Topic summary
Dependent types
Extracted from the Wikipedia article Dependent type.
Dependent types add complexity to a type system. Deciding the equality of dependent types in a program may require computations. If arbitrary values are allowed in dependent types, then deciding type equality may involve deciding whether two arbitrary programs produce the same result; hence the decidability of type checking may depend on the given type theory's semantics of equality, that is, whether the type theory is intensional or extensional.