This paper reports on a six-year collaborative effort that culminated in a complete
formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant …

This paper proposes generic design patterns to define and combine algebraic structures,
using dependent records, coercions and type inference, inside the Coq system. This …

We formally prove correct a C program that implements a numerical scheme for the
resolution of the one-dimensional acoustic wave equation. Such an implementation …

We present instance arguments: an alternative to type classes and related features in the
dependently typed, purely functional programming language/proof assistant Agda. They are …

This paper discusses the design of a hierarchy of structures which combine linear algebra
with concepts related to limits, like topology and norms, in dependent type theory. This …

This paper provides a gentle introduction to the art of programming type inference with the
mechanism of Canonical Structures. Programmable type inference has been one of the key …

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 …

The LAProof library provides formal machine-checked proofs of the accuracy of basic linear
algebra operations: inner product using conventional multiply and add, inner product using …

This paper describes a formalization of discrete real closed fields in the Coq proof assistant.
This abstract structure captures for instance the theory of real algebraic numbers, a …

We describe a step-by-step approach to the implementation and formal verification of
efficient algebraic algorithms. Formal specifications are expressed on rich data types which …