We discuss the treatment of movement and variable binding across finite clause boundaries in the continuation-based grammar of Barker and Shan (2014) and related work. We propose extensions to the theory which make such dependencies compatible with a ban on cross-clausal scope-taking as implemented in Charlow (2014). We demonstrate, however, that this resulting grammar systematically makes incorrect predictions for weak crossover in sentences that combine long-distance movement and variable binding, thus undermining one of the major advantages of continuation-based grammars according to Shan and Barker (2006). We conclude with a critical outlook and a comparison to contemporary LF syntax approaches to scope-taking.

Keywords: Barker & Shan continuations CCG scope binding movement long-distance