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Martin Hofmann and Thomas Streicher (1997)

Continuation Models are Universal for Lambda-Mu-Calculus

In: Proceedings, 12th Annual IEEE Symposium on Logic in Computer Science, Warsaw, Poland, June 29 - July 2, 1997, pp. 387-395, IEEE Computer Society (ISBN: 0-8186-7925-5).

We show that a certain simple call-by-name continuation semantics of Parigots 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.

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