I show how a conversational process that takes simple, intuitively meaningful steps may be understood as a sophisticated computation that derives the richly detailed, complex representations implicit in our knowledge of language. To develop the account, I argue that natural language is structured in a way that lets us formalize grammatical knowledge precisely in terms of rich primitives of interpretation. Primitives of interpretation can be correctly viewed intentionally, as explanations of our choices of linguistic actions; the model therefore fits our intuitions about meaning in conversation. Nevertheless, interpretations for complex utterances can be built from these primitives by simple operations of grammatical derivation. In bridging analyses of meaning at semantic and symbol-processing levels, this account underscores the fundamental place for computation in the cognitive science of language use.