One example I like for K is: Maximum subarray sum[0]. The canonical K solution (sorry, my APL is too rusty to translate) is

    |/0(0|+)\

Yes, this is the complete function, and it is the efficient O(n) solution; A K programmer is likely to recognize it immediately (using eyes for pattern recognition). Now, if I were to rewrite it in infix/paren syntax, it would become:

   mss(x):=fold(max,0,scan(lambda(a,b) max(0,a+b), 0, x))

This is not at all more readable (arguably less readable) than the K version, and it's inherent, in the sense that the K uses your organic pattern matcher (supplied by eyes and brain) much better than a haskell/lisp version ever will.

Similarly,

    ,//

Is flatten; If you were to write it verbosely, it would be

    flatten(x):=converge(fold(concatenate,x))

While this may be more readable, the K syntax (as does the APL one) gives you a concise, well defined, pattern matchable version. (Which doesn't actually need documentation - the implementation is 3 chars, so if you want to know how it behaves on an empty list -- just read the implementation!)

[0] https://en.wikipedia.org/wiki/Maximum_subarray_problem