Abstract. Higher-order programming languages (i.e., languages in which procedures or labels can occur as values) are usually defined by interpreters that are themselves written in a programming language based on the lambda calculus (i.e., an applicative language such as pure LISP). Examples include McCarthy’s definition of LISP, Landin’s SECD machine, the Vienna definition of PL/I, Reynolds ’ definitions of GEDANKEN, and recent unpublished work by L. Morris and C. Wadsworth. Such definitions can be classified according to whether the interpreter contains higher-order functions, and whether the order of application (i.e., call by value versus call by name) in the defined language depends upon the order of application in the defining language. As an example, we consider the definition of a simple applicative programming language by means of an interpreter written in a similar language. Definitions in each of the above classifications are derived from one another by informal but constructive methods. The treatment of imperative features such as jumps and assignment is also discussed.

An extension of ML with continuation primitives similar to those found in Scheme is considered. A number of alternative type systems are discussed, and several programming examples are given. A continuation-based operational semantics is defined for a small, purely functional, language, and the soundness of the Damas-Milner polymorphic type assignment system with respect to this semantics is proved. The full Damas-Milner type system is shown to be unsound in the presence of first-class continuations. Restrictions on polymorphism similar to those introduced in connection with reference types are shown to suffice for soundness. 1 Introduction First-class continuations are a simple and natural way to provide access to the flow of evaluation in functional languages. The ability to seize the "current continuation" (control state of the evaluator) provides a simple and natural basis for defining numerous higher-level constructs such as coroutines [22], exceptions [41], and logic variables [...

The original aim of the work that led to this dissertation was to extend an existing, purely functional language with facilities for input/output and modular programming. The language is based on an untyped -calculus, i.e., program execution is defined as program transformation according to a fixed set of reduction rules including fi-reduction. Consistently, the implementation comprises an interactive reduction system which is integrated with a syntax-oriented editor: any sub-expression or program result can be submitted for (stepwise) reduction. There is no distinguished main program, no `global' environment and no explicit static part of the language -- in particular, there is no static type system. It is therefore not clear how to add one of the known solutions for input/output or modular programming to such a programming environment. Furthermore, simply adding features to the language would lead to a complex language design with weakly integrated parts, thus losing much of the appe...