This paper presents a grammatical theory which has certain mathematical properties, and which produces the sentences of a language by means of two simple processes, word-entry and entry-reduction, with the meaning of each sentence being indicated directly by its construction. The reason for seeking a mathematical control on grammatical analysis lies partly in the inherent possibilities of such a connexion, and partly in the complex and somewhat haphazard nature of grammar, which makes one wonder if there is not something simpler and more principled involved. In the event, the system of grammatical analysis which is reached here is not an alternative to descriptions of grammatical patterns, but rather a complement to them; for in producing the sentences it locates and explicates those patterns as resultants of the two processes, but without cataloguing or arranging them.