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Academic literature on the topic 'Inductive types'

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Published: 11 March 2023

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Journal articles on the topic "Inductive types"

1

Kaposi, Ambrus, András Kovács, and Thorsten Altenkirch. "Constructing quotient inductive-inductive types." Proceedings of the ACM on Programming Languages 3, POPL (January 2, 2019): 1–24. http://dx.doi.org/10.1145/3290315.

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Barthe, Gilles. "Order-Sorted Inductive Types." Information and Computation 149, no. 1 (February 1999): 42–76. http://dx.doi.org/10.1006/inco.1998.2751.

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DE ANGELIS, EMANUELE, FABIO FIORAVANTI, ALBERTO PETTOROSSI, and MAURIZIO PROIETTI. "Solving Horn Clauses on Inductive Data Types Without Induction." Theory and Practice of Logic Programming 18, no. 3-4 (July 2018): 452–69. http://dx.doi.org/10.1017/s1471068418000157.

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AbstractWe address the problem of verifying the satisfiability of Constrained Horn Clauses (CHCs) based on theories of inductively defined data structures, such as lists and trees. We propose a transformation technique whose objective is the removal of these data structures from CHCs, hence reducing their satisfiability to a satisfiability problem for CHCs on integers and booleans. We propose a transformation algorithm and identify a class of clauses where it always succeeds. We also consider an extension of that algorithm, which combines clause transformation with reasoning on integer constraints. Via an experimental evaluation we show that our technique greatly improves the effectiveness of applying the Z3 solver to CHCs. We also show that our verification technique based on CHC transformation followed by CHC solving, is competitive with respect to CHC solvers extended with induction.

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Howard, Brian T. "Inductive, coinductive, and pointed types." ACM SIGPLAN Notices 31, no. 6 (June 15, 1996): 102–9. http://dx.doi.org/10.1145/232629.232640.

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LUMSDAINE, PETER LEFANU, and MICHAEL SHULMAN. "Semantics of higher inductive types." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 1 (June 17, 2019): 159–208. http://dx.doi.org/10.1017/s030500411900015x.

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AbstractHigher inductive typesare a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the “synthetic” development of homotopy theory within type theory, as well as in formalising ordinary set-level mathematics in type theory. In this paper, we construct models of a wide range of higher inductive types in a fairly wide range of settings.We introduce the notion ofcell monad with parameters: a semantically-defined scheme for specifying homotopically well-behaved notions of structure. We then show that any suitable model category hasweakly stable typal initial algebrasfor any cell monad with parameters. When combined with the local universes construction to obtain strict stability, this specialises to give models of specific higher inductive types, including spheres, the torus, pushout types, truncations, the James construction and general localisations.Our results apply in any sufficiently nice Quillen model category, including any right proper, simplicially locally cartesian closed, simplicial Cisinski model category (such as simplicial sets) and any locally presentable locally cartesian closed category (such as sets) with its trivial model structure. In particular, any locally presentable locally cartesian closed (∞, 1)-category is presented by some model category to which our results apply.

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Loader, Ralph. "Equational theories for inductive types." Annals of Pure and Applied Logic 84, no. 2 (March 1997): 175–217. http://dx.doi.org/10.1016/s0168-0072(96)00021-8.

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OGATA, K., and K. FUTATSUGI. "State Machines as Inductive Types." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E90-A, no. 12 (December 1, 2007): 2985–88. http://dx.doi.org/10.1093/ietfec/e90-a.12.2985.

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van den Berg, Benno. "Inductive types and exact completion." Annals of Pure and Applied Logic 134, no. 2-3 (July 2005): 95–121. http://dx.doi.org/10.1016/j.apal.2004.09.003.

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ABEL, ANDREAS. "Implementing a normalizer using sized heterogeneous types." Journal of Functional Programming 19, no. 3-4 (July 2009): 287–310. http://dx.doi.org/10.1017/s0956796809007266.

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AbstractIn the simply typed λ-calculus, a hereditary substitution replaces a free variable in a normal formrby another normal formsof typea, removing freshly created redexes on the fly. It can be defined by lexicographic induction onaandr, thus giving rise to a structurally recursive normalizer for the simply typed λ-calculus. We implement hereditary substitutions in a functional programming language with sized heterogeneous inductive types$\Fhat$, arriving at an interpreter whose termination can be tracked by the type system of its host programming language.

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Matthes, Ralph. "Monotone (co)inductive types and positive fixed-point types." RAIRO - Theoretical Informatics and Applications 33, no. 4-5 (July 1999): 309–28. http://dx.doi.org/10.1051/ita:1999120.

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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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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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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 three components. Well-typed terms are those preterms for which there exists a precontext and pretype such that the relation holds. However, if we use the rich metalanguage of type theory to talk about type theory, we can define well-typed terms directly as an inductive family indexed over contexts and types. We believe that this latter approach is closer to the spirit of type theory where objects come intrinsically with their types. Internalising a type theory with dependent types is challenging because of the mutual definitions of types, terms, substitution of terms and the conversion relation. We use induction induction to express this mutual dependency. Furthermore, to reduce the type-theoretic boilerplate needed for reasoning in the syntax, we encode the conversion relation as the equality type of the syntax. We use equality constructors thus we define the syntax as a quotient inductive type (a special case of higher inductive types from homotopy type theory). We define the syntax of a basic type theory with dependent function space, a base type and a family over the base type as a quotient inductive inductive type. The definition of the syntax comes with a notion of model and an eliminator: whenever one is able to define a model, the eliminator provides a function from the syntax to the model. We show that this method of representing type theory is practically feasible by defining a number of models: the standard model, the logical predicate interpretation for parametricity (as a syntactic translation) and the proof-relevant presheaf logical predicate interpretation. By extending the latter with a quote function back into the syntax, we prove normalisation for type theory. This can be seen as a proof of normalisation by evaluation. Internalising the syntax of type theory is not only of theoretical interest. It opens the possibility of type-theoretic metaprogramming in a type-safe way. This could be used for generic programming in type theory and to implement extensions of type theory which are justified by models such as guarded type theory or homotopy type theory.

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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 strong normalisation argument can be extended to non-algebraic inductive types. We emphasise that our interpretation is sound for large eliminations, e.g. allows the definition of sets by recursion. Finally we apply the extended calculus to a non-trivial problem: the formalization of the strong normalisation argument for Girard's System F. This formal proof has been developed and checked using the LEGO system, which has been implemented by Randy Pollack. We include the LEGO files in the appendix.

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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 comportements. Notre attention se porte en particulier sur les comportements représentant les types de données et de fonctions, et sur les comportements non-linéaires qui permettent la duplication d’objets. Un nouveau résultat de complétude interne pour les unions infinies dévoile la structure des types de données inductifs. Grâce à une analyse des chemins visitables,c’est-à-dire des possibles traces d’exécution, on prouve que les comportements inductifs et fonctionnels sont réguliers, ouvrant la voie pour une caractérisation de MALL en ludique. On montre également qu’un comportement fonctionnel est pur, une propriété garantissant la sûreté du typage, si et seulement si ce n’est pas un type de fonctions prenant des fonctions en argument. Enfin, on pose les bases d’une étude précise de la non-linéarité en ludique en retrouvant une forme de complétude interne et en discutant des chemins visitables
This thesis investigates the types of ludics. Within the context of the Curry–Howard correspondence,l udics is a framework in which the dynamic aspects of both logic and programming can be studied. The basic objects, called designs, are untyped infinitary proofs that can also beseen as strategies from the perspective of game semantics, and a type or behaviour is a set of designs well-behaved with respect to interaction. We are interested in observing the interactive properties of behaviours. Our attention is particularly focused on behaviours representing the types of data and functions, and on non-linear behaviours which allow the duplication of objects. A new internal completeness result for infinite unions unveils the structure of inductive data types. Thanks to an analysis of the visitable paths, i.e., the possible execution traces, we prove that inductive and functional behaviours are regular, paving the way for a characterisation of MALL in ludics. We also show that a functional behaviour is pure, a property ensuring the safety of typing, if and only if it is not a type of functions taking functions as argument. Finally,we set the bases for a precise study of non-linearity in ludics by recovering a form of internal completeness and discussing the visitable paths

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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 encodes a correctness proof, and we can use type information as a guidance on program construction. Internalism is particularly effective in the presence of inductive families, whose design can have a strong influence on program structure. Techniques and mechanisms for facilitating internalist programming are still lacking, however. This dissertation proposes that internalist programming can be facilitated by exploiting an interconnection between internalism and externalism, expressed as isomorphisms between inductive families into which data structure invariants are encoded and their simpler variants paired with predicates expressing those invariants. The interconnection has two directions: one analysing inductive families into simpler variants and predicates, and the other synthesising inductive families from simpler variants and specific predicates. They respectively give rise to two applications, one achieving a modular structure of internalist libraries, and the other bridging internalist programming with relational specifications and program derivation. The datatype-generic mechanisms supporting the applications are based on McBride’s ornaments. Theoretically, the key ornamental constructs — parallel composition of ornaments and relational algebraic ornamentation — are further characterised in terms of lightweight category theory. Most of the results are completely formalised in the Agda programming language.

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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 to write generic functions, which can be applied to any datatype. Such a generic function can be applied to datatypes that are defined at the time the generic function was written, but they can also be applied to any datatype that is defined in the future. Our solution builds upon previous work on generic programming within dependently typed programming. Type theory supports generic programming using a construction known as a universe. A universe can be considered the model of a programming language, such that writing functions over it models writing generic programs in the programming language. Historically, there has been a trade-off between the expressive power of the modeled programming language, and the kinds of generic functions that can be written in it. Our dissertation shows that no such trade-off is necessary, and that we can write future-proof generic functions in a model of a dependently typed programming language with a rich collection of types.

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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 des algorithmes corecursifs. Puis nous présentons une axiomatisation constructive et nous l'employons pour prouver l'adéquation de notre construction. Dans la deuxième partie nous étudions les calculs basées objets avec effet de bord, nous concentrant sur imp[sigma] d'Abadi et de Cardelli. Nous reformulons imp[sigma] en utilisant des techniques de codage modernes, comme la Syntaxe Abstraite d'Ordre Supérieur et des systèmes de preuve Coinductifs en Déduction Naturelle. Enfin nous formalisons imp[sigma] dans Coq et nous prouvons la correction des types
We adopt Formal Methods based on Type Theory for reasoning on the semantics of computer programs: the ultimate goal is to prove that a fragment of software meets its formal specification. Application areas of our research are the Real Numbers datatype and the Object-oriented Languages based on Objects. In the first part we construct the Real Numbers using streams, i. E. Infinite sequences, of signed digits. We implement the Reals in Coq using streams, which are managed using coinductive judgments and corecursive algorithms. Then we introduce a constructive axiomatization and we use it for proving the adequacy of our construction. In the second part we approach Object-based Calculi with side-effects, focusing on Abadi and Cardelli's imp[sigma]. We reformulate imp[sigma] using modern encoding techniques, as Higher-Order Abstract Syntax and Coinductive proof systems in Natural Deduction style. Then we formalize imp[sigma] in Coq and we prove the Type Soundness

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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 propriétés sur des programmes manipulant des pointeurs est encore complexe. Pour la simplifier, nous proposons de démarrer le développement par une implémentation haut-niveau sous la forme de programmes fonctionnels sur des types de données inductifs facilement vérifiables dans des assistants à la preuve tels que Isabelle/HOL. La représentation des structures de pointeurs est faite à l'aide d'un arbre couvrant contenant des références additionnelles. Ces programmes fonctionnels sont ensuite raffinés si nécessaire vers des programmes impératifs à l'aide de la bibliothèque Imperative_HOL. Ces programmes sont en dernier lieu extraits vers du code Scala (OO). Cette thèse décrit la méthodologie de représentation et de raffinement et fournit des outils pour la manipulation et la preuve de programmes OO dans Isabelle/HOL. L'approche est éprouvée par de nombreux exemples dont notamment l'algorithme de Schorr-Waite et la construction de Diagrammes de Décision Binaires (BDDs)
This thesis stands in the general domain of formal methods that gives semantics to programs to formally prove properties about them. It originally draws its motivation from the need for certification of systems in an industrial context where Model Driven Engineering (MDE) and object-oriented (OO) languages are common. In order to obtain efficient transformations on models (graphs), we can represent them as pointer structures, allowing space and time savings through the sharing of nodes. However verification of properties on programs manipulating pointer structures is still hard. To ease this task, we propose to start the development with a high-level implementation embodied by functional programs manipulating inductive data-structures, that are easily verified in proof assistants such as Isabelle/HOL. Pointer structures are represented by a spanning tree adorned with additional references. These functional programs are then refined - if necessary - to imperative programs thanks to the library Imperative_HOL. These programs are finally extracted to Scala code (OO). This thesis describes this kind of representation and refinement and provides tools to manipulate and prove OO programs in Isabelle/HOL. This approach is put in practice with several examples, and especially with the Schorr-Waite algorithm and the construction of Binary Decision Diagrams (BDDs)

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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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Books on the topic "Inductive types"

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Morel, Jane B. The effects of mood induction on the recognition memory of word types. Sudbury, Ont: Laurentian University, Department of Psychology, 1990.

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Deshpande, S. S., of Spectroscopy Division, Bhabha Atomic Research Centre. and Bhabha Atomic Research Centre, eds. Determination of alloying and impurity elements in various types of steels using inductively coupled plasma atomic emission spectrometry. Mumbai: Bhabha Atomic Research Centre, 2002.

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Tickle, Les. Teacher induction: The way ahead. Buckingham: Open University Press, 2000.

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Teacher induction: The way ahead. Buckingham: Open University Press, 2000.

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Beck, Caroline W. Investigation of the effect of Wild Type and Mutant NF-kB related proteins on mesoderm induction in Xenopus. [s.l.]: typescript, 1996.

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Maznev, Aleksandr, and Oleg Shatnev. Electric apparatus and circuits of rolling stock. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1014641.

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Provides information about technical data and design of electrical apparatus of control, monitoring and protection of traction motors of electric rolling stock (EPS), the principles of speed control of locomotives and trains with contactor-resistor and semiconductor converters based on modern element base, a circuit diagram of various types of EPS with manifold and induction motors in modes of traction and braking. For students of institutions of secondary professional education. It may be useful to students of higher educational institutions, courses of improvement of qualification, the railway workers related to the maintenance and repair of rolling stock.

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Kuhler, Ulirich. Tacti-Based Inductive Theorem Prover for Data Types With Partial Operations. Ios Pr Inc, 2000.

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Andreasen, Robin, and Heather Doty. Measuring Inequality. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190467715.003.0007.

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The focus of this chapter is on the argument from inductive risk in the context of social science research on disparate impact in employment outcomes. It identifies three types of situations in the testing of scientific theories, not sufficiently emphasized in the inductive risk literature, that raise considerations of inductive risk: choice of significance test, choice of how to measure disparate impact, and the operationalization of scientific variables. It argues that non-epistemic values have a legitimate role in two of these situations but not in the third. It uses this observation to build on the discussion of when and under what conditions considerations of inductive risk help to justify a role for non-epistemic values in science.

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Shulman, Michael. Homotopy Type Theory: A Synthetic Approach to Higher Equalities. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0003.

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Homotopy type theory and univalent foundations (HoTT/UF) is a new foundation of mathematics, based not on set theory but on “infinity-groupoids”, which consist of collections of objects, ways in which two objects can be equal, ways in which those ways-to-be-equal can be equal, ad infinitum. Though apparently complicated, such structures are increasingly important in mathematics. Philosophically, they are an inevitable result of the notion that whenever we form a collection of things, we must simultaneously consider when two of those things are the same. The “synthetic” nature of HoTT/UF enables a much simpler description of infinity groupoids than is available in set theory, thereby aligning with modern mathematics while placing “equality” back in the foundations of logic. This chapter will introduce the basic ideas of HoTT/UF for a philosophical audience, including Voevodsky’s univalence axiom and higher inductive types.

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Type CCL polyphase induction motors. [Hamilton, Ont.?: s.n., 1991.

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Book chapters on the topic "Inductive types"

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Turner, Raymond. "Inductive Types." In Computable Models, 1–9. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84882-052-4_15.

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Altenkirch, Thorsten, Paolo Capriotti, Gabe Dijkstra, Nicolai Kraus, and Fredrik Nordvall Forsberg. "Quotient Inductive-Inductive Types." In Lecture Notes in Computer Science, 293–310. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89366-2_16.

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Bertot, Yves, and Pierre Castéran. "Inductive Data Types." In Texts in Theoretical Computer Science An EATCS Series, 137–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-07964-5_6.

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Hugunin, Jasper. "Constructing Inductive-Inductive Types in Cubical Type Theory." In Lecture Notes in Computer Science, 295–312. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17127-8_17.

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Bertot, Yves, and Pierre Castéran. "** Foundations of Inductive Types." In Texts in Theoretical Computer Science An EATCS Series, 377–406. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-07964-5_14.

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Fiore, Marcelo P., Andrew M. Pitts, and S. C. Steenkamp. "Constructing Infinitary Quotient-Inductive Types." In Lecture Notes in Computer Science, 257–76. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_14.

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AbstractThis paper introduces an expressive class of quotient-inductive types, called QW-types. We show that in dependent type theory with uniqueness of identity proofs, even the infinitary case of QW-types can be encoded using the combination of inductive-inductive definitions involving strictly positive occurrences of Hofmann-style quotient types, and Abel’s size types. The latter, which provide a convenient constructive abstraction of what classically would be accomplished with transfinite ordinals, are used to prove termination of the recursive definitions of the elimination and computation properties of our encoding of QW-types. The development is formalized using the Agda theorem prover.

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Abbott, Michael, Thorsten Altenkirch, and Neil Ghani. "Representing Nested Inductive Types Using W-Types." In Automata, Languages and Programming, 59–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-27836-8_8.

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Voermans, Ed. "Pers as Types, Inductive Types and Types with Laws." In Declarative Programming, Sasbachwalden 1991, 274–91. London: Springer London, 1992. http://dx.doi.org/10.1007/978-1-4471-3794-8_18.

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Capretta, Venanzio. "Recursive Families of Inductive Types." In Lecture Notes in Computer Science, 73–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44659-1_5.

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Barzdins, G. "Inductive synthesis of encoding for algebraic abstract data types." In Analogical and Inductive Inference, 328–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51734-0_72.

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Conference papers on the topic "Inductive types"

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Awodey, Steve, Nicola Gambino, and Kristina Sojakova. "Inductive Types in Homotopy Type Theory." In 2012 27th Annual IEEE Symposium on Logic in Computer Science (LICS 2012). IEEE, 2012. http://dx.doi.org/10.1109/lics.2012.21.

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Kovács, András, and Ambrus Kaposi. "Large and Infinitary Quotient Inductive-Inductive Types." In LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3373718.3394770.

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Altenkirch, Thorsten, and Ambrus Kaposi. "Type theory in type theory using quotient inductive types." In POPL '16: The 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2837614.2837638.

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Coquand, Thierry, Simon Huber, and Anders Mörtberg. "On Higher Inductive Types in Cubical Type Theory." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3209108.3209197.

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Howard, Brian T. "Inductive, coinductive, and pointed types." In the first ACM SIGPLAN international conference. New York, New York, USA: ACM Press, 1996. http://dx.doi.org/10.1145/232627.232640.

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Basold, Henning, and Herman Geuvers. "Type Theory based on Dependent Inductive and Coinductive Types." In LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2933575.2934514.

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Awodey, Steve, Jonas Frey, and Sam Speight. "Impredicative Encodings of (Higher) Inductive Types." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3209108.3209130.

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Filinski, Andrzej, and Kristian Støvring. "Inductive reasoning about effectful data types." In the 2007 ACM SIGPLAN international conference. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1291151.1291168.

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Barthe, Gilles, and Tarmo Uustalu. "CPS translating inductive and coinductive types." In the 2002 ACM SIGPLAN workshop. New York, New York, USA: ACM Press, 2002. http://dx.doi.org/10.1145/503032.503043.

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Kraus, Nicolai, and Jakob von Raumer. "Path Spaces of Higher Inductive Types in Homotopy Type Theory." In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2019. http://dx.doi.org/10.1109/lics.2019.8785661.

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Reports on the topic "Inductive types"

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Greiner, John. Programming with Inductive and Co-Inductive Types. Fort Belvoir, VA: Defense Technical Information Center, January 1992. http://dx.doi.org/10.21236/ada249562.

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Diehl, Larry. Fully Generic Programming Over Closed Universes of Inductive-Recursive Types. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.5531.

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Yilma, Tilahun D. Induction or Type 1 Immune Responses to SIV by IFN-Gamma. Fort Belvoir, VA: Defense Technical Information Center, May 1999. http://dx.doi.org/10.21236/ada371068.

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Boyle, D. R., and D. C. Gregoire. 107Ag /109Ag Ratios of minerals From Various Types of Ore-Forming Environments using Inductively Coupled Mass Spectrometry. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1989. http://dx.doi.org/10.4095/127517.

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Dahal, Sachindra, and Jeffery Roesler. Passive Sensing of Electromagnetic Signature of Roadway Material for Lateral Positioning of Vehicle. Illinois Center for Transportation, November 2021. http://dx.doi.org/10.36501/0197-9191/21-039.

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Autonomous vehicles (AV) and advanced driver-assistance systems (ADAS) offer multiple safety benefits for drivers and road agencies. However, maintaining the lateral position of an AV or a vehicle with ADAS within a lane is a challenge, especially in adverse weather conditions when lane markings are occluded. For significant penetration of AV without compromising safety, vehicle-to-infrastructure sensing capabilities are necessary, especially during severe weather conditions. This research proposes a method to create a continuous electromagnetic (EM) signature on the roadway, using materials compatible with existing paving materials and construction methods. Laboratory testing of the proposed concept was performed on notched concrete-slab specimens and concrete prisms containing EM materials. An induction-based eddy-current sensor and magnetometers were implemented to detect the EM signature. The detected signals were compared to evaluate the effects of sensor height above the concrete surface, type of EM materials, EM-material volume, material shape, and volume of EM concrete prisms. A layer of up to 2 in. (5.1 cm) of water, ice, snow, or sand was placed between the sensor and the concrete slab to represent adverse weather conditions. Results showed that factors such as sensor height, EM-material volume, EM dosage, types of the EM material, and shape of the EM material in the prism were significant attenuators of the EM signal and must be engineered properly. Presence of adverse surface conditions had a negligible effect, as compared to normal conditions, indicating robustness of the presented method. This study proposes a promising method to complement existing sensors’ limitations in AVs and ADAS for effective lane-keeping during normal and adverse weather conditions with the help of vehicle-to-pavement interaction.

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Coplin, David, Isaac Barash, and Shulamit Manulis. Role of Proteins Secreted by the Hrp-Pathways of Erwinia stewartii and E. herbicola pv. gypsophilae in Eliciting Water-Soaking Symptoms and Initiating Galls. United States Department of Agriculture, June 2001. http://dx.doi.org/10.32747/2001.7580675.bard.

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Many bacterial pathogens of plants can inject pathogenicity proteins into host cells using a specialized type III secretion system encoded by hrpgenes. This system deliver effector proteins, into plant cells that function in both susceptible and resistant interactions. We have found that the virulence of Erwinia stewartii(Es; syn. Pantoea stewartii) and Erwinia herbicola pv. gypsophilae (Ehg, syn. Pantoea agglomerans), which cause Stewart's wilt of corn and galls on Gypsophila, respectively, depends on hrpgenes. The major objectives of this project were: To increase expression of hrpgenes in order to identify secreted proteins; to identify genes for proteins secreted by the type-III systems and determine if they are required for pathogenicity; and to determine if the secreted proteins can function within eukaryotic cells. We found that transcription of the hrp and effector genes in Es and Ehg is controlled by at least four genes that constitute a regulatory cascade. Environmental and/or physiological signaling appears to be mediated by the HrpX/HrpY two component system, with HrpX functioning as a sensor-kinase and HrpY as a response regulator. HrpYupregulateshrpS, which encodes a transcriptional enhancer. HrpS then activates hrpL, which encodes an alternate sigma factor that recognizes "hrp boxes". All of the regulatory genes are essential for pathogenicity, except HrpX, which appears only to be required for induction of the HR in tobacco by Es. In elucidating this regulatory pathway in both species, we made a number of significant new discoveries. HrpX is unusual for a sensor-kinase because it is cytoplasmic and contains PAS domains, which may sense the redox state of the bacterium. In Es, a novel methyl-accepting protein may function upstream of hrpY and repress hrp gene expression in planta. The esaIR quorum sensing system in Es represses hrp gene expression in Es in response to cell-density. We have discovered six new type III effector proteins in these species, one of which (DspE in Ehg and WtsE in Es) is common to both pathogens. In addition, Es wtsG, which is a homolog of an avrPpiB from P. syringae pv. pisi, and an Ehg ORF, which is a homolog of P. syringae pv. phaseolicola AvrPphD, were both demonstrated to encode virulence proteins. Two plasmidborne, Ehg Hop proteins, HsvG and PthG, are required for infection of gypsophilia, but interestingly, PthG also acts as an Avr elicitor in beets. Using a calmodulin-dependent adenylate cyclase (cyaA) reporter gene, we were successful in demonstrating that an HsvG-CyaA fusion protein can be transferred into human HeLa cells by the type-III system of enteropathogenic E. coli. This is a highly significant accomplishment because it is the first direct demonstration that an effector protein from a plant pathogenic bacterium is capable of being translocated into a eukaryotic cell by a type-III secretion system. Ehg is considered a limiting factor in Gypsophila production in Israel and Stewart’s Wilt is a serious disease in the Eastern and North Central USA, especially on sweet corn in epidemic years. We believe that our basic research on the characterization of type III virulence effectors should enable future identification of their receptors in plant cells. This may lead to novel approaches for genetically engineering resistant plants by modifying their receptors or inactivating effectors and thus blocking the induction of the susceptible response. Alternatively, hrp gene regulation might also provide a target for plant produced compounds that interfere with recognition of the host by the pathogen. Such strategies would be broadly applicable to a wide range of serious bacterial diseases on many crops throughout the USA and Israel.

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Wilson, Thomas E., Avraham A. Levy, and Tzvi Tzfira. Controlling Early Stages of DNA Repair for Gene-targeting Enhancement in Plants. United States Department of Agriculture, March 2012. http://dx.doi.org/10.32747/2012.7697124.bard.

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Gene targeting (GT) is a much needed technology as a tool for plant research and for the precise engineering of crop species. Recent advances in this field have shown that the presence of a DNA double-strand break (DSB) in a genomic locus is critical for the integration of an exogenous DNA molecule introduced into this locus. This integration can occur via either non-homologous end joining (NHEJ) into the break or homologous recombination (HR) between the broken genomic DNA and the introduced vector. A bottleneck for DNA integration via HR is the machinery responsible for homology search and strand invasion. Important proteins in this pathway are Rad51, Rad52 and Rad54. We proposed to combine our respective expertise: on the US side, in the design of zincfinger nucleases (ZFNs) for the induction of DNA DSBs at any desired genomic locus and in the integration of DNA molecules via NHEJ; and on the Israeli side in the HR events, downstream of the DSB, that lead to homology search and strand invasion. We sought to test three major pathways of targeted DNA integration: (i) integration by NHEJ into DSBs induced at desired sites by specially designed ZFNs; (ii) integration into DSBs induced at desired sites combined with the use of Rad51, Rad52 and Rad54 proteins to maximize the chances for efficient and precise HR-mediated vector insertion; (iii) stimulation of HR by Rad51, Rad52 and Rad54 in the absence of DSB induction. We also proposed to study the formation of dsT-DNA molecules during the transformation of plant cells. dsT-DNA molecules are an important substrate for HR and NHEJ-mediatedGT, yet the mode of their formation from single stranded T-DNA molecules is still obscure. In addition we sought to develop a system for assembly of multi-transgene binary vectors by using ZFNs. The latter may facilitate the production of binary vectors that may be ready for genome editing in transgenic plants. ZFNs were proposed for the induction of DSBs in genomic targets, namely, the FtsH2 gene whose loss of function can easily be identified in somatic tissues as white sectors, and the Cruciferin locus whose targeting by a GFP or RFP reporter vectors can give rise to fluorescent seeds. ZFNs were also proposed for the induction of DSBs in artificial targets and for assembly of multi-gene vectors. We finally sought to address two important cell types in terms of relevance to plant transformation, namely GT of germinal (egg) cells by floral dipping, and GT in somatic cells by root and leave transformation. To be successful, we made use of novel optimized expression cassettes that enable coexpression of all of the genes of interest (ZFNs and Rad genes) in the right tissues (egg or root cells) at the right time, namely when the GT vector is delivered into the cells. Methods were proposed for investigating the complementation of T-strands to dsDNA molecules in living plant cells. During the course of this research, we (i) designed, assembled and tested, in vitro, a pair of new ZFNs capable of targeting the Cruciferin gene, (ii) produced transgenic plants which expresses for ZFN monomers for targeting of the FtsH2 gene. Expression of these enzymes is controlled by constitutive or heat shock induced promoters, (iii) produced a large population of transgenic Arabidopsis lines in which mutated mGUS gene was incorporated into different genomic locations, (iv) designed a system for egg-cell-specific expression of ZFNs and RAD genes and initiate GT experiments, (v) demonstrated that we can achieve NHEJ-mediated gene replacement in plant cells (vi) developed a system for ZFN and homing endonuclease-mediated assembly of multigene plant transformation vectors and (vii) explored the mechanism of dsTDNA formation in plant cells. This work has substantially advanced our understanding of the mechanisms of DNA integration into plants and furthered the development of important new tools for GT in plants.

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Paradis, S., S. E. Jackson, D. Petts, G. J. Simandl, R. J. D'Souza, and T S Hamilton. Distribution of trace elements in pyrite from carbonate-hosted sulfide deposits of southern British Columbia. Natural Resources Canada/CMSS/Information Management, 2022. http://dx.doi.org/10.4095/328002.

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This paper combines petrography with in situ laser-ablation inductively coupled plasma mass spectrometry to document trace-element variations in pyrite (Py) from Mississippi Valley-type (MVT) and fracture-controlled replacement (FCR) deposits in the Kootenay Arc, British Columbia. Three generations of pyrite are Py 1, Py 2, and Py 3. Pyrite 1, the earliest (occurring in MVT deposits only), has higher Ag, Ba, Cu, Ge, Pb, Sb, Sr, Tl, and V than adjacent Py 3. It has higher Ag, Au, Ba, Cu, Ge, Pb, and Tl than Py 2. Pyrite 2 occurs in MVT and FCR deposits. Relative to FCR Py 2, MVT Py 2 is enriched in Co, Ni, Mo, Ba, Tl, and Pb and depleted in other elements. The FCR Py 2 has growth-related compositional banding, which is absent in MVT Py 2. The FCR Py 2 has Ag, Cu, Ga, Ge, In, Sn, and Zn enriched cores, intermediate Au- and As-rich bands, and Co- and Ni-rich rims. Pyrite 3, the latest occurring pyrite, present in MVT and FCR deposits, is enriched in Co and Ni near overgrowths or infillings of sphalerite. Variations in composition of Py reflect mineralogy, characteristics of ore-forming fluids, and differences in physicochemical conditions between MVT and FCR deposits at the time of ore deposition.

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Newton, Ronald, Joseph Riov, and John Cairney. Isolation and Functional Analysis of Drought-Induced Genes in Pinus. United States Department of Agriculture, September 1993. http://dx.doi.org/10.32747/1993.7568752.bard.

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Drought is a common factor limiting timber production in the U.S. and Israel. Loblolly (Pinus taeda) and alleppo pine (Pinus halepensis) seedling survival is reduced when out planted, and growth and reproduction are often hindered by periodic droughts during later stages of tree development. Molecular and gene responses to drought stress have not been characterized. The objectives were to characterize drought-induced gene clones from these pines, to determine the effects of a growth regulator on drought tolerance, ABA levels, and drought-induced gene expression in alleppo pine, and to develop procedures for loblolly pine transformation. Nearly 20 cDNA clones influenced by gradual, prolonged drought stress have been isolated. Many of these have been shown to be induced by drought stress, whereas several others are down-regulated. These are the first drought-induced genes isolated from a pine species. Two genomic clones (lp5-1 and lp3-1) have been sequenced and characterized, and each has been found to be associated with a gene family. Clone lp5 appears to code for a cell wall protein, and clone lp3 codes for a nuclear protein. The former may be associated with changing the elastic properties of the cell wall, while the latter may be involved in signal transduction and/or protection from desiccation in the nucleus. Clone lp3 is similar to a drought-induced gene from tomato and is regulated by ABA. Several DNA sequences that are specific to induction during growth-retardation in alleppo pine by uniconazole have been identified. The active DNA species is now being identified. Promoters from genomic clones, lp3 and lp5, have been sequenced. Both are functional when fused with the gus reporter gene and transferred to other plant tissues as well as responding to a simulated drought stress. Through exodeletion analysis, it has been established that the promoter ABRE element of lp3 responds to ABA and that drought-induction of lp3 expression may also involve ABA. Stable tobacco transformants carrying either the lp5 or the lp3 promoter fused to a reporter gus gene have been obtained. The lp5lgus fusion was expressed at several stages of tobacco development and differentiation including the reproductive stage. There was no difference in phenotype between the transformants and the wild type. Embryogenesis procedures were developed for slash pine, but attempts to couple this process with gene transfer and plantlet transformation were not successful. Transformation of pine using Agrobacterium appears tractable, but molecular data supporting stable integration of the Agrobacterium-transferred gene are still inconclusive.

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Eshed, Yuval, and John Bowman. Harnessing Fine Scale Tuning of Endogenous Plant Regulatory Processes for Manipulation of Organ Growth. United States Department of Agriculture, 2005. http://dx.doi.org/10.32747/2005.7696519.bard.

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Background and objectives: Manipulation of plant organ growth is one of the primary reasons for the success of mankind allowing increasing amounts of food for human and livestock consumption. In contrast with the successful selection for desirable growth characteristics using plant breeding, transgenic manipulations with single genes has met limited success. While breeding is based on accumulation of many small alterations of growth, usually arise from slight changes in expression patterns, transgenic manipulations are primarily based on drastic, non-specific up-regulation or knock down of genes that can exert different effects during different stages of development. To successfully harness transgenic manipulation to attain desirable plant growth traits we require the tools to subtly regulate the temporal and spatial activity of plant growth genes. Polar morphology along the adaxial/abaxial axis characterizes lateral organs of all plants. Juxtaposition of two cell types along this axis is a prerequisite of laminar growth induction. In the study summarized here, we addressed the following questions: Can we identify and harness components of the organ polarity establishment pathway for prolonged growth? Can we identify specific regulatory sequences allowing spatial and temporal manipulation in various stages of organ development? Can we identify genes associated with YABBY-induced growth alterations? Major conclusions and implications: We showed that regulated expression, both spatially and temporally of either organ polarity factors such as the YABBY genes, or the organ maturation program such as the CIN-TCPs can stimulate substantial growth of leaves and floral organs. Promoters for such fine manipulation could be identified by comparison of non-coding sequences of KAN1, where a highly conserved domain was found within the second intron, or by examination of multiple 5” regions of genes showing transient expression along leaf ontogeny. These promoters illustrate the context dependent action of any gene we examined thus far, and facilitate fine tuning of the complex growth process. Implications, both scientific and agricultural. The present study was carried out on the model organism Arabidopsis, and the broad application of its findings were tested in the tomato crop. We learned that all central regulators of organ polarity are functionally conserved, probably in all flowering plants. Thus, with minor modifications, the rules and mechanisms outlined in this work are likely to be general.

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