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Typing control operators in the CPS hierarchy
 13th ACMSIGPLAN International Conference on Principles and Practice of Declarative Programming (PPDP’11
, 2011
"... Abstract The CPS hierarchy of Danvy and Filinski is a hierarchy of continuations that allows for expressing nested control effects characteristic of, e.g., nondeterministic programming or certain instances of normalization by evaluation. In this article, we present a comprehensive study of a typed ..."
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Abstract The CPS hierarchy of Danvy and Filinski is a hierarchy of continuations that allows for expressing nested control effects characteristic of, e.g., nondeterministic programming or certain instances of normalization by evaluation. In this article, we present a comprehensive study of a typed version of the CPS hierarchy, where the typing discipline generalizes Danvy and Filinski's type system for control operators shift and reset. To this end, we define a typed family of control operators that give access to delimited continuations in the CPS hierarchy and that are slightly more flexible than Danvy and Filinski's family of control operators shifti and reseti, but, as we show, are equally expressive. For this type system, we prove subject reduction, soundness with respect to the CPS translation, and termination of evaluation. We also show that our results scale to a type system for even more flexible control operators expressible in the CPS hierarchy.
Fractional Types
"... Abstract. In previous work, we developed a firstorder, informationpreserving, and reversible programming language Π founded on type isomorphisms. Being restricted to firstorder types limits the expressiveness of the language: it is not possible, for example, to abstract common program fragments in ..."
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Abstract. In previous work, we developed a firstorder, informationpreserving, and reversible programming language Π founded on type isomorphisms. Being restricted to firstorder types limits the expressiveness of the language: it is not possible, for example, to abstract common program fragments into a higherlevel combinator. In this paper, we introduce a higherorder extension of Π based on the novel concept of fractional types 1/b. Intuitively, a value of a fractional type 1/v represents negative information. A function is modeled by a pair (1/v1, v2) with 1/v1 representing the needed argument and v2 representing the result. Fractional values are firstclass: they can be freely propagated and transformed but must ultimately — in a complete program — be offset by the corresponding amount of positive information. 1
Compressing Polarized Boxes
"... Abstract—The sequential nature of sequent calculus provides a simple definition of cutelimination rules that duplicate or erase subproofs. The parallel nature of proof nets, instead, requires the introduction of explicit boxes, which are global and synchronous constraints on the structure of graph ..."
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Abstract—The sequential nature of sequent calculus provides a simple definition of cutelimination rules that duplicate or erase subproofs. The parallel nature of proof nets, instead, requires the introduction of explicit boxes, which are global and synchronous constraints on the structure of graphs. We show that logical polarity can be exploited to obtain an implicit, compact, and natural representation of boxes: in an expressive polarized dialect of linear logic, boxes may be represented by simply recording some of the polarity changes occurring in the box at level 0. The content of the box can then be recovered locally and unambiguously. Moreover, implicit boxes are more parallel than explicit boxes, as they realize a larger quotient. We provide a correctness criterion and study the novel and subtle cutelimination dynamics induced by implicit boxes, proving confluence and strong normalization.
Delimited Control
, 2010
"... par Danko ILI ´K Titre de la thèse: Preuves constructives de complétude et contrôle délimité Soutenue le 22 octobre 2010 devant le jury composé de: M. Hugo HERBELIN Directeur de thèse ..."
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par Danko ILI ´K Titre de la thèse: Preuves constructives de complétude et contrôle délimité Soutenue le 22 octobre 2010 devant le jury composé de: M. Hugo HERBELIN Directeur de thèse