Abstract
We study a manifest contract system---a typed calculus of higher-order contracts where contracts are tightly integrated into a refinement type system---for a functional language with nondeterministic choice. The extension is not trivial, especially in the presence of dependent function types, because a naive extension would lead to inconsistent type equivalence, which makes contract information in refinement types meaningless. To solve the problem, we propose a new kind of nondeterministic choice called coordinated choice, in which each occurrence of a choice operator is given a name and choices of the same name coordinately take the same branch. We introduce the notion of or-thant that helps both intuitive understanding and the development of formal semantics of the new choice. We formalize a manifest contract system λ H||Φ using the coordinated choice and show its basic properties of progress, type preservation, and contract satisfaction, the last of which states correctness of contracts in refinement types.
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