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.

This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that an intensional hierarchy of computational features such as state, and their fully abstract models, can be captured as violations of the constraints on strategies in the basic functional model. Non-local control flow is shown to fit into this framework as the violation of strong and weak ‘bracketing ’ conditions, related to linear behaviour. The language µPCF (Parigot’s λµ with constants and recursion) is adopted as a simple basis for higher-type, sequential computation with access to the flow of control. A simple operational semantics for both call-by-name and call-by-value evaluation is described. It is shown that dropping the bracketing condition on games models of PCF yields fully abstract models of µPCF.

Abstract. To introduce the republication of “Definitional Interpreters for Higher-Order Programming Languages”, the author recounts the circumstances of its creation, clarifies several obscurities, corrects a few mistakes, and briefly summarizes some more recent developments.

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We investigate call-by-value continuation-passing style transforms that pass two continuations. Altering a single variable in the translation of #-abstraction gives rise to di#erent control operators: first-class continuations; dynamic control; and (depending on a further choice of a variable) either the return statement of C; or Landin's J-operator. In each case there is an associated simple typing. For those constructs that allow upward continuations, the typing is classical, for the others it remains intuitionistic, giving a clean distinction independent of syntactic details. Moreover, those constructs that make the typing classical in the source of the CPS transform break the linearity of continuation use in the target.

. We compare the expressive power of exceptions and continuations when added to a language with local state in the setting of operational semantics. Continuations are shown to be more expressive than exceptions because they can cause a function call to return more than once, whereas exceptions only allow discarding part of the calling context. 1 Introduction Exceptions are part of nearly all modern programming languages, including mainstream ones like Java and C++. Continuations are present only in Scheme and the New Jersey dialect of ML, yet are much more intensely studied by theoreticians and logicians. The relationship between exceptions and continuations is not as widely understood as one would hope, partly because continuations, though in some sense canonical, are more powerful than would at rst appear, and because the control aspect of exceptions can be obscured by intricacies of typing and syntax. We have recently shown that exceptions and continuations, when added to a purely...

. This note introduces Peter Landin's 1965 technical report "A Generalization of Jumps and Labels", which is reprinted in this volume. Its aim is to make that historic paper more accessible to the reader and to help reading it in context. To this end, we explain Landin's control operator J in more contemporary terms, and we recall Burge's solution to a technical problem in Landin's original account. Keywords: J-operator, secd-machine, call/cc, goto, history of programming languages 1. Introduction In the mid-1960's, Peter Landin was exploring functional programming extended with control. Initially, Landin had added the control operator J (for jump) to his language of Applicative Expressions in order to explicate the goto statement from Algol 60 [10]. This general control construct, however, was powerful enough to have independent interest quite beyond the application to Algol: Landin wrote a series of technical reports [11, 12, 13] on functional programming with control, the most si...

. We study the implications for the expressive power of call/cc of upward continuations, specifically the idiom of using a continuation twice. Although such control effects were known to Landin and Reynolds when they invented J and escape, the forebears of call/cc, they still act as a conceptual pitfall for some attempts to reason about continuations. We use this idiom to refute some recent conjectures about equivalences in a language with continuations, but no other effects. This shows that first-class continuations as given by call/cc have greater expressive power than one would expect from goto or exits. Keywords: call/cc, continuations, upward continuations, expressiveness, program equivalence. 1. Introduction You can enter a room once, and yet leave it twice. (Peter Landin) A common informal explanation of continuations is the comparison with forward goto. This is in some sense a very apt simile: forward gotos obviously do not give rise to loops, and continuations, without some ...

We investigate the duality between call-by-name recursion and call-by-value iteration on the -calculi. The duality between call-by-name and call-by-value was first studied by Filinski, and Selinger has studied the category-theoretic duality on the models of the call-by-name -calculus and the call-by-value one. We extend the call-by-name -calculus and the call-by-value one with a fixed-point operator and an iteration operator, respectively. We show that the dual translations constructed by Selinger can be expanded into our extended -calculi, and we also discuss their implications to practical applications.