FV Time is a small-scale verification project developed in the Coq proof assistant using the
Mathematical Components libraries. It is a library for managing conversions between time …

This document is an introduction to the definition and use of recursive types in the Coq proof
environment. It explains how recursive types like natural numbers and infinite streams are …

We describe an interface between the Coq proof assistant and the Maple symbolic
computation system, which mainly consists in importing, in Coq, Maple computations …

Coq Modulo Theory (CoqMT) is an extension of the Coq proof assistant incorporating, in its
computational mechanism, validity entailment for user-defined first-order equational …

Transitive closure logic is a known extension of first-order logic obtained by introducing a
transitive closure operator. While other extensions of first-order logic with inductive …

A cyclic proof system gives us another way of representing inductive definitions and efficient
proof search. In 2011 Brotherston and Simpson conjectured the equivalence between the …

We describe the design and implementation of an automated theorem prover realising a
fully general notion of cyclic proof. Our tool, called Cyclist, is able to construct proofs obeying …

Brotherston and Simpson [citation] have formalized and investigated cyclic reasoning,
reaching the important conclusion that it is at least as powerful as inductive reasoning …

Abstract In his book “The Art of Computer Programming”, Donald Knuth gives an algorithm to
compute the first n prime numbers. Surprisingly, proving the correctness of this simple …

Non-terminating (dependencies of) definitions can lead to logical contradictions, for example
when defining a boolean constant as its own negation. Some proof assistants thus detect …