In a large skillet heat apple juice. Add sweet potato slices, spreading evenly. Cook, covered, over low heat about 12 minutes or until potatoes are nearly tender. Stir in apple, cranberries, maple syrup, rum (if desired), and salt. Cook, covered, over low heat for 3 to 4 minutes more or just until apple is tender.
Uncover; boil gently for 3 to 4 minutes more or until liquid is syrupy. Spoon into a serving bowl. Sprinkle with nuts.