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A symbolic labelled transition system for coinductive subtyping of Fμ⩽ types

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1 Author(s)
A. Jeffery ; DePaul Univ., Chicago, IL

F is a typed λ-calculus with subtyping and bounded polymorphism. Type checking for F is known to be undecidable, because the subtyping relation on types is undecidable. F μ⩽ is an extension of F 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 Fμ⩽. We provide a symbolic labelled transition system for Fμ⩽ 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, e.g. it terminates on G. Ghelli's (1995) canonical example of non-termination

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Logic in Computer Science, 2001. Proceedings. 16th Annual IEEE Symposium on

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