Nondeterministic Manifest Contracts

Abstract

We study a manifest contract system-a typed calculus of higherorder 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 orthant 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.

Manifest Contracts with Intersection Types

“…Next we show the value inversion property, which guarantees a value of a refinement type satisfies its predicate. For PCFv∆ H , this property can be quite easily shown since PCFv∆ H does not have dependent function types, while previous manifest contract systems need quite complicated reasoning [19,24,26]. The property itself is proven by using the following two, which are for strengthening an induction hypothesis.…”

“…As we will see, PCFv∆ H uses nondeterminism for dynamic checking. The combination of dependent function types and nondeterminism poses a considerable challenge [19]. -We use refinement intersection types rather than general ones.…”

“…In fact, no other work discussed in this section supports both dependent function contracts and intersection contracts. To extend PCFv∆ H to dependent function types, we have to take care of their interaction with nondeterminism, which we studied elsewhere [19] for a manifest calculus λ H Φ with a general nondeterministic choice operator.…”