We onsider an obje t al ulus of Abadi and Leino. The language has a type system with obje t subtyping whi h allows for spe ialisation, ovariant subtyping in the return types of methods and invariant subtyping in the types of elds. We present a type inferen e algorithm for this language.

We present a core Martin-Löf type theory with subtyping; it has a cumulative hierarchy of universes and the contravariant rule for subtyping between dependent product types. We extend to this calculus the normalisation by evaluation technique defined for a variant of MLTT without subtyping. This normalisation function makes the subtyping relation and type-checking decidable. To our knowledge, t...

We investigate a technique from the literature, called the phantom-types technique, that uses parametric polymorphism, type constraints, and unification of polymorphic types to model a subtyping hierarchy. Hindley-Milner type systems, such as the one found in Standard ML, can be used to enforce the subtyping relation, at least for first-order values. We show that this technique can be used to e...

While generalized algebraic datatypes (GADTs) are now considered well-understood, adding them to a language with a notion of subtyping comes with a few surprises. What does it mean for a GADT parameter to be covariant? The answer turns out to be quite subtle. It involves fine-grained properties of the subtyping relation that raise interesting design questions. We allow variance annotations in G...

Molecular subtyping of Bacillus anthracis played an important role in differentiating and identifying strains during the 2001 bioterrorism-associated outbreak. Because B. anthracis has a low level of genetic variability, only a few subtyping methods, with varying reliability, exist. We initially used multiple-locus variable-number tandem repeat analysis (MLVA) to subtype 135 B. anthracis isolat...

We consider how the OO notion of subtyping relates to lotos testing theory. In particular, we investigate which of the standard lotos preorders is a suitable instantiation of behavioural subtyping and argue that each of the main preorders, trace preorder, trace extension, reduction and extension, is in some way deecient. Then, in the light of pre and post condition based models of OO subtyping,...