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Relevant bibliographies by topics / Linear logic; Functional programming; Nets

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Academic literature on the topic 'Linear logic; Functional programming; Nets'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Linear logic; Functional programming; Nets"

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PERRIER, G. "Concurrent programming as proof net construction." Mathematical Structures in Computer Science 8, no. 6 (December 1998): 681–710. http://dx.doi.org/10.1017/s0960129598002655.

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We propose a concurrent process calculus, called Calcul Parallèle Logique (CPL), based on the paradigm of computation as proof net construction in linear logic. CPL uses a fragment of first-order intuitionistic linear logic where formulas represent processes and proof nets represent successful computations. In these computations, communication is expressed in an asynchronous way by means of axiom links. We define testing equivalences for processes, which are based on a concept of interface, and use the power of proof theory in linear logic.

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Danos, Vincent, Jean-Baptiste Joinet, and Harold Schellinx. "A new deconstructive logic: linear logic." Journal of Symbolic Logic 62, no. 3 (September 1997): 755–807. http://dx.doi.org/10.2307/2275572.

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AbstractThe main concern of this paper is the design of a noetherian and confluent normalization for LK2 (that is, classical second order predicate logic presented as a sequent calculus).The method we present is powerful: since it allows us to recover as fragments formalisms as seemingly different as Girard's LC and Parigot's λμ, FD ([10, 12, 32, 36]), delineates other viable systems as well, and gives means to extend the Krivine/Leivant paradigm of ‘programming-with-proofs’ ([26, 27]) to classical logic; it is painless: since we reduce strong normalization and confluence to the same properties for linear logic (for non-additive proof nets, to be precise) using appropriate embeddings (so-called decorations); it is unifying: it organizes known solutions in a simple pattern that makes apparent the how and why of their making.A comparison of our method to that of embedding LK into LJ (intuitionistic sequent calculus) brings to the fore the latter's defects for these ‘deconstructive purposes’.

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Mackie, Ian. "Lilac: a functional programming language based on linear logic." Journal of Functional Programming 4, no. 4 (October 1994): 395–433. http://dx.doi.org/10.1017/s0956796800001131.

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AbstractWe take Abramsky's term assignment for Intuitionistic Linear Logic (the linear term calculus) as the basis of a functional programming language. This is a language where the programmer must embed explicitly the resource and control information of an algorithm. We give a type reconstruction algorithm for our language in the style of Milner's W algorithm, together with a description of the implementation and examples of use.

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Qian, Zesen, G. A. Kavvos, and Lars Birkedal. "Client-server sessions in linear logic." Proceedings of the ACM on Programming Languages 5, ICFP (August 22, 2021): 1–31. http://dx.doi.org/10.1145/3473567.

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We introduce coexponentials, a new set of modalities for Classical Linear Logic. As duals to exponentials, the coexponentials codify a distributed form of the structural rules of weakening and contraction. This makes them a suitable logical device for encapsulating the pattern of a server receiving requests from an arbitrary number of clients on a single channel. Guided by this intuition we formulate a system of session types based on Classical Linear Logic with coexponentials, which is suited to modelling client-server interactions. We also present a session-typed functional programming language for client-server programming, which we translate to our system of coexponentials.

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BOZZANO, MARCO, GIORGIO DELZANNO, and MAURIZIO MARTELLI. "An effective fixpoint semantics for linear logic programs." Theory and Practice of Logic Programming 2, no. 1 (December 18, 2001): 85–122. http://dx.doi.org/10.1017/s1471068402001254.

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In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of TP working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming (Minker et al., 1991). Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete (Cousot & Cousot, 1977; Giacobazzi & Ranzato, 1997) for an interesting class of LO programs encoding Petri Nets.

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Jeltsch, Wolfgang. "Towards a Common Categorical Semantics for Linear-Time Temporal Logic and Functional Reactive Programming." Electronic Notes in Theoretical Computer Science 286 (September 2012): 229–42. http://dx.doi.org/10.1016/j.entcs.2012.08.015.

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HUET, GÉRARD. "Special issue on ‘Logical frameworks and metalanguages’." Journal of Functional Programming 13, no. 2 (March 2003): 257–60. http://dx.doi.org/10.1017/s0956796802004549.

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There is both a great unity and a great diversity in presentations of logic. The diversity is staggering indeed – propositional logic, first-order logic, higher-order logic belong to one classification; linear logic, intuitionistic logic, classical logic, modal and temporal logics belong to another one. Logical deduction may be presented as a Hilbert style of combinators, as a natural deduction system, as sequent calculus, as proof nets of one variety or other, etc. Logic, originally a field of philosophy, turned into algebra with Boole, and more generally into meta-mathematics with Frege and Heyting. Professional logicians such as Gödel and later Tarski studied mathematical models, consistency and completeness, computability and complexity issues, set theory and foundations, etc. Logic became a very technical area of mathematical research in the last half century, with fine-grained analysis of expressiveness of subtheories of arithmetic or set theory, detailed analysis of well-foundedness through ordinal notations, logical complexity, etc. Meanwhile, computer modelling developed a need for concrete uses of logic, first for the design of computer circuits, then more widely for increasing the reliability of sofware through the use of formal specifications and proofs of correctness of computer programs. This gave rise to more exotic logics, such as dynamic logic, Hoare-style logic of axiomatic semantics, logics of partial values (such as Scott's denotational semantics and Plotkin's domain theory) or of partial terms (such as Feferman's free logic), etc. The first actual attempts at mechanisation of logical reasoning through the resolution principle (automated theorem proving) had been disappointing, but their shortcomings gave rise to a considerable body of research, developing detailed knowledge about equational reasoning through canonical simplification (rewriting theory) and proofs by induction (following Boyer and Moore successful integration of primitive recursive arithmetic within the LISP programming language). The special case of Horn clauses gave rise to a new paradigm of non-deterministic programming, called Logic Programming, developing later into Constraint Programming, blurring further the scope of logic. In order to study knowledge acquisition, researchers in artificial intelligence and computational linguistics studied exotic versions of modal logics such as Montague intentional logic, epistemic logic, dynamic logic or hybrid logic. Some others tried to capture common sense, and modeled the revision of beliefs with so-called non-monotonic logics. For the careful crafstmen of mathematical logic, this was the final outrage, and Girard gave his anathema to such “montres à moutardes”.

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Rocha, Pedro, and Luís Caires. "Propositions-as-types and shared state." Proceedings of the ACM on Programming Languages 5, ICFP (August 22, 2021): 1–30. http://dx.doi.org/10.1145/3473584.

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We develop a principled integration of shared mutable state into a proposition-as-types linear logic interpretation of a session-based concurrent programming language. While the foundation of type systems for the functional core of programming languages often builds on the proposition-as-types correspondence, automatically ensuring strong safety and liveness properties, imperative features have mostly been handled by extra-logical constructions. Our system crucially builds on the integration of nondeterminism and sharing, inspired by logical rules of differential linear logic, and ensures session fidelity, progress, confluence and normalisation, while being able to handle first-class shareable reference cells storing any persistent object. We also show how preservation and, perhaps surprisingly, progress, resiliently survive in a natural extension of our language with first-class locks. We illustrate the expressiveness of our language with examples highlighting detailed features, up to simple shareable concurrent ADTs.

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BOUDOU, JOSEPH, MARTÍN DIÉGUEZ, DAVID FERNÁNDEZ-DUQUE, and PHILIP KREMER. "Exploring the Jungle of Intuitionistic Temporal Logics." Theory and Practice of Logic Programming 21, no. 4 (April 22, 2021): 459–92. http://dx.doi.org/10.1017/s1471068421000089.

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AbstractThe importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible to extend functional programming languages with new features via type theory, while from the semantics perspective, several logics for reasoning about dynamical systems and several semantics for logic programming have their roots in this framework. We consider several axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. We provide two distinct interpretations of “henceforth”, both of which are natural intuitionistic variants of the classical one. We completely establish the order relation between the semantically defined logics based on both interpretations of “henceforth” and, using our soundness results, show that the axiomatically defined logics enjoy the same order relations.

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SELINGER, PETER, and BENOIT VALIRON. "A lambda calculus for quantum computation with classical control." Mathematical Structures in Computer Science 16, no. 3 (June 2006): 527–52. http://dx.doi.org/10.1017/s0960129506005238.

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In this paper we develop a functional programming language for quantum computers by extending the simply-typed lambda calculus with quantum types and operations. The design of this language adheres to the ‘quantum data, classical control’ paradigm, following the first author's work on quantum flow-charts. We define a call-by-value operational semantics, and give a type system using affine intuitionistic linear logic. The main results of this paper are the safety properties of the language and the development of a type inference algorithm.

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Dissertations / Theses on the topic "Linear logic; Functional programming; Nets"

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Eastaughffe, Katherine A. "The geometry of interaction as a theory of cut elimination with structure-sharing." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297075.

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Book chapters on the topic "Linear logic; Functional programming; Nets"

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Lux, Wolfgang. "Adding Linear Constraints over Real Numbers to Curry." In Functional and Logic Programming, 185–200. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44716-4_12.

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Sacchini, Jorge Luis. "Linear Sized Types in the Calculus of Constructions." In Functional and Logic Programming, 169–85. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07151-0_11.

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Hasegawa, Masahito. "Semantics of Linear Continuation-Passing in Call-by-Name." In Functional and Logic Programming, 229–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24754-8_17.

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Bozzano, Marco, Giorgio Delzanno, and Maurizio Martelli. "An Effective Bottom-Up Semantics for First-Order Linear Logic Programs." In Functional and Logic Programming, 138–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-44716-4_9.

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Hasegawa, Masahito. "Linearly Used Effects: Monadic and CPS Transformations into the Linear Lambda Calculus." In Functional and Logic Programming, 167–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45788-7_10.

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Matsuoka, Satoshi. "Direct Encodings of NP-Complete Problems into Horn Sequents of Multiplicative Linear Logic." In Functional and Logic Programming, 17–32. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90686-7_2.

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Baillot, Patrick, Marco Gaboardi, and Virgile Mogbil. "A PolyTime Functional Language from Light Linear Logic." In Programming Languages and Systems, 104–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11957-6_7.

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Andreoli, Jean-Marc, and Roberto Maieli. "Focusing and Proof-Nets in Linear and Non-commutative Logic." In Logic for Programming and Automated Reasoning, 320–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48242-3_20.

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Eades III, Harley, Jiaming Jiang, and Aubrey Bryant. "On Linear Logic, Functional Programming, and Attack Trees." In Graphical Models for Security, 71–89. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15465-3_5.

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Maieli, Roberto. "Retractile Proof Nets of the Purely Multiplicative and Additive Fragment of Linear Logic." In Logic for Programming, Artificial Intelligence, and Reasoning, 363–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75560-9_27.

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