Formalizing Implementation Strategies for First-Class Continuations

We present the first formalization of implementation strategies for first-class continuations. The formalization hinges on abstractmachines for continuation-passing style (CPS) programs with a specialtreatment for the current continuation, accounting for the essence offirst-class continuations. These abstract machines are proven equivalentto a standard, substitution-based abstract machine. The proof techniqueswork uniformly for various representations of continuations. As a byproduct, we also present a formal proof of the two folklore theorems that onecontinuation identifier is enough for second-class continuations and thatsecond-class continuations are stackable.A large body of work exists on implementing continuations, but it is predominantly empirical and implementation-oriented. In contrast, our formalization abstracts the essence of first-class continuations and providesa uniform setting for specifying and formalizing their representation

A Dynamic Continuation-Passing Style for Dynamic Delimited Continuations (Preliminary Version)

We present a new abstract machine that accounts for dynamic delimited continuations. We prove the correctness of this new abstract machine with respect to a definitional abstract machine. Unlike this definitional abstract machine, the new abstract machine is in defunctionalized form, which makes it possible to state the corresponding higher-order evaluator. This evaluator is in continuation+state passing style, and threads a trail of delimited continuations and a meta-continuation. Since this style accounts for dynamic delimited continuations, we refer to it as `dynamic continuation-passing style.' We illustrate that the new machine is more efficient than the definitional one, and we show that the notion of computation induced by the corresponding evaluator takes the form of a monad

A Dynamic Continuation-Passing Style for Dynamic Delimited Continuations

We present a new abstract machine that accounts for dynamic delimited continuations. We prove the correctness of this new abstract machine with respect to a pre-existing, definitional abstract machine. Unlike this definitional abstract machine, the new abstract machine is in defunctionalized form, which makes it possible to state the corresponding higher-order evaluator. This evaluator is in continuation+state passing style and threads a trail of delimited continuations and a meta-continuation. Since this style accounts for dynamic delimited continuations, we refer to it as `dynamic continuation-passing style.' We show that the new machine operates more efficiently than the definitional one and that the notion of computation induced by the corresponding evaluator takes the form of a monad. We also present new examples and a new simulation of dynamic delimited continuations in terms of static ones

An Analytical Approach to Programs as Data Objects

This essay accompanies a selection of 32 articles (referred to in bold face in the text and marginally marked in the bibliographic references) submitted to Aarhus University towards a Doctor Scientiarum degree in Computer Science.The author's previous academic degree, beyond a doctoral degree in June 1986, is an "Habilitation à diriger les recherches" from the Université Pierre et Marie Curie (Paris VI) in France; the corresponding material was submitted in September 1992 and the degree was obtained in January 1993.The present 32 articles have all been written since 1993 and while at DAIMI.Except for one other PhD student, all co-authors are or have been the author's students here in Aarhus

On Computational Small Steps and Big Steps: Refocusing for Outermost Reduction

We study the relationship between small-step semantics, big-step semantics and abstract machines, for programming languages that employ an outermost reduction strategy, i.e., languages where reductions near the root of the abstract syntax tree are performed before reductions near the leaves.In particular, we investigate how Biernacka and Danvy's syntactic correspondence and Reynolds's functional correspondence can be applied to inter-derive semantic specifications for such languages.The main contribution of this dissertation is three-fold:First, we identify that backward overlapping reduction rules in the small-step semantics cause the refocusing step of the syntactic correspondence to be inapplicable.Second, we propose two solutions to overcome this in-applicability: backtracking and rule generalization.Third, we show how these solutions affect the other transformations of the two correspondences.Other contributions include the application of the syntactic and functional correspondences to Boolean normalization.In particular, we show how to systematically derive a spectrum of normalization functions for negational and conjunctive normalization

Formalizing Implementation Strategies for First-Class Continuations

We present the first formalization of implementation strategies for first-class continuations. The formalization hinges on abstractmachines for continuation-passing style (CPS) programs with a specialtreatment for the current continuation, accounting for the essence offirst-class continuations. These abstract machines are proven equivalentto a standard, substitution-based abstract machine. The proof techniqueswork uniformly for various representations of continuations. As a byproduct, we also present a formal proof of the two folklore theorems that onecontinuation identifier is enough for second-class continuations and thatsecond-class continuations are stackable.A large body of work exists on implementing continuations, but it is predominantly empirical and implementation-oriented. In contrast, our formalization abstracts the essence of first-class continuations and providesa uniform setting for specifying and formalizing their representation

Formalizing implementation strategies for first-class continuations

Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRIC