This is of course a purely syntactic operation on atoms (not strings, although strings are accepted). The module doesn't care whether the files or directories exist or not.

The character / is assumed special. The \ is NOT assumed special

Examples for mode (+Directory,+File,-Path):

?- directory_file_path("/alpha/beta","somefile",P).
P = '/alpha/beta/somefile'.

?- directory_file_path("alpha/beta","somefile",P).
P = 'alpha/beta/somefile'.

?- directory_file_path("alpha////beta","somefile",P). % cleanup not included
P = 'alpha////beta/somefile'.

?- directory_file_path("alpha/beta/","somefile",P).
P = 'alpha/beta/somefile'.

I'm not a fan of this. That should be cleaned up:

?- directory_file_path("alpha/beta///","somefile",P).
P = 'alpha/beta///somefile'.

But this is ugly, if not buggy:

?- directory_file_path("alpha/beta/","/somefile",P).
P = "/somefile".

Similarly:

?- directory_file_path("alpha/beta/","/somefile/someotherfile",P).
P = "/somefile/someotherfile".

More edge cases:

?- directory_file_path("/","/somefile",P).
P = "/somefile".

?- directory_file_path("","/somefile",P).
P = "/somefile".

This is ugly:

?- directory_file_path("","somefile",P).
P = '/somefile'.

Because here it's different:

?- directory_file_path("foo","somefile",P).
P = 'foo/somefile'.

?- directory_file_path("foo/bar","somefile",P).
P = 'foo/bar/somefile'.

Patterns for use in expand_file_name/2 can be created:

?- directory_file_path("alpha/beta","*.pl",P).
P = 'alpha/beta/*.pl'.