AFFELDT , Reynald

We report on an original formalization of measure and integration theory in the Coq proof assistant. We build the Lebesgue measure following a standard construction that had not yet been formalized in proof assistants based on dependent type theory: by extension of a measure over a semiring of sets. We achieve this formalization by leveraging...

We are interested in the formal specification of safety properties of robot manipulators down to the mathematical physics. To this end, we have been developing a formalization of the mathematics of rigid body transformations in the COQ proof-assistant. It can be used to address the forward kinematics problem, i.e., the computation of the...

Probabilistic programming languages are used to write probabilistic models to make probabilistic inferences. A number of rigorous semantics have recently been proposed that are now available to carry out formal verification of probabilistic programs. In this paper, we extend an existing formalization of measure and integration theory with...

Formalizing analysis on a computer involves a lot of "epsilon-delta" reasoning, while informal reasoning may use some asymptotical hand-waving. Whether or not the arithmetic details are hidden using some abstraction like filters, a human user eventually has to break it down for the proof assistant anyway, and provide a witness for the...

International audience

The Mathematical Components library (hereafter, MathComp) provides, among others, a number of mathematical structures organized as hierarchies. Hierarchy Builder (hereafter, HB) is an extension of the Coq proof assistant to ease the development of hierarchies of structures. MathComp 2 is the result of the port of MathComp to HB. This document...

We report on the porting of the Mathematical Components library (hereafter MC) to the Hierarchy Builder [2] tool (hereafter HB).