Abstract
Parameterised monads have the same relationship to adjunctions with parameters as monads do to adjunctions. In this paper, we investigate algebras for parameterised monads. We identify the Eilenberg-Moore category of algebras for parameterised monads and prove a generalisation of Beck’s theorem characterising this category. We demonstrate an application of this theory to the semantics of type and effect systems.
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References
Atkey, R.: Parameterised notions of computation. Journal of Functional Programming 19 (2009)
Beck, J.M.: Triples, algebras and cohomology. Reprints in Theory and Applications of Categories 2, 1–59 (2003)
Benton, N., Kennedy, A., Hofmann, M., Beringer, L.: Reading, writing and relations. In: Kobayashi, N. (ed.) APLAS 2006. LNCS, vol. 4279, pp. 114–130. Springer, Heidelberg (2006)
Gifford, D.K., Lucassen, J.M.: Integrating functional and imperative programming. In: ACM Conference on LISP and Functional Programming (1986)
Katsumata, S.-y.: A Semantic Formulation of ⊤ ⊤-Lifting and Logical Predicates for Computational Metalanguage. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 87–102. Springer, Heidelberg (2005)
Levy, P.B., Power, J., Thielecke, H.: Modelling environments in call-by-value programming languages. Inf. and Comp. 185, 182–210 (2003)
Mac Lane, S.: Categories for the Working Mathematician, 2nd edn. Graduate Texts in Mathematics, vol. 5. Springer, Heidelberg (1998)
Moggi, E.: Notions of computation and monads. Information and Computation 93(1), 55–92 (1991)
Plotkin, G., Power, J.: Notions of computation determine monads. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 342–356. Springer, Heidelberg (2002)
Robinson, E.: Variations on algebra: Monadicity and generalisations of equational theories. Formal Asp. Comput. 13(3–5), 308–326 (2002)
Skalka, C., Smith, S.: History Effects and Verification. In: Chin, W.-N. (ed.) APLAS 2004. LNCS, vol. 3302, pp. 107–128. Springer, Heidelberg (2004)
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Atkey, R. (2009). Algebras for Parameterised Monads. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds) Algebra and Coalgebra in Computer Science. CALCO 2009. Lecture Notes in Computer Science, vol 5728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03741-2_2
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DOI: https://doi.org/10.1007/978-3-642-03741-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03740-5
Online ISBN: 978-3-642-03741-2
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