Abstract
The enriched effect calculus is an extension of Moggi’s computational metalanguage with a selection of primitives from linear logic. In this paper, we present an extended case study within the enriched effect calculus: the linear usage of continuations. We show that established call-by-value and call-by name linearly-used CPS translations are uniformly captured by a single generic translation of the enriched effect calculus into itself. As a main syntactic theorem, we prove that the generic translation is involutive up to isomorphism. As corollaries, we obtain full completeness results for the original call-by-value and call-by-name translations. The main syntactic theorem is proved using a category-theoretic semantics for the enriched effect calculus. We show that models are closed under a natural dual model construction. The canonical linearly-used CPS translation then arises as the unique (up to isomorphism) map from the syntactic initial model to its own dual. This map is an equivalence of models. Thus the initial model is self-dual.
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References
Barr, M.: ∗-autonomous categories. 752, vol. LNM (1979)
Benton, P.N.: A mixed linear and non-linear logic: Proofs, terms and models. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 933. Springer, Heidelberg (1995)
Berdine, J., O’Hearn, P.W., Reddy, U., Thielecke, H.: Linear continuation-passing. Higher Order and Symbolic Computation 15, 181–208 (2002)
Egger, J., Møgelberg, R.E., Simpson, A.: Enriching an effect calculus with linear types. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 240–254. Springer, Heidelberg (2009)
A.: Filinski. Controlling Effects. PhD thesis, School of Comp. Sci., CMU (1996)
Hasegawa, M.: Linearly used effects: Monadic and CPS transformations into the linear lambda calculus. In: Hu, Z., Rodríguez-Artalejo, M. (eds.) FLOPS 2002. LNCS, vol. 2441, pp. 167–182. Springer, Heidelberg (2002)
Hasegawa, M.: Semantics of linear continuation-passing in call-by-name. In: Kameyama, Y., Stuckey, P.J. (eds.) FLOPS 2004. LNCS, vol. 2998, pp. 229–243. Springer, Heidelberg (2004)
Kelly, G.M.: Basic Concepts of Enriched Category Theory. London Math. Society Lecture Note Series, vol. 64. Cambridge University Press, Cambridge (1982)
Lawvere, F.W.: Ordinal sums and equational doctrines. In: Seminar on Triples and Categorical Homology Theory (ETH, Zürich), pp. 141–155. Springer, Heidelberg (1969)
Levy, P.B.: Call-by-push-value. In: A functional/imperative synthesis. Semantic Structures in Computation. Springer, Heidelberg (2004)
Moggi, E.: Computational lambda-calculus and monads. In: Proc. 4th LICS, pp. 14–23 (1989)
Moggi, E.: Notions of computation and monads. Information and Computation 93, 55–92 (1991)
Parigot, M.: λμ-calculus: an algorithmic interpretation of classical natural deduction. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624, pp. 190–201. Springer, Heidelberg (1992)
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Egger, J., Møgelberg, R.E., Simpson, A. (2010). Linearly-Used Continuations in the Enriched Effect Calculus. In: Ong, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2010. Lecture Notes in Computer Science, vol 6014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12032-9_3
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DOI: https://doi.org/10.1007/978-3-642-12032-9_3
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