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Formalizing functional analysis structures in dependent type theory

Abstract : 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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https://hal.inria.fr/hal-02463336
Contributor : Marie Kerjean <>
Submitted on : Friday, January 31, 2020 - 7:42:34 PM
Last modification on : Thursday, January 7, 2021 - 3:40:10 PM
Long-term archiving on: : Friday, May 1, 2020 - 5:53:15 PM

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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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