Structural Decidable Extensions of Bounded Quantification

Abstract

We show how the subtype relation of the well-known system F , the second-order polymorphic -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 secondorder theory of one (Buchi), 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). We demonstrate an infinite class of structural decidable extensions of F , which combine traditional subtype inference rules with the above (W)SnS- interpretations. All these extensions, which we call systems F SnS , are still more powerful than F , but less coarse than the direct (W)SnS-interpretations. The main distinctive features of the systems F SnS are: 1) decidability, 2) closure w.r.t. transitivity; 3) structuredness, e.g...

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