Competing Inheritance Paths in Dependent Type Theory: A Case Study in Functional Analysis

This paper discusses the design of a hierarchy of structures which combine linear algebra with concepts related to limits, like topology 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...

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Detalles Bibliográficos
Autores principales: Affeldt, Reynald, Cohen, Cyril, Kerjean, Marie, Mahboubi, Assia, Rouhling, Damien, Sakaguchi, Kazuhiko
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7324078/
http://dx.doi.org/10.1007/978-3-030-51054-1_1
Descripción
Sumario:This paper discusses the design of a hierarchy of structures which combine linear algebra with concepts related to limits, like topology 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. Issues of a more general nature related to the inheritance of poorer structures from richer ones arise due to this combination. We present and discuss a solution, coined forgetful inheritance, based on packed classes and unification hints.

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