Continuation models are universal for /spl lambda//sub /spl mu//-calculus

Abstract

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