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Relevant bibliographies by topics / Extended Calculus of Constructions

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Academic literature on the topic 'Extended Calculus of Constructions'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Extended Calculus of Constructions"

1

Ore, Christian-Emil. "The Extended Calculus of Constructions (ECC) with inductive types." Information and Computation 99, no. 2 (1992): 231–64. http://dx.doi.org/10.1016/0890-5401(92)90031-a.

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Jouannaud, Jean-Pierre. "Membership Equational Logic, Calculus of Inductive Constructions, and Rewrite Logic (Extended Abstract)." Electronic Notes in Theoretical Computer Science 15 (1998): 388–93. http://dx.doi.org/10.1016/s1571-0661(05)80024-6.

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SELDIN, JONATHAN P. "On lists and other abstract data types in the calculus of constructions." Mathematical Structures in Computer Science 10, no. 2 (2000): 261–76. http://dx.doi.org/10.1017/s096012959900300x.

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The representation of the inductively defined abstract data type for lists was left incomplete in Seldin (1997, Section 9). Here that representation is completed, and it is proved that all extra axioms needed are consistent. Among the innovations of this paper is a definition of cdr, whose definition was left for future work in Seldin (1997, Section 9). The results are then extended to other abstract data types – those of Berardi (1993). The method used to define cdr for lists is extended to obtain the definition of an inverse for each argument of each constructor of an abstract data type. The

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4

Liu, Weiru, and Alan Bundy. "Constructing probabilistic ATMSs using extended incidence calculus." International Journal of Approximate Reasoning 15, no. 2 (1996): 145–82. http://dx.doi.org/10.1016/0888-613x(96)00031-x.

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LANZET, RAN. "A THREE-VALUED QUANTIFIED ARGUMENT CALCULUS: DOMAIN-FREE MODEL-THEORY, COMPLETENESS, AND EMBEDDING OF FOL." Review of Symbolic Logic 10, no. 3 (2017): 549–82. http://dx.doi.org/10.1017/s1755020317000053.

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AbstractThis paper presents an extended version of the Quantified Argument Calculus (Quarc). Quarc is a logic comparable to the first-order predicate calculus. It employs several nonstandard syntactic and semantic devices, which bring it closer to natural language in several respects. Most notably, quantifiers in this logic are attached to one-place predicates; the resulting quantified constructions are then allowed to occupy the argument places of predicates. The version presented here is capable of straightforwardly translating natural-language sentences involving defining clauses. A three-v

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BETARTE, GUSTAVO. "Type checking dependent (record) types and subtyping." Journal of Functional Programming 10, no. 2 (2000): 137–66. http://dx.doi.org/10.1017/s0956796899003627.

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In this work we put forward an algorithm for the mechanical verification of an extension of Martin-Löf's theory of types with dependent record types and subtyping. We first give a concise description of that theory and motivate its use for the formalization of algebraic constructions. Then we concentrate on the informal explanation and specification of a proof checker that we have implemented. The logical heart of this proof checker is a type checking algorithm for the forms of judgement of a particular formulation of the extended theory which incorporates a notion of parameter. The algorithm

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7

Seely, R. A. G. "Categorical semantics for higher order polymorphic lambda calculus." Journal of Symbolic Logic 52, no. 4 (1987): 969–89. http://dx.doi.org/10.2307/2273831.

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AbstractA categorical structure suitable for interpreting polymorphic lambda calculus (PLC) is defined, providing an algebraic semantics for PLC which is sound and complete. In fact, there is an equivalence between the theories and the categories. Also presented is a definitional extension of PLC including “subtypes”, for example, equality subtypes, together with a construction providing models of the extended language, and a context for Girard's extension of the Dialectica interpretation.

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Wallgrün, Jan Oliver, Jinlong Yang, and Alexander Klippel. "Cognitive Evaluation of Spatial Formalisms." International Journal of Cognitive Informatics and Natural Intelligence 8, no. 1 (2014): 1–17. http://dx.doi.org/10.4018/ijcini.2014010101.

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The authors present four human behavioral experiments to address the question of intuitive granularities in fundamental spatial relations as they can be found in formal spatial calculi. These calculi focus on invariant characteristics under certain (especially topological) transformations. Of particular interest to this article is the concept of two spatially extended entities overlapping each other. The overlap concept has been extensively treated in Galton's mode of overlap calculus (Galton, 1998). In the first two experiments, the authors used a category construction task to calibrate this

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BURGIN, MARK. "UNCERTAINTY AND IMPRECISION IN ANALYTICAL CONTEXT: FUZZY LIMITS AND FUZZY DERIVATIVES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 05 (2001): 563–85. http://dx.doi.org/10.1142/s021848850100106x.

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The main goal of the present paper is to extend such classical constructions as limits and derivatives making them appropriate for management of imprecise, vague, uncertain, and incomplete information. In the second part of the paper, going after introduction, elements of the theory of fuzzy limits are presented. The third part is devoted to the construction of fuzzy derivatives of real functions. Two kinds of fuzzy derivatives are introduced: weak and strong ones. It is necessary to remark that the strong fuzzy derivatives are similar to ordinary derivatives of real functions being their fuzz

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ALTENKIRCH, THORSTEN, and JAMES CHAPMAN. "Big-step normalisation." Journal of Functional Programming 19, no. 3-4 (2009): 311–33. http://dx.doi.org/10.1017/s0956796809007278.

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AbstractTraditionally, decidability of conversion for typed λ-calculi is established by showing that small-step reduction is confluent and strongly normalising. Here we investigate an alternative approach employing a recursively defined normalisation function which we show to be terminating and which reflects and preserves conversion. We apply our approach to the simply typed λ-calculus with explicit substitutions and βη-equality, a system which is not strongly normalising. We also show how the construction can be extended to system T with the usual β-rules for the recursion combinator. Our ap

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Dissertations / Theses on the topic "Extended Calculus of Constructions"

1

Luo, Zhaohui. "An extended calculus of constructions." Thesis, University of Edinburgh, 1990. http://hdl.handle.net/1842/12487.

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This thesis presents and studies a unifying theory of dependent types ECC - Extended Calculus of Constructions. ECC integrates Coquand-Huet's (impredicative) calculus of constructions and Martin-Lof's (predicative) type theory with universes, and turns out to be a strong and expressive calculus for formalization of mathematics, structured proof development and program specification. The meta-theory of ECC is studied and we show that the calculus has good meta-theoretic properties. The main proof-theoretic result is the <i>strong normalization</i> theorem, proved by using Girard-Tait's reducibi

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McKinna, James H. "Deliverables : a categorical approach to program development in type theory." Thesis, University of Edinburgh, 1992. http://hdl.handle.net/1842/506.

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This thesis considers the problem of program correctness within a rich theory of dependent types, the Extended Calculus of Constructions (ECC). This system contains a powerful programming language of higher-order primitive recursion and higher-order intuitionistic logic. It is supported by Pollack's versatile LEGO implementation, which I use extensively to develop the mathematical constructions studied here. I systematically investigate Burstall's notion of deliverable, that is, a program paired with a proof of correctness. This approach separates the concerns of programming and logic, since I

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Liu, Weiru. "Extended incidence calculus and its comparison with related theories." Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/28442.

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This thesis presents a comprehensive study of incidence calculus, a probabilistic logic for reasoning under uncertainty which extends two-value propositional logic to a multiple-value logic. There are three main contributions in this thesis. First of all, the original incidence calculus is extended considerably in three aspects: (a) the original incidence calculus is generalised; (b) an efficient algorithm for incidence assignment based on generalised incidence calculus is developed; (c) a combination rule is proposed for the combination of both independent and some dependent pieces of evidenc

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4

Ritter, Eike. "Categorical abstract machines for higher-order typed lambda calculi." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.281971.

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Finke, Axel. "On extended state-space constructions for Monte Carlo methods." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/77119/.

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This thesis develops computationally efficient methodology in two areas. Firstly, we consider a particularly challenging class of discretely observed continuous-time point-process models. For these, we analyse and improve an existing filtering algorithm based on sequential Monte Carlo (smc) methods. To estimate the static parameters in such models, we devise novel particle Gibbs samplers. One of these exploits a sophisticated non-entred parametrisation whose benefits in a Markov chain Monte Carlo (mcmc) context have previously been limited by the lack of blockwise updates for the latent point

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Gosson, Maurice A. de. "Extended Weyl calculus and application to the phase-space Schrödinger equation." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2987/.

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We show that the Schr¨odinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extendedWeyl calculus obtained by letting the Heisenberg group act on functions (or half-densities) defined on phase space. This allows us, in passing, to solve rigorously the TF equation for all quadratic Hamiltonians.

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Sacchini, Jorge Luis. "On type-based termination and dependent pattern matching in the calculus of inductive constructions." Institut national de recherche en informatique et en automatique (France). Unité de recherche (Sophia Antipolis, Alpes-Maritimes), 2011. http://pastel.archives-ouvertes.fr/pastel-00622429.

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Les assistants de preuve basés sur des théories des types dépendants sont de plus en plus utilisé comme un outil pour développer programmes certifiés. Un exemple réussi est l'assistant de preuves Coq, fondé sur le Calcul des Constructions Inductives (CCI). Coq est un langage de programmation fonctionnel dont un expressif système de type qui permet de préciser et de démontrer des propriétés des programmes dans une logique d'ordre supérieur. Motivé par le succès de Coq et le désir d'améliorer sa facilité d'utilisation, dans cette thèse nous étudions certaines limitations des implémentations actu

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Rouyer, Joseph. "Développements d'algorithmes dans le calcul des constructions." Vandoeuvre-les-Nancy, INPL, 1994. http://www.theses.fr/1994INPL042N.

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Le calcul des constructions est d'abord un lambda-calcul type d'ordre supérieur avec polymorphisme et types dépendants. La forte normalisation de ce lambda-calcul a été prouvée par Thierry Coquand qui en a fait un langage logique d'ordre supérieur permettant de coder la logique naturelle intuitionniste. Il en a démontré la cohérence et en a réalisé les premières implantations. Ce calcul des constructions initial a été enrichi (à la suite des travaux de Christine Paulin-Mohring) par de nouvelles sortes puis par les types inductifs et un procédé d'extraction de programmes. C'est dans l'implantat

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Johnson, Robert Arthur Christian. "Extended predicate constructions in German, the Pertinenzdativ as a study in relevance-based pragmatic theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0020/MQ48394.pdf.

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Johnson, Robert Arthur Christian Carleton University Dissertation Comparative literature. "Extended predicate constructions in German; the Pertinenzdativ as a study in relevance-based pragmatic theory." Ottawa, 1999.

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Books on the topic "Extended Calculus of Constructions"

1

Extended graphical calculus for categorified quantum sl(2). American Mathematical Society, 2011.

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2

Jean-Pierre, Eckmann, ed. Instabilities and fronts in extended systems. Princeton University Press, 1990.

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3

Bertot, Yves. Interactive Theorem Proving and Program Development: Coq'Art: The Calculus of Inductive Constructions. Springer Berlin Heidelberg, 2004.

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P, Castéran, ed. Interactive theorem proving and program development: Coq'Art : the calculus of inductive constructions. Springer, 2004.

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5

Taylor, Paul. Playing with Lego: Some examples of developing mathematics in the calculus of constructions. University of Edinburgh, Laboratory for Foundations in Computer Science, 1989.

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6

Renaud, Francis. Sémantique du temps et lambda-calcul. Presses universitaires de France, 1996.

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India) International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory (2010 Bangalore. Recent developments in algebraic and combinatorial aspects of representation theory: International Congress of Mathematicians Satellite Conference on Algebraic and Combinatorial Approaches to Representation Theory, August 12-16, 2010, National Institute of Advanced Studies, Bangalore, India : Conference on Algebraic and Combinatorial Approaches to Representation Theory, May 18-20, 2012, University of California, Riverside, CA. Edited by Chari, Vyjayanthi, editor of compilation and Conference on Algebraic and Combinatorial Approaches to Representation Theory (2012 : Riverside, Calif.). American Mathematical Society, 2013.

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8

Collet, Pierre, and Jean-Pierre Eckmann. Instabilities and Fronts in Extended Systems. Princeton University Press, 1990.

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Collet, Pierre, and Jean-Pierre Eckmann. Instabilities and Fronts in Extended Systems. Princeton University Press, 2014.

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Collet, Pierre, and Jean-Pierre Eckmann. Instabilities and Fronts in Extended Systems. Princeton University Press, 2014.

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Book chapters on the topic "Extended Calculus of Constructions"

1

Burstall, Rod. "Extended calculus of constructions as a specification language." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/3-540-56625-2_1.

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Chen, Gang. "Subtyping calculus of construction (extended abstract)." In Mathematical Foundations of Computer Science 1997. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0029962.

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Sz.-Nagy, Béla, Hari Bercovici, Ciprian Foias, and László Kérchy. "Extended Functional Calculus." In Harmonic Analysis of Operators on Hilbert Space. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6094-8_4.

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Blanqui, Frédéric, Jean-Pierre Jouannaud, and Mitsuhiro Okada. "The Calculus of Algebraic Constructions." In Rewriting Techniques and Applications. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48685-2_25.

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Sun, Yong. "Axiomatization of calculus of constructions." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0021086.

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Ray, Nigel. "Universal Constructions in Umbral Calculus." In Mathematical Essays in honor of Gian-Carlo Rota. Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-4108-9_18.

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Gehrke, Mai, Tomáš Jakl, and Luca Reggio. "A Duality Theoretic View on Limits of Finite Structures." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_16.

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AbstractA systematic theory of structural limits for finite models has been developed by Nešetřil and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a space of measures, where the desired limits can be computed. We show that a closely related but finer grained space of measures arises — via Stone-Priestley duality and the notion of types from model theory — by enriching the expressive power of first-order logic with certain “probabilistic operators”. We provide a sound and complete calculus for this extended logic and expose the functorial nature of this construction.The consequences are two-fold. On the one hand, we identify the logical gist of the theory of structural limits. On the other hand, our construction shows that the duality-theoretic variant of the Stone pairing captures the adding of a layer of quantifiers, thus making a strong link to recent work on semiring quantifiers in logic on words. In the process, we identify the model theoretic notion of types as the unifying concept behind this link. These results contribute to bridging the strands of logic in computer science which focus on semantics and on more algorithmic and complexity related areas, respectively.

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Grubb, Gerd. "Parametrix and Resolvent Constructions." In Functional Calculus of Pseudodifferential Boundary Problems. Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-0769-6_4.

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Papini, Odile, and Antoine Rauzy. "Revision in extended propositional calculus." In Symbolic and Quantitative Approaches to Reasoning and Uncertainty. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60112-0_38.

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Grubb, Gerd. "Parametrix and Resolvent Constructions." In Functional Calculus of Pseudo-Differential Boundary Problems. Birkhäuser Boston, 1986. http://dx.doi.org/10.1007/978-1-4757-1898-0_4.

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Conference papers on the topic "Extended Calculus of Constructions"

1

Westbrook, Edwin, Aaron Stump, and Evan Austin. "The calculus of nominal inductive constructions." In the Fourth International Workshop. ACM Press, 2009. http://dx.doi.org/10.1145/1577824.1577836.

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Chen, Gang. "Coercive subtyping for the calculus of constructions." In the 30th ACM SIGPLAN-SIGACT symposium. ACM Press, 2003. http://dx.doi.org/10.1145/604131.604145.

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Monnier, Stefan. "Inductive types deconstructed: the calculus of united constructions." In the 4th ACM SIGPLAN International Workshop. ACM Press, 2019. http://dx.doi.org/10.1145/3331554.3342607.

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Bowman, William J., and Amal Ahmed. "Typed closure conversion for the calculus of constructions." In PLDI '18: ACM SIGPLAN Conference on Programming Language Design and Implementation. ACM, 2018. http://dx.doi.org/10.1145/3192366.3192372.

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Alhadidi, Dima, Nadia Belblidia, Mourad Debbabi, and Prabir Bhattacharya. "An AOP Extended Lambda-Calculus." In Fifth IEEE International Conference on Software Engineering and Formal Methods (SEFM 2007). IEEE, 2007. http://dx.doi.org/10.1109/sefm.2007.5.

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Paulin-Mohring, C. "Extracting ω's programs from proofs in the calculus of constructions". У the 16th ACM SIGPLAN-SIGACT symposium. ACM Press, 1989. http://dx.doi.org/10.1145/75277.75285.

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Sacchini, Jorge Luis. "Type-Based Productivity of Stream Definitions in the Calculus of Constructions." In 2013 Twenty-Eighth Annual IEEE/ACM Symposium on Logic in Computer Science (LICS 2013). IEEE, 2013. http://dx.doi.org/10.1109/lics.2013.29.

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Watters, Aaron. "Interpreting a reconstructed relational calculus (extended abstract)." In the 1993 ACM SIGMOD international conference. ACM Press, 1993. http://dx.doi.org/10.1145/170035.170089.

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Flaherty, Terry. "A differentiation primitive for extended λ-calculus". У the 1988 ACM sixteenth annual conference. ACM Press, 1988. http://dx.doi.org/10.1145/322609.322611.

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Wang, Weihong, Jiangbo Li, Yuhui Cao, and Zhiqiang He. "An Extended Ambient Calculus Model Oriented Mobile Collaboration." In 2009 Second International Conference on Information and Computing Science. IEEE, 2009. http://dx.doi.org/10.1109/icic.2009.398.

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Reports on the topic "Extended Calculus of Constructions"

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Habert, Guillaume, and Francesco Pittau. Joint synthesis “Sustainable Concrete Structures” of the NRP “Energy”. Swiss National Science Foundation (SNSF), 2020. http://dx.doi.org/10.46446/publication_nrp70_nrp71.2020.5.en.

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All structures in Switzerland - that is, all buildings, roads, infrastructure constructions and so on - consume over their entire life cycle around 50 % of Switzerland's final energy requirement. They are also responsible for around 30 % of emissions of the greenhouse gas CO2. In recent decades, the energy requirements and CO2 emissions resulting from the use of such structures have fallen sharply. However, the grey energy contained within the structures as well as the CO2 emissions associated with the construction, renovation and demolition of buildings, remain high. There is great potential

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