Skip to main content
SpringerLink
Log in

Beluga: Programming with Dependent Types, Contextual Data, and Contexts

  • Conference paper
Functional and Logic Programming (FLOPS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6009))

Included in the following conference series:

Abstract

The logical framework LF provides an elegant foundation for specifying formal systems and proofs and it is used successfully in a wide range of applications such as certifying code and mechanizing meta-theory of programming languages. However, incorporating LF technology into functional programming to allow programmers to specify and reason about formal guarantees of their programs from within the programming language itself has been a major challenge.

In this paper, we present an overview of Beluga, a framework for programming and reasoning with formal systems. It supports specifying formal systems in LF and it also provides a dependently typed functional language that supports analyzing and manipulating LF data via pattern matching. A distinct feature of Beluga is its direct support for reasoning with contexts and contextual objects. Taken together these features lead to a powerful language which supports writing compact and elegant proofs.

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

Access this chapter

Log in via an institution
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 PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agda wiki (2009), http://wiki.portal.chalmers.se/agda/

  2. Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development. In: Coq’Art: The Calculus of Inductive Constructions. Springer, Heidelberg (2004)

    Google Scholar 

  3. Dowek, G., Hardin, T., Kirchner, C., Pfenning, F.: Unification via explicit substitutions: The case of higher-order patterns. In: Maher, M. (ed.) Proceedings of the Joint International Conference and Symposium on Logic Programming, Bonn, Germany, pp. 259–273. MIT Press, Cambridge (1996)

    Google Scholar 

  4. Dunfield, J., Pientka, B.: Case analysis of higher-order data. In: International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP 2008). ENTCS, vol. 228, pp. 69–84. Elsevier, Amsterdam (2009)

    Google Scholar 

  5. Felty, A.P., Pientka, B.: Reasoning with higher-order abstract syntax and contexts: A comparison. Technical report, School of Computer Science, McGill University (January 2010)

    Google Scholar 

  6. Goldfarb, W.D.: The undecidability of the second-order unification problem. Theoretical Computer Science 13, 225–230 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  7. Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. Journal of the ACM 40(1), 143–184 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Licata, D.R., Harper, R.: A universe of binding and computation. In: Hutton, G., Tolmach, A.P. (eds.) 14th ACM SIGPLAN International Conference on Functional Programming, pp. 123–134. ACM Press, New York (2009)

    Chapter  Google Scholar 

  9. Miller, D.: Unification of simply typed lambda-terms as logic programming. In: Eighth International Logic Programming Conference, Paris, France, pp. 255–269. MIT Press, Cambridge (1991)

    Google Scholar 

  10. McBride, C., McKinna, J.: The view from the left. Journal of Functional Programming 14(1), 69–111 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Necula, G.C.: Proof-carrying code. In: 24th Annual Symposium on Principles of Programming Languages (POPL 1997), pp. 106–119. ACM Press, New York (1997)

    Chapter  Google Scholar 

  12. Norell, U.: Towards a practical programming language based on dependent type theory. PhD thesis, Department of Computer Science and Engineering, Chalmers University of Technology, Technical Report 33D (September 2007)

    Google Scholar 

  13. Nanevski, A., Pfenning, F., Pientka, B.: Contextual modal type theory. ACM Transactions on Computational Logic 9(3), 1–49 (2008)

    Article  MathSciNet  Google Scholar 

  14. Pientka, B., Dunfield, J.: Programming with proofs and explicit contexts. In: ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming (PPDP 2008), pp. 163–173. ACM Press, New York (2008)

    Chapter  Google Scholar 

  15. Pfenning, F.: Logic programming in the LF logical framework. In: Huet, G., Plotkin, G. (eds.) Logical Frameworks, pp. 149–181. Cambridge University Press, Cambridge (1991)

    Google Scholar 

  16. Pfenning, F.: Unification and anti-unification in the Calculus of Constructions. In: Sixth Annual IEEE Symposium on Logic in Computer Science, Amsterdam, The Netherlands, July 1991, pp. 74–85 (1991)

    Google Scholar 

  17. Pfenning, F.: Computation and deduction (1997)

    Google Scholar 

  18. Pientka, B.: Tabled higher-order logic programming. PhD thesis, Department of Computer Science, Carnegie Mellon University, CMU-CS-03-185 (2003)

    Google Scholar 

  19. Pientka, B.: Verifying termination and reduction properties about higher-order logic programs. Journal of Automated Reasoning 34(2), 179–207 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. Pientka, B.: A type-theoretic foundation for programming with higher-order abstract syntax and first-class substitutions. In: 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 2008), pp. 371–382. ACM Press, New York (2008)

    Chapter  Google Scholar 

  21. Pottier, F.: Static name control for FreshML. In: 22nd IEEE Symposium on Logic in Computer Science (LICS 2007), pp. 356–365. IEEE Computer Society, Los Alamitos (2007)

    Chapter  Google Scholar 

  22. Pfenning, F., Schürmann, C.: System description: Twelf — a meta-logical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 202–206. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  23. Poswolsky, A.B., Schürmann, C.: Practical programming with higher-order encodings and dependent types. In: Drossopoulou, S. (ed.) ESOP 2008. LNCS, vol. 4960, pp. 93–107. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  24. Rohwedder, E., Pfenning, F.: Mode and termination checking for higher-order logic programs. In: Riis Nielson, H. (ed.) ESOP 1996. LNCS, vol. 1058, pp. 296–310. Springer, Heidelberg (1996)

    Google Scholar 

  25. Shinwell, M.R., Pitts, A.M., Gabbay, M.J.: FreshML: programming with binders made simple. In: 8th International Conference on Functional Programming (ICFP 2003), pp. 263–274. ACM Press, New York (2003)

    Chapter  Google Scholar 

  26. Twelf wiki (2009), http://twelf.plparty.org/wiki/Main_Page

Download references

Author information

Authors and Affiliations

  1. McGill University, Montreal, Canada

    Brigitte Pientka

Authors
  1. Brigitte Pientka
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Google, 20 West Kinzie Street, 60610, Chicago, IL, USA

    Matthias Blume

  2. Department of Computer and Mathematical Sciences, Tohoku University, 6-3-9 Aoba, Aramaki, Aoba-ku, Sendai-shi, 980-8579, Miyagi, Japan

    Naoki Kobayashi

  3. DSIC, MiST, Technical University of Valencia, Camino de Vera, S/N, 46022, Valencia, Spain

    Germán Vidal

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pientka, B. (2010). Beluga: Programming with Dependent Types, Contextual Data, and Contexts. In: Blume, M., Kobayashi, N., Vidal, G. (eds) Functional and Logic Programming. FLOPS 2010. Lecture Notes in Computer Science, vol 6009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12251-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12251-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12250-7

  • Online ISBN: 978-3-642-12251-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation