fragmentary ideas ䷿ intellectual what-nots ䷷ and haskell programming ䷴

The function groupBy from haskell’s standard library is defined in terms of span, the effect being that the supplied predicate function is used to compare the first element of a group with successive elements.

This isn’t clear from the docs, and you might try to do this and wonder at the output you got:

*Main> groupBy (< =) [3,4,5,3,2,1,4,4,1,1,2,3,4,5,4,5,6,7]
[[3,4,5,3],[2],[1,4,4,1,1,2,3,4,5,4,5,6,7]]

We can redefine groupBy as follows, so that the supplied predicate function compares adjacent elements one-by-one and returns True if they should be grouped together:

> groupBy' :: (a -> a -> Bool) -> [a] -> [[a]]
> groupBy' c []     = []
> groupBy' c (a:as) = (a:ys) : groupBy' c zs
>     where (ys,zs) = spanC a as
>           spanC _  []    = ([], [])
>           spanC a' (x:xs)
>             | a' `c` x   = let (ps,qs) = spanC x xs 
>                            in (x:ps,qs)
>             | otherwise = ([], x:xs)

Now we can use the groupBy function to return a list of ascending lists, like we (probably) wanted:

*Main> groupBy' (< =) [3,4,5,3,2,1,4,4,1,1,2,3,4,5,4,5,6,7]
[[3,4,5],[3],[2],[1,4,4],[1,1,2,3,4,5],[4,5,6,7]]

The functionality is of course the same for groupBy (==).