Coquand

Coquand refers primarily to Thierry Coquand, a prominent French computer scientist known for his significant contributions to type theory, constructive mathematics, and the development of proof assistants.

Coquand's most notable achievement is arguably the development of the Calculus of Constructions, in collaboration with Gérard Huet. The Calculus of Constructions is a powerful type theory that serves as the foundation for the Coq proof assistant. It allows for the formalization and verification of mathematical proofs and computer programs.

Beyond the Calculus of Constructions, Coquand has made substantial contributions to areas such as:

• Martin-Löf Type Theory: He has extensively studied and contributed to the understanding and development of Martin-Löf Type Theory, another important foundational system for constructive mathematics and programming.
• Domain Theory: His work explores the mathematical foundations for denotational semantics of programming languages.
• Cubical Type Theory: Coquand has been a key figure in the development of cubical type theory, a recent extension of type theory that provides a computational interpretation of univalence and higher inductive types. This has significant implications for formalizing homotopy type theory within proof assistants.

Coquand's work has had a profound impact on the fields of computer science, logic, and mathematics, shaping the landscape of formal verification and constructive reasoning. His ideas continue to influence the design and development of modern proof assistants and type systems. His publications are highly regarded and widely cited in the research community.