Continuation models are universal for lambda-mu-calculus
Martin R. Hofmann, Thomas Streicher · Logic in Computer Science · 1997
We show that a certain simple call-by-name continuation semantics of Parigot's lambda-mu-calculus is complete. More precisely, for every lambda-mu-theory we construct a cartesian closed category such that the ensuing continuation-style interpretation of lambda-mu, which maps terms to functions sending abstract continuations to responses, is full and faithful. Thus, any lambda-mu-category in the sense of is isomorphic to a continuation model derived from a cartesian-closed category of continuations.