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We get a tree we call Hog Plum or Tallow Plum. Fruit is kinda bitter and sweet.

http://www.eattheweeds.com/ximenia-americana-known-by-many-names-2/

I have had the cane juice fresh squeezed also. Tasted very grassy to me. Lots of islanders swear by it as a healthy drink. I can't remember what they said it was good for exactly. We gnawed on sugar...