Automatic and Transparent Transfer of Theorems along Isomorphisms in the Coq Proof Assistant

摘要

In mathematics, it is common practice to have several constructionsfor the same objects.Mathematicians will identify them modulo isomorphism and willnot worry later on which construction they use, as theorems provedfor one constructionwill be valid for all.When working with proof assistants, it is also common to see severaldata-types representing the same objects.This work aims at making the use of several isomorphic constructionsas simple and as transparent as it can be done informally inmathematics.This requires inferring automatically the missing proof-steps.We are designing an algorithm which finds and fills these missingproof-steps and we are implementing it as a plugin for Coq.