Dependent Type Theory: a ﬁrst approximation - Chu Rivera, Fernando (2023)
We present Dependent Type Theory, which combines the concepts of propositions and sets in a more general one, that of “types”. We develop the main notions of this theory, and observe that it can serve as a foundation of mathematics, replacing set theory. We exemplify this studying the natural numbers, and explain how the use of proof assistants gives us a more rigorous foundation for mathematical results.