We unify previous work on the continuation-passing style (CPS) transformations in a generic framework based on Moggi's computational meta-language. This framework is used to obtain CPS transformations for a variety of evaluation strategies and to characterize the corresponding administrative reductions and inverse transformations. We establish generic formal connections between operational semantics and equational theories. Formal properties of transformations for specific evaluation orders follow as corollaries. Essentially, we factor transformations through Moggi's computational meta-language. Mapping -terms into the meta-language captures computational properties (e.g., partiality, strictness) and evaluation order explicitly in both the term and the type structure of the meta-language. The CPS transformation is then obtained by applying a generic transformation from terms and types in the meta-language to CPS terms and types, based on a typed term representation of the continuation ...

We define a partial continuation as the difference of two continuations. We exhibit, in a single framework, several design choices and their impact on semantics. The ability of partial continuations to manipulate stack frames blurs the nature of dynamic extent; therefore, we introduce a new concept of prefixal extent that characterises the time during which a partial continuation can be reified. We propose two equivalent formal semantics for partial continuations: a context-rewriting system and a cps translation. Two new and realistic examples illustrate both the interest of partial continuations and the expressiveness of our choices.

Abstract. The PCKS-machine is an abstract machine that evaluates parallel functional programs with rst-class continuations. Parallelism is introduced by the construct pcall, which provides a fork-and-join type of parallelism. To the best of our knowledge, the PCKS-machine is the rst implementation of such a language that is proved to have a transparent construct for parallelism: every program using such a construct returns the same result as in the absence of this construct. This machine is also characterised by the non-speculative invocation of continuations whose interest is illustrated in an application. 1

. A method of preserving the sequential semantics in parallel programs with first-class continuations is to invoke continuations non-speculatively. This method, which prevents a continuation from being invoked as long as its invocation can infringe the sequential semantics, reduces parallelism by the severe conditions that it imposes, especially on upward uses. In this paper, we present new conditions for invoking continuations in an upward way and both preserving the sequential semantics and providing parallelism. This new approach is formalised in the PCKS-machine, which is proved to be correct by showing that it has the same observational equivalence theory as the sequential semantics. 1 Introduction The continuation of an expression is the computation that remains to be performed after evaluating this expression [16]. Some programming languages like Scheme [14], or SML of New Jersey [1] provide the user with two facilities to act on the interpreter continuation: the capture and th...

We present an operational semantics for a functional language with rst-class continuations and transparent constructs for parallelism fork and pcall. The sequential semantics of programs with rst-class continuations is preserved when parallel evaluation is allowed, by verifying whether some expressions have returned a value before applying a continuation. These expressions are the ones that are evaluated before this continuation is applied in a left-to-right sequential order. An implementation is proposed using a notion of higher-order continuation that we call metacontinuation. This semantics is costless when rst-class continuations are not used. Several programs also illustrate the programming style that can be adopted in such a language. Keywords: Scheme, parallelism, transparency, continuation, metacontinuation, left expression, operational semantics. 1 Introduction There are essentially two trends to extend a functional language with parallel constructs. On the one...