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Functional Programming in Sublinear Space
"... Abstract. We consider the problem of functional programming with data in external memory, in particular as it appears in sublinear space computation. Writing programs with sublinear space usage often requires one to use special implementation techniques for otherwise easy tasks, e.g. one cannot comp ..."
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Abstract. We consider the problem of functional programming with data in external memory, in particular as it appears in sublinear space computation. Writing programs with sublinear space usage often requires one to use special implementation techniques for otherwise easy tasks, e.g. one cannot compose functions directly for lack of space for the intermediate result, but must instead compute and recompute small parts of the intermediate result on demand. In this paper, we study how the implementation of such techniques can be supported by functional programming languages. Our approach is based on modelling computation by interaction using the Int construction of Joyal, Street & Verity. We derive functional programming constructs from the structure obtained by applying the Int construction to a term model of a given functional language. The thus derived functional language is formulated by means of a type system inspired Baillot & Terui’s Dual Light Affine Logic. We assess its expressiveness by showing that it captures LOGSPACE. 1
A quantum double construction in Rel
, 2010
"... We study bialgebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of ..."
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We study bialgebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of
Partially traced categories
, 1107
"... This paper deals with questions relating to Haghverdiand Scott’s notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every partially traced ..."
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This paper deals with questions relating to Haghverdiand Scott’s notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every partially traced
ComputationbyInteraction with Effects
"... Abstract. A successful approach in the semantics of programming languages is to model programs by interaction dialogues. While dialogues are most often considered abstract mathematical objects, it has also been argued that they are useful for actual computation. A manual implementation of interactio ..."
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Abstract. A successful approach in the semantics of programming languages is to model programs by interaction dialogues. While dialogues are most often considered abstract mathematical objects, it has also been argued that they are useful for actual computation. A manual implementation of interaction dialogues can be complicated, however. To address this issue, we consider a general method for extending a given language with a metalanguage that supports the implementation of dialogues. This method is based on the construction by Dal Lago and the author of the programming language INTML, which applies interaction dialogues to sublinear space computation. We show that only few assumptions on the programming languages are needed to implement a useful INTMLlike metalanguage. We identify a weak variant of the Enriched Effect Calculus (EEC) of Egger, Møgelberg & Simpson as a convenient setting for capturing the structure needed for the construction of the metalanguage. In particular, function types are not needed for the construction and iteration by means of a Conway operator is sufficient. By using EEC we show how computational effects can be accounted for
unknown title
, 2010
"... We study bialgebras and Hopf algebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of bialgebras and Hopf algebras in Rel. In particular, for any group G, we ..."
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We study bialgebras and Hopf algebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of bialgebras and Hopf algebras in Rel. In particular, for any group G, we
TRACED ∗AUTONOMOUS CATEGORIES ARE COMPACT CLOSED
"... (we write A ⊸ B for the internal hom from A to B) equipped with a dualizing object ⊥ [Barr, 1979], and that the trace ..."
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(we write A ⊸ B for the internal hom from A to B) equipped with a dualizing object ⊥ [Barr, 1979], and that the trace
Partially traced categories
"... This paper deals with questions relating to Haghverdi and Scott’s notion of partially traced categories. The main result is a representationtheorem for such categories: we provethat everypartiallytraced categorycan be faithfully embedded in a totally traced category. Also conversely, every symmetric ..."
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This paper deals with questions relating to Haghverdi and Scott’s notion of partially traced categories. The main result is a representationtheorem for such categories: we provethat everypartiallytraced categorycan be faithfully embedded in a totally traced category. Also conversely, every symmetric monoidal subcategory ofatotallytracedcategoryispartiallytraced, sothis characterizesthe partiallytracedcategoriescompletely. The main technique we use is based on Freyd’s paracategories, along with a partial version of Joyal, Street, and Verity’s Intconstruction.
On Interaction, Continuations and Defunctionalization ⋆
"... Abstract. In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used in the design of new compilation methods, e.g. in Ghica’s approach to hardware synthesis, or in joint work with Dal Lago on progra ..."
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Abstract. In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used in the design of new compilation methods, e.g. in Ghica’s approach to hardware synthesis, or in joint work with Dal Lago on programming with sublinear space. This paper relates such semantically motivated nonstandard compilation methods to more standard techniques in the compilation of functional programming languages, such as continuation passing and defunctionalization. We first show for the linear λcalculus that interpretation in a model of computation by interaction can be described as a callbyname CPS transformation followed by a defunctionalization procedure that takes into account controlflow information. We then use the interactive model to guide the extension of the compositional translation to source languages with full contraction and recursion. 1
Operational Theories and Categorical Quantum Mechanics
, 2013
"... A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative ..."
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A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative theories. Two formalisms which have been used in this context are operational theories, and categorical quantum mechanics. The aim of the present paper is to establish strong connections between these two formalisms. We show how models of categorical quantum mechanics have representations as operational theories. We then show how nonlocality can be formulated at this level of generality, and study a number of examples from this point of view, including Hilbert spaces, sets and relations, and stochastic maps. The local, quantum, and nosignalling models are characterized in these terms. 1