Max-Planck-Institut für Informatik
max planck institut
informatik
mpii logo Minerva of the Max Planck Society
 

MPI-I-94-257

Structural decidable extensions of bounded quantification

Vorobyov, Sergei

MPI-I-94-257. October 1994, 12 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
We show how the subtype relation of the well-known system Fsub, the second-order polymorphic lambda-calculus with bounded universal type quantification and subtyping, due to Cardelli, Wegner, Bruce, Longo, Curien, Ghelli, proved undecidable by Pierce (POPL'92), can be interpreted in the (weak) monadic second-order theory of one (B\"uchi), two (Rabin), several, or infinitely many successor functions. These (W)SnS-interpretations show that the undecidable system Fsub possesses consistent decidable extensions, i.e., Fsub is not essentially undecidable (Tarski, 1949). \par We demonstrate an infinite class of structural decidable extensions of Fsub, which combine traditional subtype inference rules with the above (W)SnS-interpretations. All these extensions, which we call systems FsubSnS, are still more powerful than Fsub, but less coarse than the direct (W)SnS-interpretations. \par The main distinctive features of the systems FsubSnS are: 1) decidability, 2) closure w.r.t.\ transitivity; 3)
structuredness, e.g., they never subtype a functional type to a universal one or vice versa, 4) they all contain the powerful rule for subtyping boundedly quantified types.
Note:
Also available in: Proceedings of the 22nd ACM Symposium on Principles of Programming Languages (POPL'95), January 22-25, 1995, San Francisco, U.S.A.
Acknowledgement:
Categories / Keywords: subtype relation, second-order polymorphic lambda calculus, universal type quantification, subtyping
References to related material:

To download this research report, please select the type of document that fits best your needs.Attachement Size(s):
MPI-I-94-257.pdfMPI-I-94-257.pdfMPI-I-94-257.dvi.ZMPI-I-94-257.ps.Z61 KBytes; 166 KBytes; 363 KBytes
Please note: If you don't have a viewer for PostScript on your platform, try to install GhostScript and GhostView
URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1994-257
Hide details for BibTeXBibTeX
@TECHREPORT{Vorobyov94h,
  AUTHOR = {Vorobyov, Sergei},
  TITLE = {Structural decidable extensions of bounded quantification},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-94-257},
  MONTH = {October},
  YEAR = {1994},
  ISSN = {0946-011X},
  NOTE = {Also available in: Proceedings of the 22nd ACM Symposium on Principles of Programming Languages (POPL'95), January 22-25, 1995, San Francisco, U.S.A.},
}