Advertisement

\(\mathsf {CoreFun}\): A Typed Functional Reversible Core Language

  • Petur Andrias Højgaard Jacobsen
  • Robin Kaarsgaard
  • Michael Kirkedal Thomsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11106)

Abstract

This paper presents \(\mathsf {CoreFun}\), a typed reversible functional language, which seeks to reduce typed reversible functional programming to its essentials. We present a complete formal definition of the language, including its formal semantics and type system, the latter of which is based on a combined reasoning logical system of unrestricted and relevantly typed terms, and allows special support for ancillary (read-only) variables through its unrestricted fragment. We show how, in many cases, the type system provides the possibility to statically check for the reversibility of programs. Finally, we detail how higher-level language features such as variants and type classes may be incorporated into \(\mathsf {CoreFun}\) as syntactic sugar, such that \(\mathsf {CoreFun}\) may be used as a core language for a reversible functional language in a more modern style.

Keywords

Reversible computation Functional programming Programming languages Types Formal semantics 

Notes

Acknowledgements

This work was partly supported by the European COST Action IC 1405: Reversible Computation—Extending Horizons of Computing.

References

  1. 1.
    Anderson, A.R., Belnap, N.D.: Entailment: The Logic of Relevance and Necessity, vol. 1. Princeton University Press, Princeton (1975)zbMATHGoogle Scholar
  2. 2.
    Axelsen, H.B., Glück, R.: On reversible turing machines and their function universality. Acta Informatica 53(5), 509–543 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Dunn, J.M., Restall, G.: Relevance logic. In: Gabbay, D., Guenther, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 6, pp. 1–192. Springer, Dordrecht (2002).  https://doi.org/10.1007/978-94-017-0460-1_1
  4. 4.
    Girard, J.Y.: Linear logic. Theor. Comput. Sci. 50(1), 1–101 (1987)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Glück, R., Kaarsgaard, R.: A categorical foundation for structured reversible flowchart languages. In: Silva, A. (ed.) Mathematical Foundations of Programming Semantics (MFPS XXXIII). Electronic Notes in Theoretical Computer Science, vol. 336, pp. 155–171. Elsevier (2018)Google Scholar
  6. 6.
    Green, A.S., Lumsdaine, P.L., Ross, N.J., Selinger, P., Valiron, B.: Quipper: a scalable quantum programming language. In: Conference on Programming Language Design and Implementation, PLDI, PLDI 2013, pp. 333–342. ACM (2013)Google Scholar
  7. 7.
    Huffman, D.A.: Canonical forms for information-lossless finite-state logical machines. IRE Trans. Inf. Theory 5(5), 41–59 (1959)CrossRefGoogle Scholar
  8. 8.
    James, R.P., Sabry, A.: Theseus: a high level language for reversible computing (2014), work in progress paper at RC 2014. www.cs.indiana.edu/~sabry/papers/theseus.pdf
  9. 9.
    Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5(3), 183–191 (1961)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Lecerf, Y.: Machines de Turing réversibles. Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences 257, 2597–2600 (1963)MathSciNetGoogle Scholar
  11. 11.
    Lutz, C., Derby, H.: Janus: a time-reversible language. A letter to R. Landauer (1986). http://tetsuo.jp/ref/janus.pdf
  12. 12.
    Pierce, B.C.: Types and Programming Languages, 1st edn. The MIT Press, Cambridge (2002)zbMATHGoogle Scholar
  13. 13.
    Pierce, B.C.: Types and Programming Languages. MIT Press, Cambridge (2002)zbMATHGoogle Scholar
  14. 14.
    Polakow, J.: Ordered Linear Logic and Applications. Ph.D. thesis. Carnegie Mellon University (2001)Google Scholar
  15. 15.
    Sabry, A., Valiron, B., Vizzotto, J.K.: From Symmetric pattern-matching to quantum control. In: Baier, C., Dal Lago, U. (eds.) FoSSaCS 2018. LNCS, vol. 10803, pp. 348–364. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-89366-2_19CrossRefGoogle Scholar
  16. 16.
    Schordan, M., Jefferson, D., Barnes, P., Oppelstrup, T., Quinlan, D.: Reverse code generation for parallel discrete event simulation. In: Krivine, J., Stefani, J.-B. (eds.) RC 2015. LNCS, vol. 9138, pp. 95–110. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-20860-2_6CrossRefGoogle Scholar
  17. 17.
    Schultz, U.P., Laursen, J.S., Ellekilde, L.-P., Axelsen, H.B.: Towards a domain-specific language for reversible assembly sequences. In: Krivine, J., Stefani, J.-B. (eds.) RC 2015. LNCS, vol. 9138, pp. 111–126. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-20860-2_7CrossRefzbMATHGoogle Scholar
  18. 18.
    Thomsen, M.K.: A functional language for describing reversible logic. In: Specification & Design Languages, FDL 2012, pp. 135–142. IEEE (2012)Google Scholar
  19. 19.
    Thomsen, M.K., Axelsen, H.B.: Interpretation and programming of the reversible functional language. In: Symposium on the Implementation and Application of Functional Programming Languages, IFL 2015, pp. 8:1–8:13. ACM (2016)Google Scholar
  20. 20.
    Wadler, P.: Linear types can change the world! In: IFIP TC 2 Working Conference on Programming Concepts and Methods, pp. 347–359. North Holland (1990)Google Scholar
  21. 21.
    Yokoyama, T., Axelsen, H.B., Glück, R.: Towards a reversible functional language. In: De Vos, A., Wille, R. (eds.) RC 2011. LNCS, vol. 7165, pp. 14–29. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29517-1_2CrossRefzbMATHGoogle Scholar
  22. 22.
    Yokoyama, T., Axelsen, H.B., Glück, R.: Fundamentals of reversible flowchart languages. Theor. Comput. Sci. (2015) (in Press),  https://doi.org/10.1016/j.tcs.2015.07.046
  23. 23.
    Yokoyama, T., Glück, R.: A reversible programming language and its invertible self-interpreter. In: Partial Evaluation and Program Manipulation, PEPM 2007, pp. 144–153. ACM (2007)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Petur Andrias Højgaard Jacobsen
    • 1
  • Robin Kaarsgaard
    • 1
  • Michael Kirkedal Thomsen
    • 1
  1. 1.DIKU, Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark

Personalised recommendations