Continuation models are universal for λμ-calculus

We show that a certain simple call-by-name continuation semantics of Parigot´s λ_μ-calculus (1992) is complete. More precisely, for every λμ-theory we construct a cartesian closed category such that the ensuing continuation-style interpretation of λ_μ, which maps terms to functions sending abstract continuations to responses, is full and faithful. Thus, any λ_μ-category in the sense of is isomorphic to a continuation model derived from a cartesian-closed category of continuations