A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic . The proofs of soundness and completeness are constructive and the computational content of their composition is, in particular, a β-normalisation-by-evaluation program for simply typed lambda calculus with sum types. Although the inspiration comes from Danvyʼs type-directed partial evaluator for the same lambda calculus, the use of delimited control operators is avoided. The role of (...) polymorphism is crucial – dropping it allows one to obtain a notion of model complete for classical predicate logic. (shrink)