Dependent Type Theory
Dependent Type Theory (DTT) is a formal system in mathematical logic and computer science that extends simple type theory by allowing types to depend on terms. This enables the expression of more precise specifications and invariants directly within the type system, such as vectors of a specific length or matrices with certain dimensions. It serves as the foundation for proof assistants like Coq and Agda, and is closely related to homotopy type theory.
Developers should learn Dependent Type Theory when working on formal verification, theorem proving, or developing highly reliable software where correctness is critical, such as in aerospace, finance, or security systems. It is essential for using proof assistants to verify mathematical proofs or ensure program properties, and it enhances type safety by allowing types to encode complex constraints directly.