Since Findler and Felleisen introduced higher-order contracts, many variants of their system have been proposed. Broadly, these fall into two groups: some follow Findler and Felleisen in using latent contracts, purely dynamic checks that are transparent to the type system; others use manifest contracts, where refinement types record the most recent check that has been applied. These two approaches are generally assumed to be equivalent—different ways of implementing the same idea, one retaining a simple type system, and the other providing more static information. Our goal is to formalize and clarify this folklore understanding.

Our work extends that of Gronski and Flanagan, who defined a latent calculus \lambda_C and a manifest calculus \lambda_H, gave a translation \phi from \lambda_C to \lambda_H, and proved that if a \lambda_C term reduces to a constant, then so does its \phi-image. We enrich their account with a translation \psi in the opposite direction and prove an analogous theorem for \psi.

More importantly, we generalize the whole framework to dependent contracts, where the predicates in contracts can mention variables from the local context. This extension is both pragmatically crucial, supporting a much more interesting range of contracts, and theoretically challenging. We define dependent versions of \lambda_C (following Findler and Felleisen’s semantics) and \lambda_H, establish type soundness—a challenging result in itself, for \lambda_H—and extend \phi and \psi accordingly. Interestingly, the intuition that the two systems are equivalent appears to break down here: we show that \psi preserves behavior exactly, but that a natural extension of \phi to the dependent case will sometimes yield terms that blame more because of a subtle difference in the treatment of dependent function contracts when the codomain contract itself abuses the argument.

Edit on 2009-11-03: there’s a newer version, as will appear in POPL 2010.

Edit on 2010-01-22: I have removed the link to the submission, since it is properly subsumed by our published paper.