An Operational Foundation for Delimited Continuations

We derive an abstract machine that corresponds to a definitional interpreter for the control operators shift and reset. Based on this abstract machine, we construct a syntactic theory of delimited continuations. Both the derivation and the construction scale to the family of control operators shift_n and reset_n. The definitional interpreter for shift_n and reset_n has n + 1 layers of continuations, the corresponding abstract machine has n + 1 layers of control stacks, and the corresponding syntactic theory has n + 1 layers of evaluation contexts.See also BRICS-RS-05-24

Bisimulations for Delimited-Control Operators

We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to characterize with coinductively defined relations, called bisimilarities. We consider different styles of bisimilarities (namely applicative, normal-form, and environmental) within a unifying framework, and we give several examples to illustrate their respective strengths and weaknesses. We also discuss how to extend this work to other delimited-control operators

From delimited CPS to polarisation

Appeared in the author's PhD thesis (Chapter III) along with more details. See (and cite) Guillaume Munch-Maccagnoni, Syntax and Models of a non-Associative Composition of Programs and Proofs, Université Paris-Diderot - Paris VII, 2013, .The understanding of continuation-passing style (CPS) translations, an historical source of denotational semantics for programming languages, benefits from notions brought by linear logic, such as focalisation, polarities and the involutive negation. Here we aim to show how linear logic helps as well when continuations are delimited, i.e. return and can be composed, in the sense of Danvy and Filinski. First we provide a polarised calculus with delimited control (first-class delimited continuations) which is, at the level of computation, a variant of Girard's polarised classical logic LC. It contains variants of delimited control calculi which spawned as answers to the question "what order of evaluation can we consider with delimited control?". Thus our polarised calculus is one answer which is unifying to some degree. Subsequently we decompose the calculus through polarised linear logic. The only difference with non-delimited continuations is the use of specific exponentials, that account for the specific semantics of the target of delimited CPS translation, as well as annotations of type-and-effect systems. As a by-product, we obtain an explanation of CPS translations through a factoring, each step of which accounts for distinct phenomena of CPS translations. Although the factoring also holds for non-delimited CPS translations, it did not appear in its entirety before

A Rational Deconstruction of Landin's SECD Machine

Landin's SECD machine was the first abstract machine for the lambda-calculus viewed as a programming language. Both theoretically as a model of computation and practically as an idealized implementation, it has set the tone for the subsequent development of abstract machines for functional programming languages. However, and even though variants of the SECD machine have been presented, derived, and invented, the precise rationale for its architecture and modus operandi has remained elusive. In this article, we deconstruct the SECD machine into a lambda-interpreter, i.e., an evaluation function, and we reconstruct lambda-interpreters into a variety of SECD-like machines. The deconstruction and reconstructions are transformational: they are based on equational reasoning and on a combination of simple program transformations--mainly closure conversion, transformation into continuation-passing style, and defunctionalization. The evaluation function underlying the SECD machine provides a precise rationale for its architecture: it is an environment-based eval-apply evaluator with a callee-save strategy for the environment, a data stack of intermediate results, and a control delimiter. Each of the components of the SECD machine (stack, environment, control, and dump) is therefore rationalized and so are its transitions. The deconstruction and reconstruction method also applies to other abstract machines and other evaluation functions. It makes it possible to systematically extract the denotational content of an abstract machine in the form of a compositional evaluation function, and the (small-step) operational content of an evaluation function in the form of an abstract machine

A Survey of Languages for Specifying Dynamics: A Knowledge Engineering Perspective

A number of formal specification languages for knowledge-based systems has been developed. Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Specification languages for knowledge-based systems have to cover both aspects. They have to provide the means to specify a complex and large amount of knowledge and they have to provide the means to specify the dynamic reasoning behavior of a knowledge-based system. We focus on the second aspect. For this purpose, we survey existing approaches for specifying dynamic behavior in related areas of research. In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (Transaction Logic and Dynamic Database Logic) and the generic specification framework of abstract state machine

Relating Justification Logic Modality and Type Theory in Curry–Howard Fashion

This dissertation is a work in the intersection of Justification Logic and Curry--Howard Isomorphism. Justification logic is an umbrella of modal logics of knowledge with explicit evidence. Justification logics have been used to tackle traditional problems in proof theory (in relation to Godel\u27s provability) and philosophy (Gettier examples, Russel\u27s barn paradox). The Curry--Howard Isomorphism or proofs-as-programs is an understanding of logic that places logical studies in conjunction with type theory and -- in current developments -- category theory. The point being that understanding a system as a logic, a typed calculus and, a language of a class of categories constitutes a useful discovery that can have many applications. The applications we will be mainly concerned with are type systems for useful programming language constructs. This work is structured in three parts: The first part is a a bird\u27s eye view into my research topics: intuitionistic logic, justified modality and type theory. The relevant systems are introduced syntactically together with main metatheoretic proof techniques which will be useful in the rest of the thesis. The second part features my main contributions. I will propose a modal type system that extends simple type theory (or, isomorphically, intuitionistic propositional logic) with elements of justification logic and will argue about its computational significance. More specifically, I will show that the obtained calculus characterizes certain computational phenomena related to linking (e.g. module mechanisms, foreign function interfaces) that abound in semantics of modern programming languages. I will present full metatheoretic results obtained for this logic/ calculus utilizing techniques from the first part and will provide proofs in the Appendix. The Appendix contains also information about an implementation of our calculus in the metaprogramming framework Makam. Finally, I conclude this work with a small ``outro\u27\u27, where I informally show that the ideas underlying my contributions can be extended in interesting ways