Abstract: The invention provides compounds of formula (I): wherein: R1-R4 and A have any of the values defined in the specification, and their pharmaceutically acceptable salts, are useful for inhibiting ?-lactamase enzymes, for enhancing the activity of ?-lactam antibiotics, and for treating ?-lactam resistant bacterial infections in a mammal. The invention also provides pharmaceutical compositions, processes for preparing compounds of formula (I), wherein R1 and R2 are each independently hydrogen, (C1-C10)alkyl, (C2-C10)alkenyl, (C2-C10)alkenyl, (C3-C8)cycloalkyl, (C1-C10)alkoxy, (C1-C10)alkanoyl, (C1-C10)alkanoyloxy, (C1-C10)alkoxycarbonyl, aryl, heterocycle, halo, cyano, nitro, —COORe, —C(?O)NRfRg, —OC(?O)NRfRg, NRfRg, or —S(O)nRh; R3 is hydrogen, halo, aryl, heteroaryl, —S(O)nRh, or —CH?CHC(?O)NRmRp; R4 is hydrogen; A is thio, sulfinyl, or sulfonyl; and intermediates useful for the synthesis of compounds of formula (I).