HO$$\pi $$ in Coq

Hopi Hoekstra

You are a Curator of Mammals, what does a Mammal Curator do? I head the mammal collection at Harvard’s Museum of Comparative Zoology (MCZ). The collection comprises specimens collected as early as the 1830s, the red squirrel series collected by Louis Agassiz (one of Darwin’s biggest foes), and hundreds of type specimens, including that of Gorilla gorilla. I have a terrific staff that looks afte...

Coq in Coq

We formalize the deenition and the metatheory of the Calculus of Constructions (CC) using the proof assistant Coq. In particular, we prove strong nor-malization and decidability of type inference. From the latter proof, we extract a certiied Objective Caml program which performs type inference in CC and use this code to build a small-scale certiied proof-checker.

Sets in Coq, Coq in Sets

We present a Coq reflexive tactic for deciding equalities or inequalities in Kleene algebras. This tactic is part of a larger project, whose aim is to provide tools for reasoning about binary relations in Coq: binary relations form a Kleene algebra, where the star operation is the reflexive transitive closure. Our tactic relies on an initiality theorem, whose proof goes by replaying finite auto...

Coq in

We formalize the deenition and the metatheory of the Calculus of Constructions (CC) using the proof assistant Coq. In particular, we prove strong nor-malization and decidability of type inference. From the latter proof, we extract a certiied Objective Caml program which performs type inference in CC and use this code to build a small-scale certiied proof-checker.

Health of the Navajo-Hopi Indians.