Chalk used as a toothpaste abrasive, usually paired with sodium monofluorophosphate. Cleans well; claims that it 'remineralises' teeth are mostly theory.
Calcium carbonate is a mild-to-moderate abrasive that has been used in toothpaste for over a century. Because its calcium would bind free fluoride, chalk pastes use sodium monofluorophosphate rather than sodium fluoride.
Manufacturers suggest the chalk particles also raise calcium in plaque and neutralise acid, which in theory could help fluoride work. That is plausible, but it has not been shown to prevent more decay than silica pastes with the same fluoride.
Calcium carbonate-SMFP toothpastes prevent decay in clinical trials, with the effect attributed to the fluoride. The added calcium/acid-neutralising benefit is mechanistic and comes largely from industry-authored reviews.
Sodium monofluorophosphate in calcium carbonate toothpastes is an effective anti-caries combination in numerous clinical trials; the authors propose that calcium carbonate may add benefit by raising plaque calcium and neutralising acid, which is mechanistic and not separately proven.