The cohesion of cubic solid calcium fluoride is studied theoretically within the framework of the fully ionic model by a non-empirical approach in which the major portion of the cohesion, namely that not originating from electron correlation effects, is computed ab initio using the relativistic integrals program. Electron correlation is incorporated by adding the short-range contributions calculated using density functional theory to the inter-ionic dispersive attractions evaluated with the inclusion of their damping caused by the overlap of the ion wavefunctions. The interaction of the fluoride ion with its environment in crystal significantly modifies the computed inter-ionic potentials and two different methods for describing these modifications are compared. The more sophisticated and realistic of the two methods predicts values for the lattice energy, equilibrium closest cation-anion separation and bulk modulus in excellent agreement with experiment.