Skip to main content
SpringerLink
Log in

Extracting Theory Graphs from Aldor Libraries

  • Conference paper
  • First Online:
Intelligent Computer Mathematics (CICM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14101))

Included in the following conference series:

  • 233 Accesses

Abstract

Aldor is a programming language for computer algebra that allows natural expression of algebraic objects while also allowing compilation to efficient code. Its language primitives, however, do not correspond exactly to those of modern proof assistants nor to those of data formats used in mathematical knowledge management. We discuss these difficulties and export the Aldor library as a diagram in the category of theories and theory morphisms, using a simplified model of the Aldor language that retains its essential expressivity. This allows us to capture a rich set of expert-designed interfaces for use in mathematical knowledge management settings.

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 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 74.99
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

Notes

  1. 1.

    This theory can be found at https://gl.mathhub.info/aldor/language/.

References

  1. Bronstein, M.: \(\sum ^{IT}\)—a strongly-typed embeddable computer algebra library. In: Calmet, J., Limongelli, C. (eds.) DISCO 1996. LNCS, vol. 1128, pp. 22–33. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61697-7_2

    Chapter  Google Scholar 

  2. Farmer, W.M., Guttman, J.D., Javier Thayer, F.: Little theories. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 567–581. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55602-8_192

    Chapter  Google Scholar 

  3. Jenks, R.D., Trager, B.M.: A language for computational algebra. ACM SIGPLAN Not. 16(11), 22–29 (1981)

    Article  Google Scholar 

  4. Kohlhase, M., Rabe, F.: Experiences from exporting major proof assistant libraries. J. Autom. Reason. 65(8), 1265–1298 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  5. Müller, D., Rabe, F., Kohlhase, M.: Theories as types. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds.) IJCAR 2018. LNCS (LNAI), vol. 10900, pp. 575–590. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94205-6_38

    Chapter  Google Scholar 

  6. Rabe, F., Kohlhase, M.: A scalable module system. Inf. Comput. 230(1), 1–54 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. S.M. Watt. Handbook of Computer Algebra, chapter 4.1.3 Aldor, pp. 265–270. Springer, Cham (2003). https://doi.org/10.1007/978-3-642-55826-9_4

  8. Watt, S.M.: Post facto type extension for mathematical programming. In: Proceedings of Domain-Specific Aspect Languages, pp. 26–31. SIGPLAN, ACM, October 2006

    Google Scholar 

  9. Watt, S.M., Broadbery, P.A., Dooley, S.S., Iglio, P., Steinbach, J.M., Sutor, R.S.: A first report on the \(A^\sharp \) compiler. In: Proceedings of ISSAC, pp. 25–31. ACM, July 1994

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science, University of Erlangen-Nuremberg, Erlangen, Germany

    Florian Rabe

  2. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    Stephen M. Watt

Authors
  1. Florian Rabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephen M. Watt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Florian Rabe .

Editor information

Editors and Affiliations

  1. ENSIIE, Evry, France

    Catherine Dubois

  2. University of Birmingham, Birmingham, UK

    Manfred Kerber

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rabe, F., Watt, S.M. (2023). Extracting Theory Graphs from Aldor Libraries. In: Dubois, C., Kerber, M. (eds) Intelligent Computer Mathematics. CICM 2023. Lecture Notes in Computer Science(), vol 14101. Springer, Cham. https://doi.org/10.1007/978-3-031-42753-4_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-42753-4_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-42752-7

  • Online ISBN: 978-3-031-42753-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation