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

**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 Symposium on Logic in Computer Science (LICS 2001)}, year = {2001}, month = {June}, pages = {323--333}, location = {Boston, MA, USA}, publisher = {IEEE Computer Society Press} }