"I was updating my mac, then it shut down, right in the middle of it, when I turned it back on, I couldn't open anything, but the things I updated awhile ago. Is there any programme that could restore my mac?"
The Mac still actually _boots up_ to the finder, is that correct?
What system do you have, and what were you trying to upgrade _to_?
IF you can get to the finder and then launch Safari, my suggestion is to download the "combo updater" for the update you were shooting for. Important: this is NOT done through "software update", you have to go to Apple's support area, locate the combo updater, download it, and then apply it. These are usually BIG files (hundreds of megabytes).
But sometimes running the combo updater "over" a "problem update" will fix the problems. It's worth the try.
Another suggestion:
This is exactly why you should keep a BOOTABLE BACKUP DRIVE in addition to your computer. If something goes wrong, in a moment of need, you can just boot from the backup and "attack" the problems on your main drive.
But -- DON'T use Time Machine to back up. To create a bootable backup, you'll need either CarbonCopyCloner (free) or SuperDuper.
