I don't see what Travis has to do with this. ... Each developer need to run the Sphinx target on the local machine.
My goal is to ensure that each pushed commit contains only valid docstrings (and this includes valid markups and existing function names in references). If only the developer was responsible for that it would be a decentral check with manual work. I'd like to see this "valid docstrings policy" to be enforced centrally so it cannot be forgotten. That is why TravisCI would be good possible tool to check also the docstrings (not only unit tests). Since I have never tried this with TravisCI am asking here...
Maybe Sphinx (or the "make html") should be more "--verbose" because I assume that Sphinx is able to validate such links by itself.
It is, I have just tried this by adding invalid markups in a docstring :py:func:`non_existing_function()` `config.Config()` missing namespace :func:`getConfig()` and "make html" at least indicates problems with reading sources... [100%] backintime common/backintime.py:docstring of backintime.printAboutHeader:6: WARNING: Definition list ends without a blank line; unexpected unindent. but the warning is not very intuitive (and only 1 out of 3 problems are discovered).