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

The Damas-Milner Calculus is the typed -calculus underlying the type system for ML and several other strongly typed polymorphic functional languages such as Miranda 1 and Haskell. Mycroft has extended its problematic monomorphic typing rule for recursive definitions with a polymorphic typing rule. He proved the resulting type system, which we call the Milner-Mycroft Calculus, sound with respect to Milner's semantics, and showed that it preserves the principal typing property of the Damas-Milner Calculus. The extension is of practical significance in typed logic programming languages and, more generally, in any language with (mutually) recursive definitions. In this paper we show that the type inference problem for the Milner-Mycroft Calculus is log-space equivalent to semi-unification, the problem of solving subsumption inequations between first-order terms. This result has been proved independently by Kfoury, Tiuryn, and Urzyczyn. In connection with the recently establish...

This thesis introduces the programming language Guarded Horn Clauses which is abbreviated to GHC. Guarded Horn Clauses was born from the examination of existing logic programming languages and logic programming in general, with special attention paid to parallelism. The main feature of

We propose regular expression pattern matching as a core feature of programming languages for manipulating XML. We extend conventional pattern-matching facilities (as in ML) with regular expression operators such as repetition (*), alternation (|), etc., that can match arbitrarily long sequences of subtrees, allowing a compact pattern to extract data from the middle of a complex sequence. We then show how to check standard notions of exhaustiveness and redundancy for these patterns. Regular expression patterns are intended to be used in languages with type systems based on regular expression types. To avoid excessive type annotations, we develop a type inference scheme that propagates type constraints to pattern variables from the type of input values. The type inference algorithm translates types and patterns into regular tree automata, and then works in terms of standard closure operations (union, intersection, and difference) on tree automata. The main technical challenge is dealing with the interaction of repetition and alternation patterns with the first-match policy, which gives rise to subtleties concerning both the termination and precision of the analysis. We address these issues by introducing a data structure representing these closure operations

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 present a higher-order calculus ECC which can be seen as an extension of the calculus of constructions [CH88] by adding strong sum types and a fully cumulative type hierarchy. ECC turns out to be rather expressive so that mathematical theories can be abstractly described and abstract mathematics may be adequately formalized. It is shown that ECC is strongly normalizing and has other nice proof-theoretic properties. An !\GammaSet (realizability) model is described to show how the essential properties of the calculus can be captured set-theoretically.

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Concurrent Clean is an experimental, lazy, higher-order parallel functional programming language based on term graph rewriting. An important difference with other languages is that in Clean graphs are manipulated and not terms. This can be used by the programmer to control communication and sharing of computation. Cyclic structures can be defined. Concurrent Clean furthermore allows to control the (parallel) order of evaluation to make efficient evaluation possible. With help of sequential annotations the default lazy evaluation can be locally changed into eager evaluation. The language enables the definition of partially strict data structures which make a whole new class of algorithms feasible in a functional language. A powerful and fast strictness analyser is incorporated in the system. The quality of the code generated by the Clean compiler has been greatly improved such that it is one of the best code generators for a lazy functional language. Two very powerful parall...

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Extended ML is a framework for the formal development of programs in the Standard ML programming language from high-level specifications of their required input/output behaviour. It strongly supports the development of modular programs consisting of an interconnected collection of generic and reusable units. The Extended ML framework includes a methodology for formal program development which establishes a number of ways of proceeding from a given specification of a programming task towards a program. Each such step gives rise to one or more proof obligations which must be proved in order to establish the correctness of that step. This paper is intended as a user-oriented summary of the Extended ML language and methodology. Theoretical technicalities are avoided whenever possible, with emphasis placed on the practical aspects of formal program development. An extended example of a complete program development in Extended ML is included.