Arithmetics of Dependent Types

Arithmetic of dependent types involves working with mathematical types where values can influence the type itself. Unlike simple types (e.g., integers), dependent types allow types to depend on specific data—like defining a "vector of length n," where "n" is a number. This enables more precise programming and verification, ensuring operations are valid (e.g., adding vectors of compatible sizes). The arithmetic rules for these types extend standard mathematical operations into the realm of types, so reasoning about data structure sizes and properties is built directly into the type system, leading to safer and more expressive code.