Simplifying Subtyping Constraints: A Theory

First-Order Theory of Subtyping Constraints

Subtyping Constraints in Quasi-lattices

In this report, we show the decidability and NP-completeness of the satisfiability problem for non-structural subtyping constraints in quasi-lattices. This problem, first introduced by Smolka in 1989, is important for the typing of logic and functional languages. The decidability result is obtained by generalizing Trifonov and Smith’s algorithm over lattices, to the case of quasi-lattices. Simi...

Subtyping by Constraints in Object-Oriented Databases

For many object-oriented database applications taxonomies with a setinclusion semantics among the type extents are essential. In practical cases, however, common object-oriented modeling techniques often do not result in taxonomies as they ignore application specific constraints. We will elaborate that especially in domains like CAD or similar engineering environments integrity constraints on t...

Behavioral Subtyping Using Invariants and Constraints

We present a way of de ning the subtype relation that ensures that subtype objects preserve behavioral properties of their supertypes. The subtype relation is based on the speci cations of the suband supertypes. Our approach handles mutable types and allows subtypes to have more methods than their supertypes. Dealing with mutable types and subtypes that extend their supertypes has surprising co...

Coercive Subtyping in Type Theory

We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-LL of's type theory NPS90] and the type theory UTT Luo94]. In this approach, subtyping with speciied implicit coercions is treated as a feature at the level of the logical framework; in particular, subsumption and coercion are combined in such a way that the meaning of an object ...