If you cut out fruit, as well as grains and added sugar, it makes for an extremely low-
carb diet, but to me, cutting out fruit is going a little too far.
Look into the paleo diet. Some people on paleo eat fruit, and some don't, but there is no paleo diet that includes processed foods, added sugar, or grains. Letting go of processed foods is important for health and weight loss, because among other reasons, processed foods often contain grains and added sugars.