We present a reenement of the existential object model of Pierce and Turner PT94]. In addition to signatures (or interfaces) as the types of objects, we also provide classes as the types of objects. These class types not only specify an interface, but also a particular implementation. We show that class types can be interpreted in the standard PER model. Our main result is that the standard int...

In this paper we present constructions of cpo models for second order lambda calculi with recursive types and/or subtyping. The model constructions are based on a model construction by ten Eikelder and Hemerik for second order lambda calculus with recursive types ([tEH89a]). The models will be compatible with conventional denotational semantics. For each of the systems we consider, the general ...

In this paper, we present a computer-checked, constructive soundness and completeness result for prototypic recursive type containment with respect to containment of nonwellfounded (finite or infinite) trees. The central role is played by formalisation of substitution of recursive types as a monad, with a traverse function implementing a strategy for potentially infinite recursive unfolding. In...

Subtyping relations for object-oriented formalisms describe relationships between superand subclasses which satisfy the substitutability requirement imposed on types and their subtypes. Behavioural subtyping is concerned with subtypes for active classes with an explicit dynamic behaviour, specifiable for instance by object-oriented formal methods combining state-based with behavioural formalism...

This paper studies one important aspect of distributed systems, locality, using a calculus of distributed higher-order processes in which not only basic values or channels, but also parameterised processes are transferred across distinct locations. An integration of the subtyping of λ-calculus and IO-subtyping of the π-calculus offers a tractable tool to control the locality of channel names in...

The problem of defining and checking a subtype relation between recursive types was studied in [3] for a first order type system, but for second order systems, which combine subtyping and parametric polymorphism, only negative results are known [17]. This paper studies the problem of subtype checking for recursive types in system kernel Fun, a typed -calculus with subtyping and bounded second o...

Bidirectional typechecking has become popular in advanced type systems because it works in many situations where inference is undecidable. In this paper, I show how to cleanly handle parametric polymorphism in a bidirectional setting, even in the presence of subtyping. The first contribution is a bidirectional type system that supports first-class (higher-rank and impredicative) polymorphism bu...

Complex diseases are caused by a combination of genetic and environmental factors, creating a difficult challenge for diagnosis and defining subtypes. This review article describes how distinct disease subtypes can be identified through integration and analysis of clinical and multi-omics data. A broad shift toward molecular subtyping of disease using genetic and omics data has yielded successf...

It is now widely accepted that inheritance is not subtyping [5], and that ‘‘inheritance is a relationship between implementations, while conformity is a relationship between interfaces’’ [1]. But like most maxims, these two are something of an oversimplification. Inheritance: Mechanism or Relation? As realized in Simula and Smalltalk, inheritance is a mechanism for generating new pieces of prog...

In recent work we have shown how it is possible to define very precise type systems for objectoriented languages by abstractly compiling a program into a Horn formula f . Then type inference amounts to resolving a certain goal w.r.t. the coinductive (that is, the greatest) Herbrand model of f . Type systems defined in this way are idealized, since in the most interesting instantiations both the...