. This paper reports preliminary work on the semantics of the continuation transform. Previous work on the semantics of continuations has concentrated on untyped lambda-calculi and has used primarily the mechanism of inclusive predicates. Such predicates are easy to understand on atomic values, but they become obscure on functional values. In the case of the typed lambda-calculus, we show that such predicates can be replaced by retractions. The main theorem states that the meaning of a closed term is a retraction of the meaning of the corresponding continuationized term. 2. Introduction. The method of continuations was introduced in [Strachey & Wadsworth 74] as a device for formalizing the notion of control flow in programming languages. In this method, a term is evaluated in a context which represents "the rest of the computation". If the term involves the evaluation of a subterm, then the subterm is evaluated in a new context which evaluates the rest of the term and then proceeds to ...