Skip to main content
SpringerLink
Log in

Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras

  • Conference paper
Algebra and Coalgebra in Computer Science (CALCO 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6859))

Included in the following conference series:

Abstract

Minlog is an interactive system which implements proof-theoretic methods and applies them to verification and program extraction. We give an overview of Minlog and demonstrate how it can be used to exploit the computational content in (co)algebraic proofs and to develop correct and efficient programs. We illustrate this by means of two examples: one about parsing, the other about exact real numbers in signed digit representation.

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: http://wiki.portal.chalmers.se/agda/

  2. Berger, U., Berghofer, S., Letouzey, P., Schwichtenberg, H.: Program extraction from normalization proofs. Studia Logica 82, 27–51 (2006)

    Article  MathSciNet  Google Scholar 

  3. Benl, H., Berger, U., Schwichtenberg, H., Seisenberger, M., Zuber, W.: Proof theory at work: Program development in the Minlog system. In: Bibel, W., Schmitt, P.H. (eds.) Automated Deduction. Applied Logic Series, vol. II, pp. 41–71. Kluwer, Dordrecht (1998)

    Google Scholar 

  4. Berger, U., Buchholz, W., Schwichtenberg, H.: Refined program extraction from classical proofs. APAL 114, 3–25 (2002)

    MathSciNet  MATH  Google Scholar 

  5. Berger, U.: From coinductive proofs to exact real arithmetic. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 132–146. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Berger, U., Eberl, M., Schwichtenberg, H.: Term rewriting for normalization by evaluation. Information and Computation 183, 19–42 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Berger, U., Hou, T.: Coinduction for exact real number computation. Theory of Computing Systems 43, 394–409 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Berger, U., Schwichtenberg, H.: An inverse of the evaluation functional for typed λ-calculus. In: Vemuri, R. (ed.) Proceedings 6’th Symposium on Logic in Computer Science, LICS 1991, pp. 203–211. IEEE Computer Society Press, Los Alamitos (1991)

    Google Scholar 

  9. Bauer, A., Stone, C.A.: RZ: A tool for bringing constructive and computable mathematics closer to programming practice. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds.) CiE 2007. LNCS, vol. 4497, pp. 28–42. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Berger, U., Seisenberger, M.: Proofs, programs, processes. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.) CiE 2010. LNCS, vol. 6158, pp. 39–48. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. Ciaffaglione, A., Di Gianantonio, P.: A certified, corecursive implementation of exact real numbers. Theor. Comp. Sci. 351, 39–51 (2006)

    Article  MATH  Google Scholar 

  12. Chuang, C.M.: Extraction of Programs for Exact Real Number Computation Using Agda. PhD thesis. Swansea University, Wales (2011)

    Google Scholar 

  13. The Coq Proof Assistant, http://coq.inria.fr/

  14. Crosilla, L., Seisenberger, M., Schwichtenberg, H.: A Tutorial for Minlog, Version 5.0 (2011)

    Google Scholar 

  15. Geuvers, H., Niqui, M., Spitters, B., Wiedijk, F.: Constructive analysis, types and exact real numbers. Math. Struct. Comp. Sci. 17(1), 3–36 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Isabelle, http://isabelle.in.tum.de/

  17. Kreisel, G.: Interpretation of analysis by means of constructive functionals of finite types. Constructivity in Mathematics, 101–128 (1959)

    Google Scholar 

  18. Letouzey, P.: A New Extraction for Coq. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 200–219. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  19. Miller, D.: A logic programming language with lambda–abstraction, function variables and simple unification. Jour. Logic Comput. 2(4), 497–536 (1991)

    Article  Google Scholar 

  20. The Minlog System, http://www.minlog-system.de

  21. Marcial-Romero, J.R., Escardo, M.H.: Semantics of a sequential language for exact real-number computation. Theor. Comp. Sci. 379(1-2), 120–141 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Schwichtenberg, H.: Proof search in minimal logic. In: Buchberger, B., Campbell, J.A. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 15–25. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  23. Schwichtenberg, H., Wainer, S.S.: Proofs and Computations. Perspectives in Logic. Assoc. Symb. Logic, Cambridge Univ. Press (to appear, 2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Swansea University, Wales, UK

    Ulrich Berger & Monika Seisenberger

  2. LMU University, Munich, Germany

    Kenji Miyamoto & Helmut Schwichtenberg

Authors
  1. Ulrich Berger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kenji Miyamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Helmut Schwichtenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Monika Seisenberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, 56127, Pisa, Italy

    Andrea Corradini

  2. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, 02-097, Warszawa, Poland

    Bartek Klin

  3. School of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Corina Cîrstea

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Berger, U., Miyamoto, K., Schwichtenberg, H., Seisenberger, M. (2011). Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras. In: Corradini, A., Klin, B., Cîrstea, C. (eds) Algebra and Coalgebra in Computer Science. CALCO 2011. Lecture Notes in Computer Science, vol 6859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22944-2_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22944-2_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22943-5

  • Online ISBN: 978-3-642-22944-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation