What is the haskell way to copy a directory

It's possible to use the Shelly library in order to do this, see cp_r:

cp_r "sourcedir" "targetdir"

Shelly first tries to use native cp -r if available. If not, it falls back to a native Haskell IO implementation.

For further details on type semantics of cp_r, see this post written by me to described how to use cp_r with String and or Text.

Shelly is not platform independent, since it relies on the Unix package, which is not supported under Windows.

The filesystem-trees package provides the means for a very simple implementation:

import System.File.Tree (getDirectory, copyTo_)

copyDirectory :: FilePath -> FilePath -> IO ()
copyDirectory source target = getDirectory source >>= copyTo_ target

I couldn't find anything that does this on Hackage.

Your code looks pretty good to me. Some comments:

1. dstExists <- doesDirectoryExist dst
   

   This does not take into account that a file with the destination name might exist.

2. if or [not srcExists, dstExists] then print "cannot copy"
   

   You might want to throw an exception or return a status instead of printing directly from this function.

3. paths <- forM xs $ \name -> do
       [...]
     return ()
   

   Since you're not using paths for anything, you can change this to

   forM_ xs $ \name -> do
     [...]
   

The MissingH package provides recursive directory traversals, which you might be able to use to simplify your code.