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

Abstract. Functional logic programming languages combine the most important declarative programming paradigms, and attempts to combine these paradigms have a long history. The declarative multi-paradigm language Curry is influenced by recent advances in the foundations and implementation of functional logic languages. The development of Curry is an international initiative intended to provide a common platform for the research, teaching, and application of integrated functional logic languages. This paper surveys the foundations of functional logic programming that are relevant for Curry, the main features of Curry, and extensions and applications of Curry and functional logic programming. 1

During the past few years, many researchers have begun to present semantic specifications in a style that has been strongly advocated by Plotkin in [19]. The purpose of this paper is to introduce in an intuitive manner the essential ideas of the method that we call now Natural Semantics ~ together with its connections to ideas in logic and computing. Natural Semantics is of interest per se and because it is used as a semantics specification formalism for an interactive computer system that we are currently building at INRIA. 1.

This paper presents a variant of the SML module system that introduces a strict distinction between abstract types and manifest types (types whose de nitions are part of the module speci cation), while retaining most of the expressive power of the SML module system. The resulting module system provides much better support for separate compilation. 1

We present a simple and powerful type inference method for dynamically typed languages where no type information is supplied by the user. Type inference is reduced to the problem of solvability of a system of type inclusion constraints over a type language that includes function types, constructor types, union, intersection, and recursive types, and conditional types. Conditional types enable us to analyze control flow using type inference, thus facilitating computation of accurate types. We demonstrate the power and practicrdity of the method with examples and performance results from an implementation. 1

This paper presents a soft type systems that retains the expressiveness of dynamic typing, but offers the early error detection and improved optimization capabilities of static typing. The key idea underlying soft typing is that a type checker need not reject programs containing "ill-typed" phrases. Instead, the type checker can insert explicit run-time checks, transforming "ill-typed" programs into type-correct ones.

This paper presents a program transformation that allows languages with polymorphic typing (e.g. ML) to be implemented with unboxed, multi-word data representations, more efficient than the conventional boxed representations. The transformation introduces coercions between various representations, based on a typing derivation. A prototype ML compiler utilizing this transformation demonstrates important speedups.

Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, debuggers, equality functions, unifiers, pattern matchers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of user-defined datatypes. This paper extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks definitions of polytypic functions, and infers the types of all other expressions using an extension of Jones ' theories of qualified types and higher-order polymorphism. The semantics of the programs in the extended language is obtained by adding type arguments to functions in a dictionary passing style. Programs in the extended language are translated to Haskell. 1

Languages that support abstraction and modular structure, such as Standard ML, Modula, Ada, and (more or less) C++, may have deeply nested dependency hierarchies among source files. In ML the problem is particularly severe because ML's powerful parameterized module (functor) facility entails dependencies among implementation modules, not just among interfaces.

We present a small language L and its typing system based on the idea of interaction, one of the important notions in parallel and distributed computing. L is based on, apart from such constructs as parallel composition and process creation, three pairs of communication primitives which use the notion of a session, a semantically atomic chain of communication actions which can interleave with other such chains freely, for high-level abstraction of interaction-based computing. Three primitives enable programmers to elegantly describe complex interactions among processes with a rigorous type discipline similar to ML [4]. The language is given formal operational semantics and a type inference system, regarding which we prove that if a program is well-typed in the typing system, it never causes run-time error due to type inconsistent communication patterns, offering a new foundation for type discipline in parallel programming languages. 1 Introduction The idea of interaction, that is, rec...