root edited this page Oct 11, 2017 · 23 revisions

Constructive Coq Repository at Nijmegen

FAQ about C-Corn

  1. In algebraic structures, why hava a separate structure for the axioms (as in is_CGroup) instead of putting the axioms with the group sturcture (CGroup)?

Sometimes the axiom structure is useful when an algebraic structure can be viewed as two different substructures. For example the additive structure of a CRing is an Abelian group and the multiplicative stucture is a monoid. By using a separate structure for the axioms, it is easy for the same stursture to share the same universe.

The same technique could be used to define a vector space as an Abelian group with a field action plus a distributive law.

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