Haut PDF The Three Gap Theorem : Specification and Proof in Coq
The Three Gap Theorem : Specification and Proof in Coq
... Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, ` NANCY 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES Unit´e de recherche INRIA Rennes, Ir[r] ...
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Specification and Proof of High-Level Functional Properties of Bit-Level Programs
... tools and experiments. Stefan Berghofer (Secunet, Germany) is using the sup- port for bit vectors in SPARK, on the big number package of libsparkcrypto ( https: ...discharge the VCs ...
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Coq Coq Correct! Verification of Type Checking and Erasure for Coq, in Coq
... France Coq is built around a well-delimited kernel that perfoms typechecking for definitions in a variant of the Calculus of Inductive Constructions ...Although the metatheory of CIC is very ...
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CoqIOA : a formalization of IO automata in the Coq proof assistant
... a proof assistant, but the approaches do not support proper compositional ...automata in the Larch Prover [ 11 ], does not support automata composition at ...automata specification ...
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Implementation of Bourbaki's Elements of Mathematics in Coq: Part Three Structures
... T. In this case X = Y and X 0 = Y 0 ...(our proof relies in the fact that 0 = ;, 1 = {0}, 2 = {0, 1} and 3 = {0, 1, 2}; but obviously a set with three elements cannot be a ...
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Coqoon An IDE for interactive proof development in Coq
... Introduction In the last decade, computer-aided proof development has been gaining mo- ...Interactive proof assistants allow their users to state a mathematical theorem in a ...
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A Formal Proof in Coq of LaSalle's Invariance Principle
... the existence of an equilibrium plays no role in the validity of Theorem ...removed the hypothesis F (0) = 0. Still regarding the vector field F , the assumption “F has ...
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The proof-theoretic strength of Ramsey's theorem for pairs and two colors
... program and finitistic reductionism During the early 20th century, mathematics went through a serious foundational crisis, with the discovery of various paradoxes and ...e and Brouwer ...
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A Formal Proof in Coq of a Control Function for the Inverted Pendulum
... use the notation A `&` B for the intersection of A with B and A !=set0 for exists p, A ...p. In our formalization of the inverted pendulum from Lozano et ...that the set K is ...
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A Generic Coq Proof of Typical Worst-Case Analysis
... read the specification and the main correctness theorem; there is no need to look at the proof itself which is ...a proof assistant brings other benefits. Since ...
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A Case Study in Formalizing Projective Geometry in Coq: Desargues Theorem
... geometry in the Coq proof assistant [1, 7] and studies Desargues property both in the plane and in an at least three dimensional setting (noted ≥ ...
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Applications of Foundational Proof Certificates in theorem proving
... written in OCaml side by side with a formalization of this MaxChecker in Coq which was restricted to the propositional ...fragment. In extending this treatment to the ...
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Short proof of Menger's Theorem in Coq (Proof Pearl)
... while the library could profit from some additional cleanup ...conventions and additional documentation), it is already quite usable. In order to establish the library as generally useful, ...
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Formalizing Desargues' theorem in Coq using ranks in Coq
... ely in
iden
e re- lations in a 3D setting thanks to ranks and designed an axiom system to apture proje
tive geometry using ...Desargues' theorem. We presented proof engineering te
...
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Parameterized Specification and Verification of PLC Systems in Coq
... that the specification language they choose is TLA + ...extensively in the field of ...Besides the benefits it brings to the software development, it also helps the formal ...
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An Existence Theorem of Nash Equilibrium in Coq and Isabelle
... of the base case were proved independently in [12] and ...[11]. The fact that the idea behind the theorem emerged in different communities suggests that it is ...
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Design of a proof assistant: Coq version 7
... presented the new implementation of the system Coq. It ombines the eÆ
ien
y and safety requirements in a ompletely new design, where the riti
al part of the system, ...
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A Geometric Proof of Hermite’s Theorem in Function Fields
... be the Galois closure of K over ...not, in general, a geo- metric extension, so there remains some work to be ...be the con- stant field of L. Then, L is a geometric and Galois extension of k ...
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A PROOF OF THE CAFFARELLI CONTRACTION THEOREM VIA ENTROPIC REGULARIZATION
... In the setting of Theorem 1, it turns out that much more can be said about the functions f and ...explained in the following result, which seems of independent ...
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Money Transfer Made Simple: a Specification, a Generic Algorithm, and its Proof
... that the previously cited reliable broadcast algorithms do not use sequence ...represents the current value of p i ’s account. This object provides the processes with two operations denoted balance() ...
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