A discrete analogue of the theory of DC programming is constructed on the basis of discrete convex analysis. Since there are two classes of discrete convex functions (M-convex functions and L-convex functions), there are four types of discrete DC functions (an M-convex function minus an M-convex function, an M-convex function minus an L-convex function, and so on) and four types of DC programs. The discrete Toland-Singer duality establishes the relation among the four types of discrete DC programs.