Contracts made manifest

Abstract

Since Findler and Felleisen introduced higher-order contracts , many variants 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 to each value. These two approaches are commonly 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 λ _C and a manifest calculus λ _H , gave a translation φ from λ _C to λ _H , and proved that, if a λ _C term reduces to a constant, then so does its φ-image. We enrich their account with a translation Ψ from λ _H to λ _C and prove an analogous theorem.

We then generalize the whole framework to dependent contracts , whose predicates can mention free variables. This extension is both pragmatically crucial, supporting a much more interesting range of contracts, and theoretically challenging. We define dependent versions of λ _H and two dialects ("lax" and "picky") of λ _C , establish type soundness---a substantial result in itself, for λ _H ---and extend φ and Ψ accordingly. Surprisingly, the intuition that the latent and manifest systems are equivalent now breaks down: the extended translations preserve behavior in one direction but, in the other, sometimes yield terms that blame more.

References

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Index Terms

• General and reference

  • Cross-computing tools and techniques

    • Reliability

    • Validation

• Software and its engineering

  • Software creation and management

    • Software verification and validation

  • Software notations and tools

    • Formal language definitions

      • Semantics

• Theory of computation

  • Semantics and reasoning

    • Program semantics