[1]. Recently renewed interest in non transformational approaches to syntax [2] suggests that it might be well to take another look at categorial grammars, since they seem to have been neglected largely because they had been shown to be equivalent to context free phrase structure grammars in weak generative capacity and it was believed that such grammars were incapable of describing natural languages in a natural way. It is my purpose here to sketch a theory of grammar which represents a generalization of categorial grammars of the sort invented by Ajdukiewicz (1935) and further elaborated especially by Bar Hillel (1953) and Lambek (1961).