Type- Theoretical Foundations of the Derivation System in Coq

This paper presents an analysis of a type theory, which serves as a solid foundation for usage of the derivation system in Coq proof assistant. An overview of the extension path from simply typed lambda calculus to Calculus of Inductive Constructions provides important insights about the type system of highly expressive functional programming language inside Coq, called Gallina. The correspondence between type theory expressions and Coq constructions is established.