Subtyping Union Types

Subtyping rules can be fairly complex for union types, due to interactions with other types, such as function types. Furthermore, these interactions turn out to depend on the calculus considered: for instance, a call-by-value calculus and a call-by-name calculus will have different possible subtyping rules. In order to abstract ourselves away from this dependence, we consider a fairly large class of calculi. We define types in a semantic fashion, as sets of terms. Then, a type can be a subtype of another type if its denotation is included in the denotation of the other type. We first consider a simple type system with union, function, pair and constant types. Using inference rules, we specify a subtyping relation which is both sound and complete with respect to the class of calculi. We then extend this result to a richer type system with ML-style polymorphism and type constructors. We expect this framework to allow the study of subtyping relations that only hold for some calculi by ...

• Type: Conference
• Year: 2004
• Where: CSL
• Authors: Jerome Vouillon
• Keywords: CSL 2004, Function Types, Possible Subtyping Rules, Subtyping