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of LISP, Landin’s SECD machine, the Vienna definition of PL/I, Reynolds ’ definitions of GEDANKEN, and recent unpublished work by L. Morris and C. Wadsworth.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.

We give a brief account of the discoveries of continuations and related concepts by, A. Van Wijngaarden , A. W. Mazurkiewicz , F. L. Morris , C. P. Wadsworth , J. H. Morris , M. J. Fischer , and S. K. Abdali.

A lambda-calculus schema is an expression of the lambda calculus augmented by uninterpreted constant and operator symbols. It is an abstraction of programming languages such as LISP which permit functions to be passed to and returned from other functions. When given an interpretation for its constant and operator symbols, certain schemata, called lambda abstractions, naturally define partial functions over the domain of interpretation. Two implementation strategies are considered: the retention strategy in which all variable bindings are retained until no longer needed (implying the use of some sort of garbage-collected store) and the deletion strategy, modeled after the usual stack implementation of ALGOL 60, in which variable bindings are destroyed when control leaves the procedure (or block) in which they were created. Not all lambda abstractions evaluate correctly under the deletion strategy. Nevertheless, both strategies are equally powerful in the sense that any lambda abstraction can be mechanically translated into another that evaluates correctly under the deletion strategy and defines the same partial function over the domain of interpretation as the original. Proof is by translation into continuation-passing style.

The last few years have seen a renewed interest in continuations for expressing advanced control structures in programming languages, and new models such as Abstract Continuations have been proposed to capture these dimensions. This article investigates an alternative formulation, exploiting the latent expressive power of the standard continuation-passing style (CPS) instead of introducing yet other new concepts. We build on a single foundation: abstracting control as a hierarchy of continuations, each one modeling a specific language feature as acting on nested evaluation contexts. We show how iterating the continuation-passing conversion allows us to specify a wide range of control behavior. For example, two conversions yield an abstraction of Prologstyle backtracking. A number of other constructs can likewise be expressed i...

Functional programs are organized into procedures, each encapsulating a specific task. A procedure should not cause its callers to repeat its work. This forced repetition of work we call leakage. In this paper we describe several common instances of leakage, and show how they can be eliminated using an extension of continuation-passing style. 1 Introduction A goal of programming is to divide a complex task into simpler parts. In a well organized program each of these simpler tasks is represented by a procedure. Each procedure should perform a distinct action. Its user should not have to be conscious about the details of its implementation and should not have to undo or repeat work performed by it. This excess interaction between procedures is called leakage. When leakage is eliminated, the clarity and correctness of programs is enhanced. Our goal in this paper is to show how some leakage can be removed by using a generalization of continuation-passing style. We emphasize the developm...