Some aspects of meaning come from a compositional process that combines the meanings of lexical elements into the meanings of complex phrases. Other aspects come from context and the recognition of speaker intentions. How do compositional build-up and contextual interpretation hang together? In this talk I will sketch a theory in which the two processes work closely in tandem. An interpretation calculus will be defined that takes a meaning recipe—a lambda term encoding how meanings are to be combined—as its input and then helps compute the concrete intended meaning, given the context. The process is abductive—each noncontradictory branch of the interpretation tree that is developed corresponds to a limited menu of possible context updates. The task of a hearer is to pick the option that is intended in each case.