[go: up one dir, main page]

Skip to main content

Algorithm Design with the Selection Monad

  • Conference paper
  • First Online:
Trends in Functional Programming (TFP 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13401))

Included in the following conference series:

  • 295 Accesses

Abstract

The selection monad has proven useful for modelling exhaustive search algorithms. It is well studied in the area of game theory as an elegant way of expressing algorithms that calculate optimal plays for sequential games with perfect information; composition of moves is modeled as a ‘product’ of selection functions. This paper aims to expand the application of the selection monad to other classes of algorithms. The structure used to describe exhaustive search problems can easily be applied to greedy algorithms; with some changes to the product function, the behaviour of the selection monad can be changed from an exhaustive search behaviour to a greedy one. This enables an algorithm design framework in which the behaviour of the algorithm can be exchanged modularly by using different product functions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Bolt, J., Hedges, J., Zahn, P.: Sequential games and nondeterministic selection functions. arXiv preprint arXiv:1811.06810 (2018)

  2. Escardó, M., Oliva, P.: Selection functions, bar recursion and backward induction. Math. Struct. Comput. Sci. 20(2), 127–168 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Escardó, M., Oliva, P.: What sequential games, the Tychonoff theorem and the double-negation shift have in common. In: Proceedings of the Third ACM SIGPLAN Workshop on Mathematically Structured Functional Programming, pp. 21–32 (2010)

    Google Scholar 

  4. Escardó, M., Oliva, P.: Sequential games and optimal strategies. Proc. R. Soc. A: Math. Phys. Eng. Sci. 467(2130), 1519–1545 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hartmann, J.: Finding optimal strategies in sequential games with the novel selection monad. arXiv preprint arXiv:2105.12514 (2018)

  6. Hartmann, J.: Dependently typed selection monad (2022). https://github.com/IncredibleHannes/DependentlyTypedSelectionMonad

  7. Hedges, J.: The selection monad as a CPS transformation. arXiv preprint arXiv:1503.06061 (2015)

  8. Hedges, J.M.: Towards compositional game theory. Ph.D. thesis, Queen Mary University of London (2016)

    Google Scholar 

  9. Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36(6), 1389–1401 (1957)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Johannes Hartmann .

Editor information

Editors and Affiliations

Appendices

Appendix

A Proof that Product Equals Sequence

figure eg

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hartmann, J., Gibbons, J. (2022). Algorithm Design with the Selection Monad. In: Swierstra, W., Wu, N. (eds) Trends in Functional Programming. TFP 2022. Lecture Notes in Computer Science, vol 13401. Springer, Cham. https://doi.org/10.1007/978-3-031-21314-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-21314-4_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-21313-7

  • Online ISBN: 978-3-031-21314-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics