Exploring services for digital libraries (DLs) include two major paradigms, browsing and searching, as well as other services such as clustering and visualization. In this paper, we formalize and generalize DL exploring services within a DL theory. We develop theorems to indicate that browsing and searching can be converted or mapped to each other under certain conditions. The theorems guide the design and implementation of exploring services for an integrated archaeological DL, ETANA-DL. Its integrated browsing and searching can support users in moving seamlessly between these operations, minimizing context switching, and keeping users focused. It also integrates browsing and searching into a single visual interface for DL exploration. A user study to evaluate ETANA-DL's exploring services helped validate our hypotheses.