Abstract
We seek a unified account of modularity for computational effects, using the notion of enriched Lawvere theory, together with its relationship with strong monads, to reformulate Moggi’s paradigm for modelling computational effects. Effects qua theories are then combined by appropriate bifunctors (on the category of theories). We give a theory of the commutative combination of effects, which in particular yields Moggi’s side-effects monad transformer. And we give a theory for the sum of computational effects, which in particular yields Moggi’s exceptions monad transformer.
This work has been done with the support of EPSRC grant GR/M56333, a British Council grant and the COE budget of Japan.
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References
M. Barr and C. Wells, Category Theory for Computing Science, Prentice-Hall, 1990.
N. Benton, J. Hughes, and E. Moggi, Monads and E f fects, APPSEM ‘00 Summer School, 2000.
P. Cenciarelli and E. Moggi, A Syntactic Approach to Modularity in Denotational Semantics, CWI Technical Report, 1983.
P. J. Freyd, Algebra-Valued Functors in General and Tensor Products in Particular, Colloq. Math. Wroclaw Vol. 14, pp. 89–106, 1966.
R. Heckmann, Probabilistic Domains, in Proc. CAAP ‘84, LNCS, Vol. 136, pp. 21–56, Berlin: Springer-Verlag, 1994.
M. C. B. Hennessy, Algebraic Theory of Processes, Cambridge, Massachusetts: MIT Press, 1988.
M. C. B. Hennessy and G. D. Plotkin, Full Abstraction for a Simple Parallel Programming Language, in Proc. MFCS ‘79 (ed. J. Beevâî), LNCS, Vol. 74, pp. 108–120, Berlin: Springer-Verlag, 1979.
J. M. E. Hyland and A. J. Power, Pseudo-Closed 2-Categories and PseudoCommutativities, J. Pure Appl. Algebra,to appear.
C. Jones, Probabilistic Non-Determinism, Ph.D. Thesis, University of Edinburgh, Report ECS-LFCS-90–105, 1990.
C. Jones and G. D. Plotkin, A Probabilistic Powerdomain of Evaluations, in Proc. LICS ‘89, pp. 186–195, Washington: IEEE Press, 1989.
G. M. Kelly, Basic Concepts of Enriched Category Theory, Cambridge: Cambridge University Press, 1982.
G. M. Kelly and A. J. Power, Adjunctions whose Counits are Coequalizers, and Presentations of Finitary Enriched Monads, J. Pure Appl. Algebra, Vol. 89, pp. 163–179, 1993.
E. G. Manes, Algebraic Theories, Graduate Texts in Mathematics, Vol. 26, New York: Springer-Verlag, 1976.
M. W. Mislove, Nondeterminism and Probabilistic Choice: Obeying the Laws, in International Conference on Concurrency Theory,pp. 350–364, URL: http://www.math.tulane.edu/ mwm, 2000.
E. Moggi, Computational Lambda-Calculus and Monads, in Proc. LICS ‘89, pp. 14–23, Washington: IEEE Press, 1989.
E. Moggi, An Abstract View of Programming Languages, University of Edinburgh, Report ECS-LFCS-90–113, 1989.
E. Moggi, Notions of Computation and Monads, Inf. and Comp., Vol. 93, No. 1, pp. 55–92, 1991.
G. D. Plotkin, A Powerdomain Construction, SIAM J. Comput. Vol. 5, No. 3, pp. 452–487, 1976.
G. D. Plotkin, Domains, URL: http://www.dcs.ed.ac.uk/home/gdp 1983.
G. D. Plotkin and A. J. Power, Adequacy for Algebraic Effects, in Proc. FOSSACS 2001 (eds. F. Honsell and M. Miculan), LNCS, Vol. 2030, pp. 1–24, Berlin: Springer-Verlag, 2001.
G. D. Plotkin and A. J. Power, Semantics for Algebraic Operations (extended abstract), in Proc. MFPS XVII (eds. S. Brookes and M. Mislove), ENTCS, Vol. 45, Amsterdam: Elsevier, 2001.
G. D. Plotkin and A. J. Power, Notions of Computation Determine Monads, in Proc. FOSSACS 2002 (eds. M. Neilsen and U. Engberg), LNCS, Vol. 2303, pp. 342–356, Berlin: Springer-Verlag, 2002.
A. J. Power, Enriched Lawvere Theories, in Theory and Applications of Categories, pp. 83–93, 2000.
A. J. Power and E. P. Robinson, Modularity and Dyads, in Proc. MFPS X V (eds. S. Brookes, A. Jung, M. Mislove and A. Scedrov), ENTCS Vol. 20, Amsterdam: Elsevier, 1999.
E. Robinson, Variations on Algebra: Monadicity and Generalisations of Equational Theories,to appear, URL: http://www.dcs.qmul.ac.uk/edmundr/publications.html, 2001.
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Hyland, M., Plotkin, G., Power, J. (2002). Combining Computational Effects: Commutativity and Sum. In: Baeza-Yates, R., Montanari, U., Santoro, N. (eds) Foundations of Information Technology in the Era of Network and Mobile Computing. IFIP — The International Federation for Information Processing, vol 96. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35608-2_39
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DOI: https://doi.org/10.1007/978-0-387-35608-2_39
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