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Untyped Algorithmic Equality for Martin-Löf’s Logical Framework with Surjective Pairs

  • Andreas Abel
  • Thierry Coquand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3461)

Abstract

An untyped algorithm to test βη-equality for Martin-Löf’s Logical Framework with strong Σ -types is presented and proven complete using a model of partial equivalence relations between untyped terms.

Keywords

Type Theory Logical Framework Dependent Pair Conversion Algorithm Extensionality Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [AC05]
    Abel, A., Coquand, T.: Untyped algorithmic equality for Martin-Löf’s logical framework with surjective pairs (extended version). Tech. rep., Department of Computer Science, Chalmers, Göteborg, Sweden (2005)Google Scholar
  2. [Ada01]
    Adams, R.: Decidable equality in a logical framework with sigma kinds, Unpublished note, see (2001), http://www.cs.man.ac.uk/~radams/
  3. [Bar84]
    Barendregt, H.: The Lambda Calculus: Its Syntax and Semantics. North Holland, Amsterdam (1984)zbMATHGoogle Scholar
  4. [Coq91]
    Coquand, T.: An algorithm for testing conversion in type theory. In: Huet, G., Plotkin, G. (eds.) Logical Frameworks, pp. 255–279. Cambridge University Press, Cambridge (1991)CrossRefGoogle Scholar
  5. [Coq96]
    Coquand, T.: An algorithm for type-checking dependent types. In: Möller, B. (ed.) MPC 1995. LNCS, vol. 947, pp. 167–177. Springer, Heidelberg (1996)Google Scholar
  6. [CPT03]
    Coquand, T., Pollack, R., Takeyama, M.: A logical framework with dependently typed records. In: Hofmann, M.O. (ed.) TLCA 2003. LNCS, vol. 2701, pp. 105–119. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. [Gog99]
    Goguen, H.: Soundness of the logical framework for its typed operational semantics. In: Girard, J.-Y. (ed.) TLCA 1999. LNCS, vol. 1581, pp. 177–197. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. [Gog05]
    Goguen, H.: Justifying algorithms for βη conversion. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 410–424. Springer, Heidelberg (2005) (To appear)Google Scholar
  9. [HHP93]
    Harper, R., Honsell, F., Plotkin, G.: A Framework for Defining Logics. Journal of the Association of Computing Machinery 40(1), 143–184 (1993)zbMATHMathSciNetGoogle Scholar
  10. [HP05]
    Harper, R., Pfenning, F.: On equivalence and canonical forms in the LF type theory. ACM Transactions on Computational Logic 6(1), 61–101 (2005)CrossRefMathSciNetGoogle Scholar
  11. [Klo80]
    Klop, J.W.: Combinatory reducion systems. Mathematical Center Tracts 27 (1980)Google Scholar
  12. [NPS00]
    Nordström, B., Petersson, K., Smith, J.: Martin-löf’s type theory. In: Handbook of Logic in Computer Science, 5th edn. Oxford University Press, Oxford (2000)Google Scholar
  13. [Sar04]
    Sarnat, J.: LFΣ: The metatheory of LF with Σ types. Unpublished technical report, kindly provided by Carsten Schürmann (2004)Google Scholar
  14. [Vau04]
    Vaux, L.: A type system with implicit types, English version of his mémoire de maîtrise (2004)Google Scholar
  15. [VC02]
    Vanderwaart, J.C., Crary, K.: A simplified account of the metatheory of Linear LF. Tech. rep., Dept. of Comp. Sci., Carnegie Mellon (2002)Google Scholar
  16. [Vou04]
    Vouillon, J.: Subtyping union types. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 415–429. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andreas Abel
    • 1
  • Thierry Coquand
    • 1
  1. 1.Department of Computer ScienceChalmers University of Technology 

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