A symbolic labelled transition system for coinductive subtyping of F/sub /spl mu//spl les// types

Abstract

F/sub /spl les// is a typed /spl lambda/-calculus with subtyping and bounded polymorphism. Type checking for F/sub /spl les// is known to be undecidable, because the subtyping relation on types is undecidable. F/sub /spl mu//spl les// is an extension of F/sub /spl les// 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/sub /spl mu//spl les//. We provide a symbolic labelled transition system for F/sub /spl mu//spl les// types, together with an appropriate notion of simulation, which coincides with the existing co-inductive 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/sub /spl les//, e.g. it terminates on G. Ghelli's (1995) canonical example of non-termination.