Reseña: Experience implementing a performant category-theory library in Coq
Se ha publicado un artículo de razonamiento formalizado en Coq titulado Experience implementing a performant category-theory library in Coq
Sus autores son Jason Gross, Adam Chlipala y David Spivak (del MIT).
Su resumen es
*We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to cope with large categorical constructions without slowing proof script processing unacceptably. In this paper, we share the lessons we have learned about how to represent very abstract mathematical objects and arguments in Coq and how future proof assistants might be designed to better support such reasoning. One particular encoding trick to which we draw attention allows category-theoretic arguments involving duality to be internalized in Coq’s logic with definitional equality. Ours may be the largest Coq development to date that uses the relatively new Coq version developed by homotopy type theorists, and we reflect on which new features were especially helpful. *
El trabajo se presentó el 14 de julio en el ITP 2014 (5th Conference on Interactive Theorem Proving).
El código de las correspondientes teorías en Coq se encuentra aquí.