Starting from Marr's ideas about levels of explanation, a theory of the data structures and access processes in human memory is demonstrated on 10 tasks. Functional characteristics of human memory are captured implementation-independently. Our theory generates a multidimensional task classification subsuming existing classifications such as the distinction between tasks that are implicit versus explicit, data driven versus conceptually driven, and simple associative (two-way bindings) versus higher order (threeway bindings), providing a broad basis for new experiments. The formal language clarifies the binding problem in episodic memory, the role of input pathways in both episodic and semantic (lexical) memory, the importance of the input set in episodic memory, and the ubiquitous calculation of an intersection in theories of episodic and lexical access.