Intensional Type Theories

Intensional Type Theories are frameworks used in mathematics and computer science to formalize the concepts of logical statements and computations, where the focus is on how terms and types are constructed and their internal structure. They distinguish between the identity of objects based on their construction, allowing for richer reasoning about equality and equivalence. This approach supports advanced features like dependent types, enabling more precise definitions and proofs, especially in programming languages and formal verification. Essentially, intensional type theories provide a rigorous foundation to represent and manipulate complex, structured mathematical and logical entities.