This is one of my favorite sauces: Its deep, purpley, cranberry color is reason enough for that designation, but then again so is the bright strawberry/kiwi/watermelon flavor, with its hints of the unbridled tropics. And the fact that you can tell your guests you're serving them cactus fruit (and that it is delicious) gives you a decidedly exotic edge.
The puree is very watery, like watermelon juice, so in order to give the sauce some body but not take away all the fruit's freshness, I've directed you to rapidly boil down part of the puree with sugar, then cool it and add the remaining uncooked puree. This method works well with watermelon puree, too, should you not be able to find prickly pears. You will need about 3 cups seeded, pureed watermelon pulp.