Primality Tests and Prime Certificate

This note presents a formalisation done in Coq of Lucas-Lehmer test and Pocklington certificate for prime numbers. They both are direct consequences of Fermat little theorem. Fermat little theorem is proved using elementary group theory and in particular Lagrange theorem

A Formalisation of the Generalised Towers of Hanoi

This notes explains how the optimal algorithm for the generalised towers of Hanoi has been formalised in the Coq proof assistant using the SSReflect extension

Stålmarck's Algorithm in Coq: A Three-Level Approach

One of the most efficient method to check if a boolean proposition is a tautology is Stålmarck's algorithm. This paper reports on some experiments in integrating this algorithm inside the Coq theorem prover in a safe way

Proving the group law for elliptic curves formally

This report presents a formal proof of the group law for elliptic cu rves done in Co

Simplifying Polynomial Expressions in a Proof Assistant

This paper presents a simple way of performing polynomial simplifications in a proof assistant. This method has been implemented and tested within the Coq prover

Playing with the Tower of Hanoi Formally

The Tower of Hanoi is a typical example that illustrates all the power of recursion in programming. In this paper, we show that it is also a very nice example for inductive proofs and formal verification. We present some non-trivial results about it that have been formalised in the Coq proof assistant

A Formalisation of a Fast Fourier Transform

This notes explains how a standard algorithm that constructs the discrete Fourier transform has been formalised and proved correct in the Coq proof assistant using the SSReflect extension

A Formalisation of Algorithms for Sorting Network

This notes explains how standard algorithms that construct sorting networks have been formalised and proved correct in the Coq proof assistant using the SSReflect extension