Abstract
We give a simple effect system for non-deterministic programs, tracking static approximations to the number of results that may be produced by each computation. A relational semantics for the effect system establishes the soundness of both the analysis and its use in effect-based program transformations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
It is tempting to replace \(S \sim _{X} S'\) by \(S/[\![X]\!]= S'/[\![X]\!]\), but \(S/[\![X]\!]\) contains the empty set when there is an \(x\in S\) with \((x,x)\notin [\![X]\!]\).
- 2.
Phil was involved in this debate at least as far back as 1997 [11].
References
Ahman, D., Plotkin, G.D.: Refinement types for algebraic effects. In: Abstracts of the 21st Meeting ‘Types for Proofs and Programs’ (TYPES), Institute of Cybernetics, Tallinn University of Technology, pp. 10–11 (2015)
Benton, N.: Simple relational correctness proofs for static analyses and program transformations. In: 31st ACM SIGPLAN Symposium on Principles of Programming Languages (POPL), pp. 14–25. ACM (2004)
Benton, N., Buchlovsky, P.: Semantics of an effect analysis for exceptions. In: 3rd ACM SIGPLAN Workshop on Types in Language Design and Implementation (TLDI), pp. 15–26. ACM (2007)
Benton, N., Hofmann, M., Nigam, V.: Abstract effects and proof-relevant logical relations. In: 41st ACM SIGPLAN Symposium on Principles of Programming Languages (POPL), pp. 619–632. ACM (2014)
Benton, N., Hofmann, M., Nigam, V.: Effect-dependent transformations for concurrent programs arXiv:1510.02419 (2015)
Benton, N., Hughes, J., Moggi, E.: Monads and effects. In: Barthe, G., Dybjer, P., Pinto, L., Saraiva, J. (eds.) APPSEM 2000. LNCS, vol. 2395, p. 42. Springer, Heidelberg (2002)
Benton, A., Kennedy, L. Beringer, N., Hofmann, M.: Relational semantics for effect-based program transformations with dynamic allocation. In: 9th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming (PPDP), pp. 87–96. ACM (2007)
Benton, N., Kennedy, A., Hofmann, M.O., Beringer, L.: Reading, writing and relations: towards extensional semantics for effects analyses. In: Kobayashi, N. (ed.) APLAS 2006. LNCS, vol. 4279, pp. 114–130. Springer, Heidelberg (2006)
Benton, N., Kennedy, A., Russell, G.: Compiling Standard ML to Java bytecodes. In: Third ACM SIGPLAN International Conference on Functional Programming (ICFP), pp. 129–140. ACM (1998)
Braem, C., Le Charlier, B., Modart, S., Van Hentenryck, P.: Cardinality analysis of Prolog. In: International Symposium on Logic Programming, pp. 457–471. MIT Press (1994)
Claessen, K., Wadler, P. et al.: Laws for monads with zero and plus. In: Haskell mailing list, May 1997. http://www.mail-archive.com/haskell%40haskell.org/msg01583.html. Accessed January 2016
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Fourth ACM SIGPLAN Symposium on Principles of Programming Languages (POPL), pp. 238–252. ACM (1977)
Debray, S.K., Warren, D.S.: Functional computations in logic programs. ACM Trans. Program. Lang. Syst. (TOPLAS) 11(3), 451–481 (1989)
Fischer, S., Kiselyov, O., Shan, C.-C.: Purely functional lazy nondeterministic programming. J. Funct. Program. 21(4/5), 413–465 (2011)
Gifford, D.K., Lucassen, J.M.: Integrating functional and imperative programming. In: ACM Conference on LISP and Functional Programming, pp. 28–38. ACM (1986)
Henderson, F., Somogyi, Z., Conway, T.: Determinism analysis in the Mercury compiler. In: Proceedings of the Australian Computer Science Conference, pp. 337–34 (1996)
Hinze, R.: Deriving backtracking monad transformers. In: Fifth ACM SIGPLAN International Conference on Functional Programming (ICFP), pp. 186–197. ACM (2000)
Kammar, O., Plotkin, G.D.: Algebraic foundations for effect-dependent optimizations. In: 39th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL), pp. 349–360. ACM (2012)
Katsumata, S.: Parametric effect monads and semantics of effect systems. In: 41st ACM SIGPLAN Symposium on Principles of Programming Languages (POPL), pp. 633–646. ACM (2014)
López-García, P., Bueno, F., Hermenegildo, M.V.: Determinacy analysis for logic programs using mode and type information. In: Etalle, S. (ed.) LOPSTR 2004. LNCS, vol. 3573, pp. 19–35. Springer, Heidelberg (2005)
Lucassen, J.M., Gifford, D.K.: Polymorphic effect systems. In: 15th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL), pp. 47–57. ACM (1988)
Moggi, E.: Computational lambda-calculus and monads. In: 4th Annual Symposium on Logic in Computer Science (LICS), pp. 14–23. IEEE Computer Society (1989)
Peyton Jones, S., Wadler, P.: Comprehensive comprehensions. In: ACM SIGPLAN Workshop on Haskell, pp. 61–72. ACM (2007)
Reynolds, J.C.: The meaning of types - from intrinsic to extrinsic semantics. Technical report BRICS RS-00-32, BRICS, University of Aarhus, December 2000
Rivas, E., Jaskelioff, M., Schrijvers, T.: From monoids to near-semirings: the essence of monadplus and alternative. In: 17th International Symposium on Principles and Practice of Declarative Programming (PPDP), pp. 196–207. ACM (2015)
Tolmach, A.: Optimizing ML using a hierarchy of monadic types. In: Leroy, X., Ohori, A. (eds.) TIC 1998. LNCS, vol. 1473, pp. 97–115. Springer, Heidelberg (1998)
Uustalu, T.: A divertimento on MonadPlus and nondeterminism. J. Logical Algebraic Methods Program. (2016, to appear)
Wadler, P.: How to replace failure by a list of successes: a method for exception handling, backtracking, and pattern matching in lazy functional languages. In: Jouannaud, J.-P. (ed.) FPCA 1985. LNCS, vol. 201, pp. 113–128. Springer, Heidelberg (1985)
Wadler, P.: Theorems for free!. In: Fourth International Symposium on Functional Programming Languages and Computer Architecture (FPCA), pp. 347–359. ACM (1989)
Wadler, P.: The marriage of effects and monads. In: Third ACM SIGPLAN International Conference on Functional Programming (ICFP), pp. 63–74. ACM (1998)
Wadler, P., Thiemann, P.: The marriage of effects and monads. ACM Trans. Comput. Logic 4(1), 1–32 (2003)
Yakeley, A. et al.: MonadPlus reform proposal (2006). https://wiki.haskell.org/MonadPlus_reform_proposal. Accessed January 2016
Acknowledgements
We thank the referees for their thorough and helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated to Philip Wadler on the occasion of his $$60^{th}$$ 60 th birthday.
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Benton, N., Kennedy, A., Hofmann, M., Nigam, V. (2016). Counting Successes: Effects and Transformations for Non-deterministic Programs. In: Lindley, S., McBride, C., Trinder, P., Sannella, D. (eds) A List of Successes That Can Change the World. Lecture Notes in Computer Science(), vol 9600. Springer, Cham. https://doi.org/10.1007/978-3-319-30936-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-30936-1_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30935-4
Online ISBN: 978-3-319-30936-1
eBook Packages: Computer ScienceComputer Science (R0)