This paper develops a version of the scope theory of intensionality couched within continuation semantics -- a general approach to scope-taking using delimited continuations, developed in a number of works by Chris Barker and Chung-chieh Shan (see Barker & Shan 2014 for an overview). The general perspective taken here is that intensionality is an example of a linguistic "side-effect" (Shan 2005). Intensionality is modelled explicitly using a technique developed in the functional programming literature for modelling environment sensitivity, namely the Reader monad (see Wadler 1995 on monads in functional programming). The resulting picture is one on which noun phrases are environment-sensitive, and must scope-out and compose with predicates via monadic bind. Since this account uses monads explicitly, it can avail itself of Charlow's (2014, 2019) associativity-based account of exceptionally-scoping indefinites. This is shown to make good predictions regarding the (in)sensitivity of de re readings to scope islands. Further advantages include an account of Fodor's third reading via mechanisms for split scope, and an explanation for constraints on de re readings uncovered by Percus (2000) and Romoli & Sudo (2019).