DDtype

DDtype is a theoretical data type used in programming language research to explore the combination of dependent and dynamic typing. It provides a framework for encoding invariants that depend on values as well as on types, allowing a single construct to express both compile-time guarantees and runtime flexibility.

A DDtype value pairs a runtime value with a type index, and the accompanying type expresses a predicate P(index, value). The index can be a natural number, a shape parameter, or any dependent parameter. In practice, a DDtype can encode structures such as vectors, matrices, or maps where size, shape, or key constraints must hold. If the index is not known at compile time, runtime checks enforce the constraint.

Example: a DDtype representing a vector of length n with elements of type T would carry the length n in its type; operations must maintain the invariant that the resulting vector's length matches its type index. When the index is unknown, the type system may require runtime validation to preserve safety.

Implementation and scope: DDtype is primarily a theoretical construct but has influenced language features in dependent type systems and gradual typing. It can improve safety in APIs and data modeling by making invariants explicit in types; however, it adds complexity and potential runtime overhead for checks.

Relation and further reading: Related concepts include dependent types, refinement types, multi-parameter type families, and gradual typing. See also dependent type, refinement type, dynamic typing, type safety.