The calculus of constructions can be extended with an infinite hierarchy of universes and cumulative subtyping. Subtyping is usually left implicit in the typing rules. We present an alternative version of the calculus of constructions where subtyping is explicit. We avoid problems related to coercions and dependent types by using the Tarski style of universes and by adding equations to reflect ...

We study subtyping of recursive types in the presence of associative and commutative products—that is, subtyping modulo a restricted form of type isomorphisms. We show that this relation, which we claim is useful in practice, is a composition of the usual subtyping relation with the recently proposed notion of equality up to associativity and commutativity of products, and we propose an efficie...

Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. W...

Avian influenza virus (AIV) infection is a major cause of bird or human mortality and morbidity, therefore the rapid identification of the virus is of important clinical and epidemiological implication. Methods: A multiplex Reverse Transcriptase PCR (RT-PCR) was optimized for the detection of influenza A virus and the H5 and H9 subtypes. The influenza type A specific primers were directed to t...

27 28 The recent association of certain Influenza A subtypes with clinically relevant phenotypes has 29 led to the increasing importance of subtyping by clinical virology laboratories. To provide 30 clinical laboratories with a definitive immunofluorescence assay for the subtyping of influenza A 31 virus isolates, we generated a panel of monoclonal antibodies (MAbs) against the major 32 circula...