How should time travel work in an ideal programming language?

How should time travel work in an ideal programming language?

ToonTalk provides users with a time travel ability. They can go back to an earlier time in their session and replay or revise the past. These time travel records can be copied and shared with others.

The implementation sometimes imposes an unacceptable performance penalty upon the system but in other cases it is very useful for undoing, reviewing, and creating demos for others. A more clever implementation could dramatically reduce the performance cost in many cases.

ToonTalk's time travel enables one to reply the past from the viewpoint it was viewed when recorded. A more general and useful version would allow one to "move the camera" while replaying. Or maybe to join the scene as a ghost until such time as one is ready to fork the time line.