We present a new approach to proving type soundness for Hindley/Milner-style polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the language semantics. The approach easily extends from polymorphic functional languages to imperative languages that provide references, exceptions, continuations, and similar features. We illustrate the technique with a type soundness theorem for the core of Standard ML, which includes the first type soundness proof for polymorphic exceptions and continuations. 1 Type Soundness Static type systems for programming languages attempt to prevent the occurrence of type errors during execution. A definition of type error depends on a specific language and type system, but always includes the use of a function on arguments for which it is not defined, and the attempted application of a non-function. ...

Several related typed languages for modular programming and data abstraction have been proposed recently, including Pebble, SOL, and ML modules. We review and compare the basic type-theoretic ideas behind these languages and evaluate how they

Object-oriented programming is becoming a popular approach to the construction of complex software systems. Benefits of object orientation include support for modular design, code sharing, and extensibility. In order to make the most of these advantages, a type theory for objects and their interactions should be developed to aid checking and

data types Inheritance Object-based concurrency 1.

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In this paper we overview the design and implementation of a language extension to C++ for abstracting types and for decoupling subtyping and inheritance. This extension gives the user more of the flexibility of dynamic typing while retaining the efficiency and security of static typing. We discuss the syntax and semantics of this language extension, show examples of its use, and present and analyze the cost of three different implementation techniques: a preprocessor to a C++ compiler, an implementation in the front end of a C++ compiler, and a low-level back-end based implementation.

Many computer programs have the property that they work correctly on a variety of types of input; such programs are called polymorphic. Polymorphic type systems support polymorphism by allowing programs to be given multiple types. In this way, programs are permitted greater flexibility of use, while still receiving the benefits of strong typing. One especially successful polymorphic type system is the system of Hindley, Milner, and Damas, which is used in the programming language ML. This type system allows programs to be given universally quantified types as a means of expressing polymorphism. It has two especially nice properties. First, every well-typed program has a “best ” type, called the principal type, that captures all the possible types of the program. Second, principal types can be inferred, allowing programs to be written without type declarations. However, two useful kinds of polymorphism cannot be expressed in this type system: overloading and subtyping. Overloading is the kind of polymorphism exhibited by a function like addition, whose types cannot be captured by a single universally quantified type formula.

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C++ uses inheritance as a substitute for subtype polymorphism. We give examples where this makes the type system too inflexible. We then describe a conservative language extension that allows us to define an abstract type hierarchy independent of any implementation hierarchies, to retroactively abstract over an implementation, and to decouple subtyping from inheritance. This extension gives the user more of the flexibility of dynamic typing while retaining the efficiency and security of static typing. With default implementations and views we provide flexible mechanisms for implementing an abstract type by different concrete class types. We first show how our language extension can be implemented in a preprocessor to a C++ compiler, and then detail and analyze the efficiency of an implementation we directly incorporated in the GNU C++ compiler.