Results 11 to 20 of about 927,891 (245)
A modular construction of type theories
Logical Methods in Computer Science, 2023 The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of U corresponding to each of these systems, and prove that, when a proof in U uses only symbols of a ...
Frédéric Blanqui +4 more
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Hajós-Type Constructions and Neighborhood Complexes [PDF]
SIAM Journal on Discrete Mathematics, 2020 Any graph $G$ with chromatic number $k$ can be constructed by iteratively performing certain graph operations on a sequence of graphs starting with $K_k$, resulting in a variety of Hajós-type constructions for $G$. Finding such constructions for a given graph or family of graphs is a challenging task.
Benjamin Braun, Julianne Vega
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Constructions with Countable Subshifts of Finite Type [PDF]
Fundamenta Informaticae, 2013 We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable SFT whose iterated derivatives are maximally complex from the computational point of view, constructions of ...
Ville Salo, Ilkka Törmä
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Constructive Bounds for a Ramsey-Type Problem [PDF]
Graphs and Combinatorics, 1997 Many important bounds for the Ramsey function \(R(s,t)\) are proved using probabilistic techniques. Some additional constructive ideas have been developed in recent years, but they usually give weaker bounds. The authors consider a more general Ramsey type function, and give constructive bounds for this function. In particular, given integers \(r\) and
Noga Alon, Michael Krivelevich
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Typed closure conversion for the calculus of constructions [PDF]
ACM SIGPLAN Notices, 2018 Dependently typed languages such as Coq are used to specify and verify the full functional correctness of source programs. Type-preserving compilation can be used to preserve these specifications and proofs of correctness through compilation into the generated target-language programs.
Bowman, William J., Ahmed, Amal
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Archiv für Mathematische Logik und Grundlagenforschung, 1966 Publisher Summary This chapter explains constructive order types. The theory of constructive order types constitutes a new approach to the problem of providing a constructive analogue of ordinal number theory. Ordinal number theory may be approached in two ways: (1) ordinals may be considered as being generated in a certain way, and (2) ordinals may ...
Crossley, John N., Aczel, P.H.G.
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A dependently-typed construction of semi-simplicial types [PDF]
Mathematical Structures in Computer Science, 2014 This paper presents a dependently-typed construction of semi-simplicial sets in a type theory where sets are taken to be types. This addresses an open question raised on the wiki of the special year on Univalent Foundations at the Institute of Advanced Study (2012–2013).
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Construction and deduction in type theories [PDF]
, 1999 This dissertation is concerned with interactive proof construction and automated proof search in type theories, in particular the Calculus of Construction and its subsystems. Type theories can be conceived as expressive logics which combine a functional programming language, strong typing and a higher-order logic.
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An explicit construction of type A Demazure atoms [PDF]
Journal of Algebraic Combinatorics, 2008 15 pages; final ...
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Virtual Evidence: A Constructive Semantics for Classical Logics [PDF]
, 2014 This article presents a computational semantics for classical logic using constructive type theory. Such semantics seems impossible because classical logic allows the Law of Excluded Middle (LEM), not accepted in constructive logic since it does not have
Constable, Robert L.
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