Consistent subtyping is employed in some gradual type systems to validate type conversions. The original definition by Siek and Taha serves as a guideline for designing gradual type systems with subtyping. Polymorphic types à la System F also induce a subtyping relation that relates polymorphic types to their instantiations. However Siek and Taha’s definition is not adequate for polymorphic sub...

Nominal subtyping and structural subtyping each have their own strengths and weaknesses. Nominal subtyping allows programmers to explicitly express design intent, and, when types are associated with run-time tags, enables efficient run-time type tests (e.g., downcasts) and external/multimethod dispatch. On the other hand, structural subtyping is flexible and compositional, allowing unanticipate...

In this paper we study the interaction of subtyping and parametricity. We describe a logic for a programming language with parametric polymorphism and subtyping. The logic supports the formal definition and use of relational parametricity. We give two models for it, and compare it with other formal systems for the same language. In particular, we examine the “Penn interpretation” of subtyping a...

This paper discusses subtyping of tree-structured data encountered on the Web, e.g. XML and HTML data. Our long range objective is to define a type system for Web and/or Semantic Web query languages amenable to static type checking. We propose a type formalism motivated by XML Schema and accommodating two concepts of subtyping: inclusion subtyping (corresponding to XML Schema notion of type res...

Coercive subtyping ooers a general approach to subtyping and inheritance by introducing a simple abbreviational mechanism to constructive type theories. In this paper, we study coercion completion in coercive subtyping and prove that the formal extension with coercive subtyping of a type theory such as Martin-LL of's type theory and UTT is a conservative extension. The importance of coherence c...

System F ! is an extension of system F ! with subtyping and bounded quantiication. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higher-order typed-calculus with subtyping, bounded quan-tiication and order-sorted inductive types, i.e. data types with built-in subtyping and overloading. Moreover we show t...

We expose a new approach to tackle non-structural subtyping problems. We introduce uniform subtyping as a means to capture some properties of non-structural subtyping. In the uniform theory, we show that the validity of a first-order sentence is decidable, and entailment is PSPACEhard. In addition, we give decidable approximations to entailment and subtyping constrained types — two problems whi...

In nominal type systems, the subtype relation is between names of types, and subtype links are explicitly declared. In structural type systems, names are irrelevant; in determining type compatibility, only the structure of types is considered, and a type name is just an abbreviation for the full type. We analyze structural and different flavors of nominal subtyping from the perspective of compo...

salmonella infections are the second leading cause of zoonotic bacterial foodborne illness. main source of infection in human is contaminated food products. the aim of this study was sub typing isolates of salmonella entericaobtained during our previous study bypulsed field gel electrophoresis (pfge) technique. all 46 salmonella isolates were serotyped and then subjected to pfge. total isolates...

Coercive subtyping is a useful and powerful framework of subtyping for type theories. In this thesis, we point out the problem in the old formulation of coercive subtyping in [Luo99], give a new and adequate formulation T [C], the system that extends a type theory T with coercive subtyping based on a set C of basic subtyping judgements, and show that coercive subtyping is a conservative extensi...