Fsub with Recursive Types: `Types-as-Propositions' Interpretations M. Rabin's S2S

Subtyping judgments of the polymorphic second-order typed lambda-calculus Fsub extended by recursive types and different known inference rules for these types could be interpreted in S2S, M.Rabin's monadic second-order theory of two successor functions. On the one hand, this provides a comprehensible model of the parametric and inheritance polymorphisms over recursive types, on the other, proves that the corresponding subtyping theories are not essentially undecidable, i.e., possess consistent decidable extensions