Formal Adventures in Convex and Conical Spaces

[2004.12713] Formal Adventures in Convex and Conical Spaces

We formalize in Coq an intrinsic axiomatization of convex sets, namely convex spaces, based on an operation taking barycenters of points.

Abstract. Convex sets appear in various mathematical theories, and are used to define notions such as convex functions and hulls. As an.

Formal Adventures in Convex and Conical Spaces

and conical spaces. Multiary ax- iomatizations of convex spaces. Conclusion and future work. Formal Adventures in Convex and Conical. Spaces.

Formal Adventures in Convex and Conical Spaces - Semantic Scholar

This work formalizes in Coq an intrinsic axiomatization of convex sets, namely convex spaces, based on an operation taking barycenters of points, ...

Formal Adventures in Convex and Conical Spaces

A convex space corresponds to a specific type that does not refer to a surrounding vector space. This simplifies the definitions of functions on ...

Formal Adventures in Convex and Conical Spaces | Request PDF

Request PDF | Formal Adventures in Convex and Conical Spaces | Convex sets appear in various mathematical theories, and are used to define notions such as ...

Formal Adventures in Convex and Conical Spaces - OUCI

Affeldt, R., Cohen, C., Rouhling, D.: Formalization techniques for asymptotic reasoning in classical analysis. J. Formaliz. Reason. 11(1), 43–76 (2018) ...

Locally Convex Cones - SpringerLink

Reynald Affeldt - DBLP

Formal Adventures in Convex and Conical Spaces. CICM 2020: 23-38 ... Formal Adventures in Convex and Conical Spaces. CoRR abs ...

Convexity theories IV. Klein-Hilbert parts in convex modules

‪Takafumi Saikawa‬ - ‪Google Scholar‬

Monadic equational reasoning in Coq. R Affeldt, J Garrigue, D Nowak, T Saikawa, C Sauvage, K Tanaka. 4, 2019. Formal adventures in convex and conical spaces. R ...

Mathematical Components: Research Papers

Formal adventures in convex and conical spaces. CICM 2020. pdf; Reynald Affeldt, Jacques Garrigue, Takafumi Saikawa. Reasoning with conditional probabilities ...

On strongly E-convex sets and strongly E-convex cone ... - R Discovery

We define strongly -convex hull, strongly -convex cone, and strongly ... Formal Adventures in Convex and Conical Spaces. Reynald Affeldt ... Takafumi ...

[PDF] Semiconvex geometry | Semantic Scholar

Formal Adventures in Convex and Conical Spaces · Reynald AffeldtJacques ... 2020. TLDR. This work formalizes in Coq an intrinsic axiomatization of convex sets, ...

Probability theory can be fun and simple with dependent types (Yet ...

Reynald Affeldt, Jacques Garrigue, and Takafumi Saikawa. Formal adventures in convex and conical spaces. In. 13th Conference on Intelligent ...

Bibliographies: 'Conical space' – Grafiati

AbstractLet X be a locally convex space. Kluvánek associated to each X-valued ... "Formal Adventures in Convex and Conical Spaces." In Lecture Notes in ...

ACM 204, FALL 2018: LECTURES ON CONVEX GEOMETRY JOEL ...

convex topological vector spaces. Compact sets in infinite-dimensional ... A convex cone is a convex set K ⊂ Rd that is positively homogeneous: 𝜆K ...

Luenberger's Optimization by Vector Space Methods

... Convex Sets 131. *5.13 Duality in Minimum Norm Problems 134. 5.14 Problems 137 ... formal definition of a vector space is not given until. Chapter 2, we ...

A Trustful Monad for Axiomatic Reasoning with Probability ... - arXiv

We use convex spaces to define convex sets and convex hulls. As ... Formal adventures in convex and conical spaces. In Benzmüller, C ...

Jacques Garrigue - Papers - researchmap

Formal Adventures in Convex and Conical Spaces. Reynald Affeldt, Jacques Garrigue, Takafumi Saikawa. Lecture Notes in Computer Science, 23-38, 2020. Formal ...