On the semantic expressiveness of recursive types

Recursive types extend the simply-typed lambda calculus (STLC) with additional expressive power to enable diverging computation and encode recursive data-types (e.g., lists). Two formulations of exist: iso-recursive equi-recursive. The relative advantages iso- equi-recursion are well- studied when it comes their impact on type-inference. However, semantic expressiveness two remains unclear so far. This paper studies STLC equi-recursive types, proving that these equally expressive. In fact, we prove they both as only term-level recursion. We phrase equi-expressiveness results in terms full abstraction three canonical compilers between languages (STLC iso-, recursion). Our choice allows us study interacting over a recursively-typed interface. proofs all rely typed version proof technique called approximate backtranslation. Together, our show there is no difference STLCs types. this paper, focus setting but believe scale more powerful type systems like System F.