Dependent Types with Subtyping and Late-Bound Overloading

A semantics for λ { } str : a calculus with overloading and late - binding

Up to now there was no interpretation available for λ-calculi featuring overloading and late-binding, although these are two of the main principles of any object-oriented programming language. In this paper we provide a new semantics for a stratified version of Castagna’s λ{}, a λ-calculus combining overloading with late-binding. The model-construction is carried out in EETJ + (Tot) + (F-IN), a...

Overloading, subtyping and late binding - functional foundation of object-oriented programming

Order-Sorted Inductive Types

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...

Object-Oriented Verification Based on Record Subtyping in Higher-Order Logic

We show how extensible records with structural subtyping can be represented directly in Higher-Order Logic (HOL). Exploiting some speci c properties of HOL, this encoding turns out to be extremely simple. In particular, structural subtyping is subsumed by naive parametric polymorphism, while overridable generic functions may be based on overloading. Taking HOL plus extensible records as a start...

Principal Type Schemes for Functional Programs with Overloading and Subtyping

We show how the Hindley/Milner polymorphic type system can be extended to incorporate overloading and subtyping. Our approach is to attach constraints to quantified types in order to restrict the allowed instantiations of type variables. We present an algorithm for inferring principal types and prove its soundness and completeness. We find that it is necessary in practice to simplify the inferr...