Subtyping over a lattice (abstract)

  • Jerzy Tiuryn
Invited Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1289)


This talk, in the first part, will overview the main advances in the area of subtyping for the simply typed lambda calculus. In the second part of the talk we will propose a new system of notations for types, which we call alternating direct acyclic graphs, and show that for a system of sybtype inequalities over a lattice, if it has a solution then there is a solution whose alternating dag is of polynomial size in the size of the original system. There are examples showing that the well known dag representation of types is not good enough for this purpose, already for the two-element lattice.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ben93]
    M. Benke. Efficient type reconstruction in the presence of inheritance. In Eds. A. M. Borzyszkowski, S. Sokolowski, editor, MFCS'93: Mathematical Foundations of Computer Science, Proc. 18th Intern. Symp., volume 711 of Lecture Notes in Computer Science, pages 272–280. Springer Verlag, 1993.Google Scholar
  2. [DKM84]
    C. Dwork, P. Kanellakis, and J.C. Mitchell. On the sequential nature of unification. J. Logic Programming, 1:35–50, 1984.Google Scholar
  3. [Fre97]
    A. Frey. Solving subtype inequalities in polynomial space. available from, 1997.Google Scholar
  4. [HM95]
    M. Hoang and J.C. Mitchell. Lower bounds on type inference with subtypes. In Conf. Rec. 22nd ACM Symposium on Principles of Programming Languages, pages 176–185, 1995.Google Scholar
  5. [Tiu92]
    J. Tiuryn. Subtype inequalities. In Proc. IEEE Symp. on Logic in Computer Science, pages 308–315, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jerzy Tiuryn
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarsawPoland

Personalised recommendations