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A Concurrent Model for Linear Logic
"... We build a realizability model for linear logic using a namepassing process calculus. The construction is based on testing semantics for processes, drawing ideas from spatial and modal logics, and yields a new type system for process calculi that ensures termination while allowing significantly con ..."
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Cited by 16 (3 self)
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We build a realizability model for linear logic using a namepassing process calculus. The construction is based on testing semantics for processes, drawing ideas from spatial and modal logics, and yields a new type system for process calculi that ensures termination while allowing significantly concurrent behaviours. Then we study how embeddings of intuitionistic and classical logics into linear logic induce typed translations of λ and λµ calculi in which new concurrent instructions can be introduced, thus sketching the basis for a CurryHoward interpretation of linear and classical proofs in terms of concurrent interaction.
Sequentiality vs. Concurrency in Games and Logic
 Math. Structures Comput. Sci
, 2001
"... Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic. ..."
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Cited by 14 (0 self)
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Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.
Relating StateBased and ProcessBased Concurrency through Linear Logic
, 2006
"... This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, mu ..."
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Cited by 12 (1 self)
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This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the wellestablished statetransformation model inspired to Petri nets and multiset rewriting, and the prolific processbased models such as the πcalculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic. In the second part of the paper, we propose a completely new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic. The resulting interpretation is extended with a majority of linear connectives into the language of ωmultisets. This interpretation drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication, and more. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. For example, a simple translation maps process constructors of the asynchronous πcalculus to rewrite operators, while the structural equivalence corresponds directly to logicallymotivated structural properties of ωmultisets (with one exception).
A logic of events
, 2003
"... There is a wellestablished theory and practice for creating correctbyconstruction functional programs by extracting them from constructive proofs of assertions of the form ∀x: A.∃y: B.R(x, y). There have been several efforts to extend this methodology to concurrent programs, say by using linear l ..."
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Cited by 11 (7 self)
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There is a wellestablished theory and practice for creating correctbyconstruction functional programs by extracting them from constructive proofs of assertions of the form ∀x: A.∃y: B.R(x, y). There have been several efforts to extend this methodology to concurrent programs, say by using linear logic, but there is no practice and the results are limited. In this paper we define a logic of events that justifies the extraction of correct distributed processes from constructive proofs that system specifications are achievable, and we describe an implementation of an extraction process in the context of constructive type theory. We show that a class of message automata, similar to IO automata and to active objects, are realizers for this logic. We provide a relative consistency result for the logic. We show an example of protocol derivation in this logic, and show how to embed temporal logics such as T LA+ in the event logic. 1
Computability structures, simulations and realizability
, 2011
"... We generalize the standard construction of realizability models (specifically, of categories of assemblies) to a very wide class of computability structures, broad enough to embrace models of computation such as labelled transition systems and process algebras. We also discuss a general notion of si ..."
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We generalize the standard construction of realizability models (specifically, of categories of assemblies) to a very wide class of computability structures, broad enough to embrace models of computation such as labelled transition systems and process algebras. We also discuss a general notion of simulation between such computability structures, and show that such simulations correspond precisely to certain functors between the realizability models. Furthermore, we show that our class of computability structures has good closure properties — in particular, it is ‘cartesian closed ’ in a slightly relaxed sense. We also investigate some important subclasses of computability structures and of simulations between them. We suggest that our 2category of computability structures and simulations may offer a framework for a general investigation of questions of computational power, abstraction and simulability for a wide range of computation models from across computer science.
through Linear Logic
"... This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, mu ..."
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This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the wellestablished statetransformation model inspired by Petri nets and multiset rewriting, and the prolific processbased models such as the πcalculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic and observe that, possibly modulo duality, they invariably target a small semantic fragment of linear logic that we call LV obs. In the second part of the paper, we propose a new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of
A Causal Logic of Events in Formalized Computational Type Theory ∗
"... We provide a logic for distributed computing that has the explanatory and technical power of constructive logics of computation. In particular, we establish a proof technology that supports correctbyconstruction programming based on the notion that concurrent processes can be extracted from proofs ..."
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We provide a logic for distributed computing that has the explanatory and technical power of constructive logics of computation. In particular, we establish a proof technology that supports correctbyconstruction programming based on the notion that concurrent processes can be extracted from proofs that specifications are achievable. 1
Published In Relating StateBased and ProcessBased Concurrency through Linear Logic
"... This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, mu ..."
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This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the wellestablished statetransformation model inspired by Petri nets and multiset rewriting, and the prolific processbased models such as the picalculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic and observe that, possibly modulo duality, they invariably target a small semantic fragment of linear logic that we call LVobs. In the second part of the paper, we propose a new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of