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Abstract:
We show how the subtype relation of the well-known system Fsub, the second-order polymorphic lambda-calculus with bounded universal type quantification and subtyping, due to Cardelli, Wegner, Bruce, Longo, Curien, Ghelli, proved undecidable by Pierce (POPL'92), can be interpreted in the (weak) monadic second-order theory of one (B\"uchi), two (Rabin), several, or infinitely many successor functions. These (W)SnS-interpretations show that the undecidable system Fsub possesses consistent decidable extensions, i.e., Fsub is not essentially undecidable (Tarski, 1949). \par We demonstrate an infinite class of structural decidable extensions of Fsub, which combine traditional subtype inference rules with the above (W)SnS-interpretations. All these extensions, which we call systems FsubSnS, are still more powerful than Fsub, but less coarse than the direct (W)SnS-interpretations. \par The main distinctive features of the systems FsubSnS are: 1) decidability, 2) closure w.r.t.\ transitivity; 3)
structuredness, e.g., they never subtype a functional type to a universal one or vice versa, 4) they all contain the powerful rule for subtyping boundedly quantified types.
