Alternative to set theory, and some say it is better for proof assistants, and many of the most popular proof assistants of the 2020s use it e.g. Lean and Coq.
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Type theory is a branch of mathematical logic and computer science that deals with the classification of entities into types. It serves as a framework for formalizing reasoning about programs and mathematical propositions, providing a foundation for understanding and manipulating both data and functions. Here are some key aspects of type theory: 1. **Types as a Foundation**: In type theory, everything has a type, which describes the nature of a value or expression.