Proofs and Types

Proofs and types are ideas from mathematics and computer science that help verify correctness. A *proof* demonstrates that a statement is true, much like a convincing argument. *Types* categorize data and functions, ensuring they are used correctly—for example, distinguishing numbers from text. In programming, types help prevent errors by confirming inputs and outputs match expectations. Combining these concepts, a system can automatically check that a program not only runs but also adheres to its specifications, making software more reliable and safe.