Ice Cream with Rum Mango Sauce

1 ripe mango, peeled and diced
3/4 cup pineapple juice
2 tablespoons honey
2 tablespoons dark rum or 1/4 teaspoon rum extract
2 tablespoons fresh lime juice
2 teaspoons cornstarch
1 tablespoon water
Grated zest of 1 lime
Vanilla low-fat or non-fat ice cream or ice milk,
    or flavor of your choice

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