Coercive subtyping ooers a conceptually simple but powerful framework to understand subtyping and subset relationships in type theory. In this paper we study some of its proof-theoretic and computational properties.

Ageism research tends to lump "older people" together as one group, as do policy matters that conceptualize everyone over-65 as "senior." This approach is problematic primarily because it often fails to represent accurately a rapidly growing, diverse, and healthy older population. In light of this, we review the ageism literature, emphasizing the importance of distinguishing between the still-a...

Coercive subtyping is a useful and powerful framework of subtyping for type theories. The key idea of coercive subtyping is subtyping as abbreviation. In this paper, we give a new and adequate formulation of 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 extension and, in a...

Constrained type systems are a natural generalization of Hindley/Milner type inference to languages with subtyping. This paper develops several subtyping relations on constrained types. We establish a full type abstraction property that equates an operational notion of subtyping with a semantic notion based on regular trees. The decidability of this notion of subtyping is open; we present a dec...

Subtyping is a common tool in the design of type systems that finds its roots in the η-expansion of arrow types and the notion of type containment obtained by closing System F by η-expansion. Although strongly related, subtyping and type containment still significantly differ from one another when put into practice. We introduce coercion constraints to relate and generalize subtyping and type c...

Mitchell de ned and axiomatized a subtyping relationship (also known as containment, coercibility, or subsumption) over the types of System F (with \!" and \8"). This subtyping relationship is quite simple and does not involve bounded quanti cation. Tiuryn and Urzyczyn quite recently proved this subtyping relationship to be undecidable. This paper supplies a new undecidability proof for this su...

J. Tiuryn. A sequent calculus for subtyping polymorphic types. unpublished , 1996. TU96] J. Tiuryn and P. Urzyczyn. The subtyping problem for second-order types is undecidable. In this short survey, we have presented subtyping for two type systems: Cò for System-F(c) and P ; for. There are several common features in these studies. From the syntactic point of view, both in Cò and transitivity is...

In this paper, we propose an integration of structural subtyping with boolean connectives and semantic subtyping to define a Java-like programming language that exploits the benefits of both techniques. Semantic subtyping is an approach for defining subtyping relation based on set-theoretic models, rather than syntactic rules. On the one hand, this approach involves some non-trivial mathematica...

We study a calculus with both subtyping and datatype deenitions. Our primary goal is to understand the interaction of subtyping with mutually recursive types, which raises diiculties beyond those addressed in previous studies. A second aim is to clarify the relations between structural subtyping and the user-declared subtyping found in languages such as C++, Eiiel, and Java.

Subtyping for inductive types in dependent type theories is studied in the framework of coercive subtyping. General structural subtyping rules for parameterised inductive types are formulated based on the notion of inductive schemata. Certain extensional equality rules play an important role in proving some of the crucial properties of the type system with these subtyping rules. In particular, ...