The continuation-passing-style interpretation, like the type-shifting approach, makes it possible to assign syntactic type np both to proper names and to quantificational noun phrases: in the target calculus, the translation of np has the appropriate semantic type (e → t) → t.  But the lifting strategy is now generalized to all source types: a transitive verb (np\s)/np) is mapped to ((e → e → t) → t) → t, etc.  For the translation of lexical constants of type A, the default recipe is λk.(k c), c a non-logical constant of type A′.  The default translation simply passes the semantic value for these lexical items to the continuation parameter k. But quantificational noun phrases effectively exploit the continuation parameter: they take scope over their continuation, leading to lexical recipes λk.(∀ λx.(k x)), λk.(∃ λx.(k x)) for ‘everyone’ and ‘someone’. The choice between the evaluation strategies, in combination with these lexical recipes, then results in different interpretations for a single derivation in the source calculus M = (everyone⊳(loves⊲someone)), with ·v producing the surface scope construal, and ·n the inverted scope reading.