Martin-Löf type theory

Martin-Löf type theory is a mathematical framework that combines logic and computation, providing a formal system to define, reason about, and verify mathematical objects and their relationships. It treats types as collections of objects and uses rules to construct and validate proofs, ensuring consistency and correctness. Think of it as a foundational language that helps mathematicians and computer scientists rigorously describe complex concepts, formalize proofs, and develop verified software. Its structured approach allows for precise, constructive reasoning about what exists and how entities relate within a logical universe.