Generative communication is the basis of a new distributed programming langauge that is intended for systems programming in distributed settings generally and on integrated network computers in particular. It differs from previous interprocess communication models in specifying that messages be added in tuple-structured form to the computation environment, where they exist as named, independent entities until some process chooses to receive them. Generative communication results in a number of distinguishing properties in the new language, Linda, that is built around it. Linda is fully distributed in space and distributed in time; it allows distributed sharing, continuation passing, and structured naming. We discuss these properties and their implications, then give a series of examples. Linda presents novel implementation problems that we discuss in Part II. We are particularly concerned with implementation of the dynamic global name space that the generative communication model requires.