About: 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.   Goto Sponge  NotDistinct  Permalink

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  • 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.
Subject
  • Mathematical analysis
  • Topology
  • Numerical analysis
  • Algebra
  • Linear algebra
  • Mathematical structures
  • Type theory
  • Functional languages
  • Free theorem provers
  • Proof assistants
  • OCaml software
  • Dependently typed programming
  • Type systems
  • 1989 software
  • Dependently typed languages
  • Educational math software
  • Extensible syntax programming languages
  • Free software programmed in OCaml
  • Programming languages created in 1984
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