 43.49 ms) variance introduced by outliers: 19% (moderately inflated) Costs and Drawbacks ------------------- The only cost I see is the reduced performance when sorting already sorted lists. However, since this remains quite efficient, indeed over 4 times faster than sorting unsorted lists, I think it is an acceptable tradeoff. Final note ---------- My Haskell is very rusty. I worked on this a couple years ago when I was learning Haskell, and meant to propose it to the Haskell community, but never got to it at the time.