Closed Cell Foam
Closed cell foam mats are light and puncture proof. However they are also bulky and not as comfortable as an airmat. Never-the-less they are probably the best choice for alpine climbing as they are so light and can't go wrong. Karrimor were marketing closed cell foam mats when many of you were in nappies. Alas, the firm is now defunct in all but name, but the Karrimat (which was made by Beacons Products), will last a lifetime and appears indestructible (unless you attack it with a knife or chew it).
Top tip: Puncture a hole in the centre of one end of your mat and tie half a metre of elastic cord to it. Then tie a loop of suitable size in the other end of the cord. Now you will always have something to roll your mat up with, and always have something to anchor it with on a windy day.