In categorial grammar, the syntax of languages is represented using a different sort of generalization of the functional notation than in Montague semantics. In Montague Semantics, the lambda abstractor is used to move the meaning of an expression to the location that the expression occupies in a sentence. In categorial grammar, predicates and many other sorts of expressions are taken to be functions of sorts. But there is a distinction in categorial grammar between two sorts of application of a function to its arguments. 