Abstract. Landin’s SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin’s J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continuation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke’s doublebarrelled continuations and to Felleisen’s encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions

Dynamic binding and delimited control are useful together in many settings, including Web applications, database cursors, and mobile code. We examine this pair of language features to show that the semantics of their interaction is ill-defined yet not expressive enough for these uses. We solve this open and subtle problem. We formalise a typed language DB+DC that combines a calculus DB of dynamic binding and a calculus DC of delimited control. We argue from theoretical and practical points of view that its semantics should be based on delimited dynamic binding: capturing a delimited continuation closes over part of the dynamic environment, rather than all or none of it; reinstating the captured continuation supplements the dynamic environment, rather than replacing or inheriting it. We introduce a type- and reduction-preserving translation from DB + DC to DC, which proves that delimited control macro-expresses dynamic binding. We use this translation to implement DB + DC in Scheme, OCaml, and Haskell. We extend DB + DC with mutable dynamic variables and a facility to obtain not only the latest binding of a dynamic variable but also older bindings. This facility provides for stack inspection and (more generally) folding over the execution context as an inductive data structure.

Abstract not found

Abstract not found

Abstract not found

Abstract. There is a correspondence between classical logic and programming language calculi with first-class continuations. With the addition of control delimiters, the continuations become composable and the calculi become more expressive. We present a fine-grained analysis of control delimiters and formalise that their addition corresponds to the addition of a single dynamically-scoped variable modelling the special top-level continuation. From a type perspective, the dynamically-scoped variable requires effect annotations. In the presence of control, the dynamically-scoped variable can be interpreted in a purely functional way by applying a store-passing style. At the type level, the effect annotations are mapped within standard classical logic extended with the dual of implication, namely subtraction. A continuation-passing-style transformation of lambda-calculus with control and subtraction is defined. Combining the translations provides a decomposition of standard CPS transformations for delimited continuations. Incidentally, we also give a direct normalisation proof of the simply-typed lambda-calculus with control and subtraction.

Abstract. We propose a semantic framework for modelling the linear usage of continuations in typed call-by-name programming languages. On the semantic side, we introduce a construction for categories of linear continuations, which gives rise to cartesian closed categories with “linear classical disjunctions ” from models of intuitionistic linear logic with sums. On the syntactic side, we give a simply typed call-by-name λµcalculus in which the use of names (continuation variables) is restricted to be linear. Its semantic interpretation into a category of linear continuations then amounts to the call-by-name continuation-passing style (CPS) transformation into a linear lambda calculus with sum types. We show that our calculus is sound for this CPS semantics, hence for models given by the categories of linear continuations.

In “Functional Unparsing ” (JFP 8(6): 621–625, 1998), Danvy presented a type-safe printf function using continuations and an accumulator to achieve the effect of dependent types. The key technique employed in Danvy’s solution is the non-standard use of continuations: not all of its calls are tail calls, i.e., it uses delimited continuations. Against this backdrop, we present three new solutions to the printf problem: a simpler one that also uses delimited continuations but that does not use an accumulator, and the corresponding two in direct style with the delimited-control operators, shift and reset. These two solutions are the direct-style counterparts of the two continuation-based ones. The last solution pinpoints the essence of Danvy’s solution: shift is used to change the answer type of delimited continuations. Besides providing a new application of shift and reset, the solutions in direct style raise a key issue in the typing of first-class delimited continuations and require Danvy and Filinski’s original type system. The resulting types precisely account for the behavior of printf. This is the extended version of the previous technical report OCHA-IS 07-1. It contains an introduction to continuation-passing style and delimited-control operators, shift and reset.

Abstract. We study the dynamic control operators for delimited continuations, control and prompt. Based on recent developments on purely functional CPS translations for them, we introduce a polymorphically typed calculus for these control operators which allows answer-type modification. We show that our calculus enjoys type soundness and is compatible with the CPS translation. We also show that the typed dynamic control operators can macro-express the typed static ones (shift and reset), while the converse direction is not possible, which exhibits a sharp contrast with the type-free case.

Abstract: Logical relations, defined inductively on the structure of types, provide a powerful tool to characterize higher-order functions. They often enable us to prove correctness of a program transformer written with higher-order functions concisely. This paper demonstrates that the technique of logical relations can be used to characterize call-by-value functions as well as delimited continuations. Based on the traditional logical relations for call-by-name functions, logical relations for call-by-value functions are first defined, whose CPS variant is used to prove the correctness of an offline specializer for the call-by-value λcalculus. They are then modified to cope with delimited continuations and are used to establish the correctness of an offline specializer for the call-by-value λcalculus with delimited continuation constructs, shift and reset. This is the first correctness proof for such a specializer. Along the development, correctness of the continuation-based and shift/reset-based let-insertion and A-normalization is established.