We study the molecular content and chemistry of a circumstellar disk surrounding the Herbig Ae star AB Aur at (sub-)millimeter wavelengths. Our aim is to reconstruct the chemical history and composition of the AB Aur disk and to compare it with disks around low-mass, cooler T Tauri stars. We observe the AB Aur disk with the IRAM Plateau de Bure Interferometer in the C- and D- configurations in rotational lines of CS, HCN, C2H, CH3OH, HCO+, and CO isotopes. Using an iterative minimization technique, observed columns densities and abundances are derived. These values are further compared with results of an advanced chemical model that is based on a steady-state flared disk structure with a vertical temperature gradient, and gas-grain chemical network with surface reactions. We firmly detect HCO+ in the 1--0 transition, tentatively detect HCN, and do not detect CS, C2H, and CH3OH. The observed HCO+ and 13CO column densities as well as the upper limits to the column densities of HCN, CS, C2H, and CH3OH are in good agreement with modeling results and those from previous studies. The AB Aur disk possesses more CO, but is less abundant in other molecular species compared to the DM Tau disk. This is primarily caused by intense UV irradiation from the central Herbig A0 star, which results in a hotter disk where CO freeze out does not occur and thus surface formation of complex CO-bearing molecules might be inhibited.Read less <