Van der Sandt's algorithm for handling presupposition is based on a ``presupposition as anaphora'' paradigm and is expressed in the realm of Kamp's DRT. In recent years, we have proposed a type-theoretic rebuilding of DRT that allows Montague's semantics to be combined with discourse dynamics. Here we explore van der Sandt's theory along the line of this formal framework. It then results that presupposition handling may be expressed in a purely Montagovian setting, and that presupposition accommodation amounts to exception handling.