Our objective is to understand the notion of type in programming languages, present a model of typed, polymorphic programming languages that reflects recent research in type theory, and examine the relevance of recent research to the design of practical programming languages. Object-oriented languages provide both a framework and a motivation for exploring the interaction among the concepts of type, data abstraction, and polymorphism, since they extend the notion of type to data abstraction and since type inheritance is an important form of polymorphism. We develop a λ-calculus-based model for type systems that allows us to explore these interactions in a simple setting, unencumbered by complexities of production programming languages. The evolution of languages from untyped universes to monomorphic and then polymorphic type systems is reviewed. Mechanisms for polymorphism such as overloading, coercion, subtyping, and parameterization are examined. A unifying framework for polymorphic type systems is developed in terms of the typed λ-calculus augmented to include binding of types by quantification as well as binding of values by abstraction. The typed λ-calculus is augmented by universal quantification to model generic functions with type parameters, existential quantification and packaging (information hiding) to model abstract data types, and

There are two major ways of structuring data in programming languages. The first and common one, used for example in Pascal, can be said to derive from standard branches of mathematics. Data is organized as cartesian products (i.e. record types), disjoint sums (i.e. unions or variant types) and function spaces (i.e. functions and procedures).

There exists an identifiable programming style based on the widespread use of type information handled through mechanical typechecking techniques. This typeful programming style is in a sense independent of the language it is embedded in; it adapts equally well to functional, imperative, object-oriented, and algebraic programming, and it is not incompatible with relational and concurrent programming. The main purpose of this paper is to show how typeful programming is best supported by sophisticated type systems, and how these systems can help in clarifying programming issues and in adding power and regularity to languages. We start with an introduction to the notions of types, subtypes and polymorphism. Then we introduce a general framework, derived in part from constructive logic, into which most of the known type systems can be accommodated and extended. The main part of the paper shows how this framework can be adapted systematically to cope with actual programming constructs. For concreteness we describe a particular programming language with advanced features; the emphasis here is on the combination of subtyping and polymorphism. We then discuss how typing concepts apply to large programs, made of collections of modules, and very large programs, made of collections of large programs. We also sketch how typing applies to system programming; an area which by nature escapes rigid typing. In summary, we compare the most common programming styles, suggesting that many of them are compatible with, and benefit from, a typeful discipline.

Object-oriented techniques increase program modularity, decrease coupling, and improve data abstraction by supporting encapsulation through narrow, rigidly defined and strongly enforced interfaces to objects. Applying object-oriented techniques to address problems of building scalable and maintainable distributed systems seems an obvious approach since reducing coupling and increasing modularity are of obvious benefit. Unfortunately, object-oriented interfaces and mechanisms are usually only accessible and enforced through programming language mechanisms and support. This severely limits the degree to which disjoint, unrelated components can interact in a multilingual, loosely coupled distributed system. An accepted solution to the language dependence problem is the use of high-level interface description languages (IDLs) to provide a description mechanism for an object's interface that is independent of any programming language. Implementations of these interfaces can be provided by a...

2. System tutorial 3. The big picture 3.1. Kinds, types, and values 3.2. Signatures and bindings

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The Amber machine is a stack machine designed as an intermediate language for compiling higher-order languages. The current version is specialized for the Amber language. The machine supports a set of basic and structured data types, functional closures, signals, bitmap graphics, persistent objects and meta-level execution. The latter is needed as the Amber compiler is entirely written in Amber (above the Amber machine level) and needs to switch level when executing a program it has just compiled. A set of implementation strategies are admissible for this machine, including bytecode interpretation, threaded code interpretation and compilation to native code. The current implementation is based on a byte-code interpreter and a one-space compacting collector, and runs on a Macintosh. Introduction The Amber machine is a stack machine designed as an intermediate language for compiling higher-order languages, in the tradition of SECD machines [Landin 64] and combinator machines [Turner 7...