Logic in Computer Science (LICS 2001)

Paper: A Symbolic Labelled Transition System for Coinductive Subtyping of F_{\mu\leq} Types (at LICS 2001)

Authors: Alan Jeffrey

Abstract

F_\leq is a typed lambda-calculus with subtyping and bounded polymorphism. Typechecking for F_\leq is known to be undecidable, because the subtyping relation on types is undecidable. F_{\mu\leq} is an extension of F_\leq with recursive types. In this paper, we show how symbolic labelled transition system techniques from concurrency theory can be used to reason about subtyping for F_{\mu\leq}. We provide a symbolic labelled transition system for F_{\mu\leq} types, together with an an appropriate notion of simulation, which coincides with the existing coinductive definition of subtyping. We then provide a 'simulation up to' technique for proving subtyping, for which there is a simple model checking algorithm. The algorithm is more powerful than the usual one for F_\leq, for example it terminates on Ghelli's canonical example of nontermination.

BibTeX

  @InProceedings{Jeffrey-ASymbolicLabelledTr,
    author = 	 {Alan Jeffrey},
    title = 	 {A Symbolic Labelled Transition System for Coinductive Subtyping of F_{\mu\leq} Types},
    booktitle =  {Proceedings of the Sixteenth Annual IEEE Symp. on Logic in Computer Science, {LICS} 2001},
    year =	 2001,
    editor =	 {Joseph Halpern},
    month =	 {June}, 
    pages =      {323--333},
    location =   {Boston, MA, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }