We present GJ, a design that extends the Java programming language with generic types and methods. These are both explained and implemented by translation into the unextended language. The translation closely mimics the way generics are emulated by programmers: it erases all type parameters, maps type variables to their bounds, and inserts casts where needed. Some subtleties of the translation are caused by the handling of overriding. GJ increases expressiveness and safety: code utilizing generic libraries is no longer buried under a plethora of casts, and the corresponding casts inserted by the translation are guaranteed to not fail. GJ is designed to be fully backwards compatible with the current Java language, which simplifies the transition from non-generic to generic programming. In particular, one can retrofit existing library classes with generic interfaces without changing their code. An implementation of GJ has been written in GJ, and is freely available on the web.

This paper presents an overview of the programming language Modula-3, and a more detailed description of its type system. 1

Set-based analysis (SBA) produces good predictions about the behavior of functional and objectoriented programs. The analysis proceeds by inferring constraints that characterize the data flow relationships of the analyzed program. Experiences with MrSpidey, a static debugger based on SBA, indicate that SBA can adequately deal with programs of up to a couple of thousand lines of code. SBA fails, however, to cope with larger programs because it generates systems of constraints that are at least linear, and possibly quadratic, in the size of the analyzed program. This article presents theoretical and practical results concerning methods for reducing the size of constraint systems. The theoretical results include a proof-theoretic characterization of the observable behavior of constraint systems for program components, and a complete algorithm for deciding the observable equivalence of constraint systems. In the course of this development we establish a close connection between the observable equivalence of constraint systems and the equivalence of regular-tree grammars. We then exploit this connection to adapt a variety of algorithms for simplifying grammars to the problem of simplifying constraint systems. Based on the resulting algorithms, we have developed componential set-based analysis, a modular and polymorphic variant of SBA. Experimental results verify the effectiveness of the simplification

A constrained type is a type that comes with a set of subtyping constraints on variables occurring in the type. Constrained type inference systems are a natural generalization of Hindley/Milner type inference to languages with subtyping. This paper develops several subtyping relations on polymorphic constrained types of a general form that allows recursive constraints and multiple bounds on type variables. We establish a full type abstraction property that equates a novel operational notion of subtyping with a semantic notion based on regular trees. The decidability of this notion of subtyping is open; we present a decidable approximation. Subtyping constrained types has applications to signature matching and to constrained type simplification. The relation will thus be a critical component of any programming language incorporating a constrained typing system. 1 Introduction A constrained type is a type that is additionally constrained by a set of subtyping constraints on the free ty...

Mixin modules are proposed as a new construct for module languages, allowing recurslye definitions to span module boundaries. Mixin modules are proposed specifically for the Standard ML language. Several applications are described, including the resolution of cycles in module import dependency graphs, as well as functionality related to Haskell type classes and CLOS generic functions, though without any complications to the core language semantics. Mixin modules require no changes to the core ML type system, and only a very minor change to its run-time semantics. A type system and reduction semantics are provided, and the former is verified to be sound relative to the latter.

We present a new predicative and decidable type system, called ML , suitable for languages that integrate functional programming and parametric polymorphism in the tradition of ML [21, 28], and class-based objectoriented programming and higher-order multi-methods in the tradition of CLOS [12]. Instead of using extensible records as a foundation for object-oriented extensions of functional languages, we propose to reinterpret ML datatype declarations as abstract and concrete class declarations, and to replace pattern matching on run-time values by dynamic dispatch on run-time types. ML is based on universally quantified polymorphic constrained types. Constraints are conjunctions of inequalities between monotypes built from type constructors organized into extensible and partially ordered classes. We give type checking rules for a small, explicitly typed functional language `a la XML [20] with multi-methods, show that the resulting system has decidable minimal types, and discuss subject ...

Cecil is a purely object-oriented language intended to support rapid construction of high-quality, extensible software. Cecil combines multi-methods with a simple classless object model, a kind of dynamic inheritance, modules, and optional static type checking. Instance variables in Cecil are accessed solely through messages, allowing instance variables to be replaced or overridden by methods and vice versa. Cecil’s predicate objects mechanism allows an object to be classified automatically based on its run-time (mutable) state. Cecil’s static type system distinguishes between subtyping and code inheritance, but Cecil enables these two graphs to be described with a single set of declarations, streamlining the common case where the two graphs are parallel. Cecil includes a fairly flexible form of parameterization, including explicitly parameterized objects, types, and methods, as well as implicitly parameterized methods related to the polymorphic functions commonly found in functional languages. By making type declarations optional, Cecil aims to allow mixing of and migration between exploratory and production programming styles. Cecil supports a module mechanism that enables independently-developed subsystems to be encapsulated, allowing them to be type-checked and reasoned about in isolation despite the presence of multi-methods and subclassing. Objects can be extended externally with additional

We develop an imperative calculus that provides a formal model for both single and mixin inheritance. By introducing classes and mixins as the basic object-oriented constructs in a -calculus with records and references, we obtain a system with an intuitive operational semantics. New

Abstract. Precise type information is invaluable for analysis and optimization of object-oriented programs. Some forms of polymorphism found in object-oriented languages pose significant difficulty for type inference, in particular data polymorphism. Agesen’s Cartesian Product Algorithm (CPA) can analyze programs with parametric polymorphism in a reasonably precise and efficient manner, but CPA loses precision for programs with data polymorphism. This paper presents a precise constraintbased type inference system for Java. It uses Data-Polymorphic CPA (DCPA), a novel constraint-based type inference algorithm which extends CPA with the ability to accurately and efficiently analyze data polymorphic programs. The system is implemented for the full Java language, and is used to statically verify the correctness of Java downcasts. Benchmark results are given which show that DCPA is significantly more accurate than CPA and the efficiency of DCPA is close to CPA. 1

Objective ML is a small practical extension to ML with objects and top level classes. It is fully compatible with ML; its type system is based on ML polymorphism, record types with polymorphic access, and a better treatment of type abbreviations. Objective ML allows for most features of object-oriented languages including multiple inheritance, methods returning self and binary methods as well as parametric classes. This demonstrates that objects can be added to strongly typed languages based on ML polymorphism.