Relevant bibliographies by topics / Inductive types

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Academic literature on the topic 'Inductive types'

Author: Grafiati
Published: 11 March 2023

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Dissertations / Theses on the topic "Inductive types"

1

Bruin, Peter Johan de. "Inductive types in constructive languages." [S.l. : [Groningen] : s.n.] ; [University Library Groningen] [Host], 1995. http://irs.ub.rug.nl/ppn/128570415.

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2

Grimley, Allan. "Inductive types in functional programming." Thesis, University of Kent, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.253737.

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3

Kaposi, Ambrus. "Type theory in a type theory with quotient inductive types." Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/41385/.

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Type theory (with dependent types) was introduced by Per Martin-Löf with the intention of providing a foundation for constructive mathematics. A part of constructive mathematics is type theory itself, hence we should be able to say what type theory is using the formal language of type theory. In addition, metatheoretic properties of type theory such as normalisation should be provable in type theory. The usual way of defining type theory formally is by starting with an inductive definition of precontexts, pretypes and preterms and as a second step defining a ternary typing relation over these
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4

Altenkirch, Thorsten. "Constructions, inductive types and strong normalization." Thesis, University of Edinburgh, 1993. http://hdl.handle.net/1842/11967.

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This thesis contains an investigation of Coquand's Calculus of Construction, a basic impredicative Type Theory. We review syntactic properties of the calculus, in particular decidability of equality and type-checking, based on the equality-as-judgement presentation. We present a set-theoretic notion of model, CC-structures, and use this to give a new strong normalisation proof based on a modification of the realizability interpretation. An extension of the core calculus by inductive types is investigated and we show, using the example of infinite trees, how the realizability semantics and the
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5

Pavaux, Alice. "Inductive, Functional and Non-Linear Types in Ludics." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCD092.

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Cette thèse est consacrée à une exploration des types de la ludique. S’inscrivant dans un contexte marqué par la correspondance de Curry–Howard, la ludique est un cadre permettant d’étudier l’aspect dynamique de la logique et de la programmation. Les objets de base, appelés desseins, sont des preuves infinitaires non-typées qui peuvent également être vues comme des stratégies sous l’angle de la sémantique des jeux, et un type ou comportement est un ensemble de desseins se conduisant de la même manière du point de vue de l’interaction. On s’intéresse aux propriétés interactives des comportement
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6

Ko, Hsiang-Shang. "Analysis and synthesis of inductive families." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:2bc39bde-ce59-4a49-b499-3afdf174bbab.

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Based on a natural unification of logic and computation, Martin-Löf’s intuitionistic type theory can be regarded simultaneously as a computationally meaningful higher-order logic system and an expressively typed functional programming language, in which proofs and programs are treated as the same entities. Two modes of programming can then be distinguished: in externalism, we construct a program separately from its correctness proof with respect to a given specification, whereas in internalism, we encode the specification in a sophisticated type such that any program inhabiting the type also e
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7

Diehl, Larry. "Fully Generic Programming Over Closed Universes of Inductive-Recursive Types." PDXScholar, 2017. https://pdxscholar.library.pdx.edu/open_access_etds/3647.

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Dependently typed programming languages allow the type system to express arbitrary propositions of intuitionistic logic, thanks to the Curry-Howard isomorphism. Taking full advantage of this type system requires defining more types than usual, in order to encode logical correctness criteria into the definitions of datatypes. While an abundance of specialized types helps ensure correctness, it comes at the cost of needing to redefine common functions for each specialized type. This dissertation makes an effort to attack the problem of code reuse in dependently typed languages. Our solution is t
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8

Ciaffaglione, Alberto. "Certified reasoning on real numbers and objects in co-inductive type theory." Vandoeuvre-les-Nancy, INPL, 2003. http://docnum.univ-lorraine.fr/public/INPL_T_2003_CIAFFAGLIONE_A.pdf.

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Nous adoptons des Méthodes Formelles basées sur la Théorie de Type pour raisonner sur la sémantique des programmes: le but final est montrer qu'un fragment de logiciel répond à ses spécifications formelles. Les domaines d'application de notre recherche sont le type des données des Nombres Réels et les Langages orientés Objets. Dans la première partie nous construisons les réels en utilisant des streams, c. -à-d. Des suites infinies, de chiffres signés. Nous mettons en application les Nombres Réels dans Coq en utilisant les streams, qui sont contrôlés en utilisant des jugements coinductifs et d
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9

Giorgino, Mathieu. "Inductive representation, proofs and refinement of pointer structures." Toulouse 3, 2013. http://thesesups.ups-tlse.fr/2076/.

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Cette thèse s'intègre dans le domaine général des méthodes formelles qui donnent une sémantique aux programmes pour vérifier formellement des propriétés sur ceux-ci. Sa motivation originale provient d'un besoin de certification des systèmes industriels souvent développés à l'aide de l'Ingénierie Dirigée par les Modèles (IDM) et de langages orientés objets (OO). Pour transformer efficacement des modèles (ou graphes), il est avantageux de les représenter à l'aide de structures de pointeurs, économisant le temps et la mémoire grâce au partage qu'ils permettent. Cependant la vérification de propri
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10

Arkoudas, Kostas. "On the termination of recursive algorithms in pure first-order functional languages with monomorphic inductive data types." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/39074.

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