We study an extension of the Hindley Milner system with explicit type scheme annotations and type declarations. The system can express polymorphic function arguments, user-de ned data types with abstract components, and structure types with polymorphic elds. More generally, all programs of the polymorphic lambda calculus can be encoded by a translation between typing derivations. We show that type reconstruction in this system can be reduced to the decidable problem of rst-order uni cation under a mixed pre x.

Many statically typed programming languages provide an abstract data type construct, such as the module in Modula-2. However, in most of these languages, implementations of abstract data types are not first-class values. Thus, they cannot be assigned to variables, passed as function parameters, or returned as function results. Several higher-order functional languages feature strong and static type systems, parametric polymorphism, algebraic data types, and explicit type variables. Most of them rely on Hindley-Milner type inference instead of requiring explicit type declarations for identifiers. Although some of these languages support abstract data types, it appears that none of them directly provides light-weight abstract data types whose implementations are first-class values. We show how to add significant expressive power to statically typed functional languages with explicit type variables by incorporating first-class abstract types as an extension of algebraic data types. Furthermore, we extend record types to allow abstract components. The components of such abstract records are selected using the dot notation. Following Mitchell and Plotkin, we formalize abstract types in terms of existentially quantified types. We give a syntactically sound and complete type inference algorithm and prove that our type system is semantically sound with respect to standard denotational semantics.

In Java, an interface specifies public abstract methods and associated public constants. Conformance of a class to an interface is by name. We propose to allow structural conformance to interfaces as well: Any class that provides an implementation for each method in an interface conforms structurally to the interface, and any instance of the class can be used where a value of the interface type is expected. We argue that structural conformance results in a major gain in flexibility in situations that require retroactive abstraction over types. Our extension comes almost for free. No additional syntax and only minor modifications to the Java compiler and virtual machine are required. Our extension is type-safe: a cast-free program that compiles without errors will not have any type errors at run time, and it is conservative: existing Java programs compile and run in the same manner as under the original language definition. Finally, our extension works well with recent extensions such as the Java Distributed Object Model. We have implemented our extension of Java with structural interface conformance by modifying the Java Developers Kit 1.0.2 source release for Solaris. We have also created a test suite for the extension.

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We argue that the novel combination of type classes and existential types in a single language yields significant expressive power. We explore this combination in the context of higher-order functional languages with static typing, parametric polymorphism, algebraic data types and Hindley–Milner type inference. Adding existential types to an existing functional language that already features type classes requires only a minor syntactic extension. We first demonstrate how to provide existential quantification over type classes by extending the syntax of algebraic data type definitions, and give examples of possible uses. We then develop a type system and a type inference algorithm for the resulting language. Finally, we present a formal semantics by translation to an implicitly-typed second-order λ-calculus and show that the type system is semantically sound. Our extension has been implemented in the Chalmers Haskell B. system, and all examples from this paper have been developed using this system.