Evans and Gazdar (Evans and Gazdar, 1989a; Evans and Gazdar, 1989b) introduced DATR as a simple, non-monotonic language for representing natural language lexicons. Although a number of implementations of DATR exist, the full language has until now lacked an explicit, declarative semantics. This paper rectifies the situation by providing a mathematical semantics for DATR. We present a view of DATR as a language for defining certain kins of partial functions by cases. The formal model provides a transparent treatment of DATR's notion of global context. It is shown that DATR's default mechanism can be accounted for by interpreting value descriptors as families of values indexed by paths.