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We define interface, module and the meaning of M offers I, where M denotes a module and I an interface. For a module M and disjoint interfaces U and L, the meaning of M using L offers U is also defined. For a linear hierarchy of modules and interfaces, M1, I1, M2, I2, ..., Mn, In, we present the following composition theorem: If M1 offers I1 and, for i=2,..., n, Mi using Ii-1 offers Ii, then the hierarchy of modules offers Ii.Our theory is applied to solve a problem posed by Leslie Lamport at the 1987 Lake Arrowhead Workshop. We first present a formal specification of a serializable database interface. We then provide specifications of two modules, one based upon two-phase locking and the other multi-version timestamps; the two-phase locking module uses an interface offered by a physical database. We prove that each module offers the serializable interface.