SAKAGUCHI , Kazuhiko

It is nowadays customary to organize libraries of machine checked proofs around hierarchies of algebraic structures [2, 6, 8, 16, 18, 23, 27]. One influential example is the Mathematical Components library on top of which the long and intricate proof of the Odd Order Theorem could be fully formalized [14]. Still, building algebraic...

Using order structures in a proof assistant naturally raises the problem of working with multiple instances of a same structure over a common type of elements. This goes against the main design pattern of hierarchies used for instance in Coq's MathComp or Lean's mathlib libraries, where types are canonically associated to at most one instance...

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The Mathematical Components library (hereafter, MathComp) provides, among others, a number of mathematical structures organized as hierarchies. Hierarchy Builder (hereafter, HB) is an extension of the Coq proof assistant to ease the development of hierarchies of structures. MathComp 2 is the result of the port of MathComp to HB. This document...

We report on the porting of the Mathematical Components library (hereafter MC) to the Hierarchy Builder [2] tool (hereafter HB).