This paper defines a notion of binding trees that provide a suitable model for second-order type systems with F-bounded quantifiers and equirecursive types. It defines a notion of regular binding trees that correspond in the right way to notions of regularity in the first-order case. It defines a notion of subtyping on these trees and proves various properties of the subtyping relation. It defi...

Source attribution of cases of food-borne disease represents a valuable tool for identifying and prioritizing effective food-safety interventions. Microbial subtyping is one of the most common methods to infer potential sources of human food-borne infections. So far, Salmonella microbial subtyping source attribution models have been implemented by using serotyping and phage-typing data. Molecul...

Two processes of stereotyping, subtyping and subgrouping, are compared. Subtyping occurs when perceivers respond to members of a target group who disconfirm their stereotypes by seeing them as exceptions to the rule and placing them in a separate subcategory apart from members who confirm the stereotype. The more recently defined process of subgrouping refers to the perceiver’s organization of ...

Behavioral subtyping is an established idea that enables modular reasoning about behavioral properties of object-oriented programs. It requires that syntactic subtypes are behavioral refinements. It validates reasoning about a dynamically-dispatched method call, say E .m(), using the specification associated with the static type of the receiver expression E . For languages with references and m...

Laboratory surveillance systems for salmonellosis should ideally be based on the rapid serotyping and subtyping of isolates. However, current typing methods are limited in both speed and precision. Using 783 strains and isolates belonging to 130 serotypes, we show here that a new family of DNA repeats named CRISPR (clustered regularly interspaced short palindromic repeats) is highly polymorphic...

In this paper we solve an open problem posed in our previous work on asynchronous subtyping [12], extending the method to higher-order session communication and functions. Our system provides two complementary methods for communication code optimisation, mobile code and asynchronous permutation of session actions, within processes that utilise structured, typed communications. In order to prove...

This paper gives the first proof that the subtyping relation of a higherorder lambda calculus, F ≤, is anti-symmetric, establishing in the process that the subtyping relation is a partial order—reflexive, transitive, and anti-symmetric up to β-equality. While a subtyping relation is reflexive and transitive by definition, anti-symmetry is a derived property. The result, which may seem obvious t...

Object-orientation supports code reuse and incremental programming. Multiple inheritance increases the power of code reuse, but complicates the binding of method calls and thereby program analysis. Behavioral subtyping allows program analysis under an open world assumption; i.e., under the assumption that class hierarchies are extensible. However, method redefinition is severely restricted by b...

We consider a type algebra equipped with recursive, product, function, intersection, union, and complement types together with type variables and implicit universal quantification over them. We consider the subtyping relation recently defined by Castagna and Xu over such type expressions and show how this relation can be decided in EXPTIME, answering an open question. The novelty, originality a...

Behavioral subtyping forces objects of subtypes to behave in the same way as objects of supertypes. It is often favored over standard subtyping because it provides a means to obtain a modular program logic. Relative completeness is a formal property of a Hoare logic that ensures that any failed attempt to verify the correctness of a program is not caused by a weakness of its Hoare rules. In thi...