Preheat oven to 350F. In a mixing bowl, cream butter and sugar, beating until light. Beat in eggs, one at a time. Stir in chopped apples, cheese and nuts. In a separate bowl, combine flour, baking powder, baking soda, and salt. Gradually and gently stir into apple mixture. Mix well. Pour into a greased 9 by 5 3-inch loaf pan. Bake at 350F for 40-50 minutes. Cool on a wire rack and cut into 1-inch slices.