Categorial grammars, as I have already suggested, have a long and distinguished history, but one which is quite distinct from the back­ ground to phrase-structure grammars, and unfamiliar to many lin­ guists. They are rooted in the mathematical logic of Frege (1879, 1891, 1892) and Ajdukiewicz (1935), developing in two independent and very different streams through early work in computational treat­ ments of syntax by Bar-Hillel (1953) and in formal semantics by Richard Montague (Thomason 1974b), and finding an explosive very recent productivity most clearly initiated by the fusion of logic, com­ putation, syntax and semantics in Ades and Steedman (1982). It is worth outlining this background, as it will be helpful in understanding the concerns and concepts of the theory as it now stands.