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Pré-Publication, Document De Travail Année : 2020

Formalizing functional analysis structures in dependent type theory

Résumé

This paper discusses the design of a hierarchy of structures which combine linear algebra with concepts related to limits, like topol-ogy and norms, in dependent type theory. This hierarchy is the backbone of a new library of formalized classical analysis, for the Coq proof assistant. It extends the Mathematical Components library, geared towards algebra, with topics in analysis. This marriage arouses issues of a more general nature, related to the inheritance of poorer structures from richer ones. We present and discuss a solution, coined forgetful inheritance, based on packed classes and unification hints.
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Dates et versions

hal-02463336 , version 1 (31-01-2020)
hal-02463336 , version 2 (17-04-2020)

Identifiants

  • HAL Id : hal-02463336 , version 1

Citer

Reynald Affeldt, Cyril Cohen, Marie Kerjean, Assia Mahboubi, Damien Rouhling, et al.. Formalizing functional analysis structures in dependent type theory. 2020. ⟨hal-02463336v1⟩

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