Chris Brooks wrote:

I was 17 miles EAST of the airport, intercepting the localizer. I was at
5000 feet, and just got "cleared for the approach". I was IFR.


Also, if he said cross HAIGS at or above 4,000 feet, is that a clearence
to
descend to 4,000 feet?

Yes.

Can you provide a reference for that fact? So if that is the case, when can
the descent be initiated? Pilots discretion?


Did you read the ATC Handbook references I provided to you? The current ATC
Handbook is on the FAA's web site:

http://www.faa.gov/atpubs/ATC/index.htm