Reporting on joint work with V. Danos and I. Garnier, I will present a novel formulation of graph rewriting that permits to phrase the concept in a fashion akin to statistical physics. The key ingredient of this approach is the rule algebra framework, in which rewriting rules are interpreted as a type of diagrams endowed with a notion of sequential compositions. The focus of this talk will be the stochastic mechanics applications: once an associative algebra of rewriting rules is available in the form of the rule algebras, the full theory of continuous time Markov chains is at ones disposal. A number of explicit examples for computing in this formalism will be presented.

tba

Numerous contributions have been made for some years to allow users to exchange formal proofs between different provers. The main propositions consist in ad hoc pointwise translations, e.g. between HOL Light and Isabelle in the Flyspeck project or uses of more or less complete certificates. We propose a methodology to combine proofs coming from different theorem provers. This methodology relies on the Dedukti logical framework as a common formalism in which proofs can be translated and combined. To relate the independently developed mathematical libraries used in proof assistants, we rely on the structuring features offered by FoCaLiZe, in particular parameterized modules and inheritance to build a formal library of transfer theorems called MathTransfer. We finally illustrate this methodology on the Sieve of Eratosthenes, which we prove correct using HOL and Coq in combination.