Results 11 to 20 of about 173,804,276 (284)
Definitions by rewriting in the Calculus of Constructions [PDF]
Mathematical Structures in Computer Science, 2002 Journal version of LICS ...
Blanqui, Frédéric
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Inductive Types in the Calculus of Algebraic Constructions [PDF]
, 2003 In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules.
Blanqui, Frédéric
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Classical Program Extraction in the Calculus of Constructions [PDF]
, 2007 We show how to extract classical programs expressed in Krivine λc-calculus from proof-terms built in a proof-irrelevant and classical version of the calculus of constructions with universes. For that, we extend Krivine's realisability model of classical second-order arithmetic to the calculus of constructions with universes using a structure of Π-set ...
Miquel, Alexandre
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Investigations on a Pedagogical Calculus of Constructions
J. Univers. Comput. Sci., 2012 18 ...
Colson,Loïc, Demange,Vincent
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Variants of the basic calculus of constructions
Journal of Applied Logic, 2004 Different formulations of the calculus of constructions, introduced by Coquand in 1985, are compared. The different formulations have some things in common, namely the terms and forms of judgements, the axiom (just a single axiom for all the variants), and the form of the application and product rules.
Martin W. Bunder, Jonathan P. Seldin
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A calculus of constructions with explicit subtyping [PDF]
, 2014 International audienceThe calculus of constructions can be extended with an infinite hierarchy of universes and cumulative subtyping. In this hierarchy, each universe is contained in a higher universe.
Assaf, Ali
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An Iterator Construct for the Refinement Calculus [PDF]
Electronic Workshops in Computing, 2000 This paper concerns the introduction of an iterator into the refinement calculus. The construct is based on concepts from functional programming, and the work gives an interesting example of cross-fertilisation between the functional and imperative programming worlds.
Steve King 0001, Carroll Morgan
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Proof-irrelevant model of CC with predicative induction and judgmental equality [PDF]
Logical Methods in Computer Science, 2011 We present a set-theoretic, proof-irrelevant model for Calculus of Constructions (CC) with predicative induction and judgmental equality in Zermelo-Fraenkel set theory with an axiom for countably many inaccessible cardinals. We use Aczel's trace encoding
Gyesik Lee, Benjamin Werner
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A simple model construction for the Calculus of Constructions [PDF]
, 1996 We present a model construction for the Calculus of Constructions (CC) where all dependencies are carried out in a set-theoretical setting. The Soundness Theorem is proved and as a consequence of it Strong Normalization for CC is obtained. Some other applications of our model constructions are: showing that CC + Classical logic is consistent (by ...
Stefanova, M., Geuvers, H.
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Letnikov vs. Marchaud: A Survey on Two Prominent Constructions of Fractional Derivatives
Mathematics, 2017 In this survey paper, we analyze two constructions of fractional derivatives proposed by Aleksey Letnikov (1837–1888) and by André Marchaud (1887–1973), respectively. These derivatives play very important roles in Fractional Calculus and its applications.
Sergei Rogosin, Maryna Dubatovskaya
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