Relating Church-Style and Curry-Style Subtyping

Type theories with higher-order subtyping or singleton types are examples of systems where computation rules for variables are affected by type information in the context. A complication for these systems is that bounds declared in the context do not interact well with the logical relation proof of completeness or termination. This paper proposes a natural modification to the type syntax for F-Omega-Sub, adding variable's bound to the variable type constructor, thereby separating the computational behavior of the variable from the context. The algorithm for subtyping in F-Omega-Sub can then be given on types without context or kind information. As a consequence, the metatheory follows the general approach for type systems without computational information in the context, including a simple logical relation definition without Kripke-style indexing by context. This new presentation of the system is shown to be equivalent to the traditional presentation without bounds on the variable type constructor.Comment: In Proceedings ITRS 2010, arXiv:1101.410

Using Kinds to Represent Heterogeneous Collections in a Static Type System (Extended Abstract)

We consider the problem of representing heterogeneous collections of objects in a typed polymorphic programming language in such a way that common properties of members of a collection, such as having commonly named field with a common type can be expressed in the type system. The use of such collections is widespread in object-oriented and database programming and has so far been achieved in statically typed systems only through the use of a single dynamic type, which effectively hides all the structure of a value. In this paper we exploit a system of types and kinds (sets of types) to represent dynamic values with some known properties. The type system is shown to be sound and to have a complete type inference algorithm

A Unified Type System for Object-Oriented Programming

We present a new type system for object-oriented languages with assignments. Types are sets of classes, subtyping is set inclusion, and genericity is class substitution. The type system enables separate compilation, and unifies, generalizes, and simplifies the type systems underlying SIMULA/BETA, C++, EIFFEL, and Typed Smalltalk, and the type system with type substitutions proposed by Palsberg and Schwartzbach, Classes and types are both modeled as node-labeled, ordered regular trees; this allows an efficient type-checking algorithm

Semantic Predicate Types and Approximation for Class-based Object Oriented Programming

We apply the principles of the intersection type discipline to the study of class-based object oriented programs and; our work follows from a similar approach (in the context of Abadi and Cardelli's Varsigma-object calculus) taken by van Bakel and de'Liguoro. We define an extension of Featherweight Java, FJc and present a predicate system which we show to be sound and expressive. We also show that our system provides a semantic underpinning for the object oriented paradigm by generalising the concept of approximant from the Lambda Calculus and demonstrating an approximation result: all expressions to which we can assign a predicate have an approximant that satisfies the same predicate. Crucial to this result is the notion of predicate language, which associates a family of predicates with a class.Comment: Proceedings of 11th Workshop on Formal Techniques for Java-like Programs (FTfJP'09), Genova, Italy, July 6 200

Mixin Composition Synthesis based on Intersection Types

We present a method for synthesizing compositions of mixins using type inhabitation in intersection types. First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with records. Intersection types with records and record-merge are used to assign meaningful types to these terms without resorting to recursive types. Second, typed terms are translated to a repository of typed combinators. We show a relation between record types with record-merge and intersection types with constructors. This relation is used to prove soundness and partial completeness of the translation with respect to mixin composition synthesis. Furthermore, we demonstrate how a translated repository and goal type can be used as input to an existing framework for composition synthesis in bounded combinatory logic via type inhabitation. The computed result is a class typed by the goal type and generated by a mixin composition applied to an existing class

Introduction to the Literature on Programming Language Design

This is an introduction to the literature on programming language design and related topics. It is intended to cite the most important work, and to provide a place for students to start a literature search

Privacy via subsumption

We describe an object calculus allowing object extension and structural subtyping. Each object has a “dictionary ” to mediate the connection between names and components. This extra indirection yields the first object calculus combining both object extension and full width subtyping in a type-safe manner. If class inheritance is modeled with object extension, private fields and methods can be achieved directly by scoping restrictions: private fields or methods are those hidden by subsumption. We prove that the type system is sound, discuss a variant allowing covariant self types, and give some examples of the expressiveness of the calculus. C ○ 2002 Elsevier Scienc