This paper presents type classes, a new approach to ad-hoc polymorphism. Type classes permit overloading of arithmetic operators such as multiplication, and generalise the "eqtype variables" of Standard ML. Type classes extend the Hindley/Milner polymorphic type system, and provide a new approach to issues that arise in object-oriented programming, bounded type quantification, and abstract data types. This paper provides an informal introduction to type classes, and defines them formally by means of type inference rules. 1 Introduction Strachey chose the adjectives ad-hoc and parametric to distinguish two varieties of polymorphism [Str67]. Ad-hoc polymorphism occurs when a function is defined over several different types, acting in a different way for each type. A typical example is overloaded multiplication: the same symbol may be used to denote multiplication of integers (as in 3*3) and multiplication of floating point values (as in 3.14*3.14). Parametric polymorphism occurs wh...

From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus.

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Standard ML is a major revision of earlier dialects of the functional language ML. We describe the first compiler written for Standard ML in Standard ML. The compiler incorporates a number of novel features and techniques, and is probably the largest system written to date in Standard ML. Great attention was paid to modularity in the construction of the compiler, leading to a successful large-scale test of the modular capabilities of Standard ML. The front end is useful for purposes other than compilation, and the back end is easily retargetable (we have code generators for the VAX and MC68020). The module facilities of Standard ML were taken into account early in the design of the compiler, and they particularly influenced the environment management component of the front end. For example, the symbol table structure is designed for fast access to opened structures. The front end of the compiler is a single phase that integrates parsing, environment management, and type checking. The m...

We study the problem of type inference for a family of polymorphic type disciplines containing the power of Core-ML. This family comprises all levels of the stratification of the second-order lambda-calculus by "rank" of types. We show that typability is an undecidable problem at every rank k >= 3 of this stratification. While it was already known that typability is decidable at rank 2, no direct and easy-to-implement algorithm was available. To design such an algorithm, we develop a new notion of reduction and show howto use it to reduce the problem of typability at rank 2 to the problem of acyclic semi-unification. A by-product of our analysis is the publication of a simple solution procedure for acyclic semi-unification.

A theory of data types and a programming language based on category theory are presented. Data types play a crucial role in programming. They enable us to write programs easily and elegantly. Various programming languages have been developed, each of which may use different kinds of data types. Therefore, it becomes important to organize data types systematically so that we can understand the relationship between one data type and another and investigate future directions which lead us to discover exciting new data types. There have been several approaches to systematically organize data types: algebraic specification methods using algebras, domain theory using complete partially ordered sets and type theory using the connection between logics and data types. Here, we use category theory. Category theory has proved to be remarkably good at revealing the nature of mathematical objects, and we use it to understand the true nature of data types in programming.

The runtime data structures of the Standard ML of New Jersey compiler are simple yet general. As a result, code generators are easy to implement, programs execute quickly, garbage collectors are easy to implement and work efficiently, and a variety of runtime facilities can be provided with ease.

We extend a fragment of the programming language ML by incorporating a more general form of record pattern matching and providing for user-declared subtypes. Together, these two enhancements may be used to support a restricted object-oriented programming style. In keeping with the framework of ML, we present typing rules for the language, and develop a type inference aJgorithm. We prove that the algorithm is sound with respect to the typing rules, and that it infers a most general typing for every typable expression.

. This paper, which is partly tutorial in nature, summarizes some basic research goals in the study and development of typed objectoriented programming languages. These include both immediate repairs to problems with existing languages and the long-term development of more flexible and expressive, yet type-safe, approaches to program organization and design. We summarize and compare three object models used in the theoretical literature. We also consider approaches to a few technical problems, including changes in the type of a method (member function) from super (base) class to sub (derived) class and the use of types that give information about the implementations as well as the interfaces of objects. Such implementation types seem essential for adequate typing of binary operations on objects, for example. 1 Introduction A number of largely "theoretical" research efforts over the last five to ten years have developed and analyzed type systems for model object-oriented languages. Thi...