intuitionistic type theory

Intuitionistic type theory is a foundational framework for mathematics and logic that emphasizes constructive proof—which means proving something by explicitly demonstrating it rather than assuming it exists. It uses "types" to categorize mathematical objects and ideas, ensuring that every statement corresponds to a well-defined construct. This approach aligns with computational perspectives, as proofs can be viewed as programs or constructions. Unlike classical logic, it doesn't accept the law of the excluded middle (that every statement is either true or false without proof). Overall, intuitionistic type theory provides a rigorous and constructive foundation for reasoning about mathematics and computation.