Formalizing the trading theorem in Coq

Formalizing C in Coq

The CH2O project at the RU Nijmegen works towards developing a Coq formalization of a significant fragment of the C programming language as described by the C11 standard. In this project, we have developed a (non-deterministic small step) operational and executable semantics of a typed C core language, a type correct translation of actual C programs into this core language, and extensions of se...

Formalizing Stålmarck's Algorithm in Coq

We present the development of a machine-checked implementation of St̊almarck’s algorithm. First, we prove the correctness and the completeness of an abstract representation of the algorithm. Then, we give an effective implementation of the algorithm that we prove correct.

Formalizing the Hamming Stream in Coq

A case study in formalizing projective geometry in Coq: Desargues theorem

Formalizing geometry theorems in a proof assistant like Coq is challenging. As emphasized in the literature, the non-degeneracy conditions lead to long technical proofs. In addition, when considering higher-dimensions, the amount of incidence relations (e.g. point-line, point-plane, line-plane) induce numerous technical lemmas. In this article, we investigate formalizing projective plane geomet...

Formalizing Projective Plane Geometry in Coq

We investigate how projective plane geometry can be formalized in a proof assistant such as Coq. Such a formalization increases the reliability of textbook proofs whose details and particular cases are often overlooked and left to the reader as exercises. Projective plane geometry is described through two different axiom systems which are formally proved equivalent. Usual properties such as dec...