C4type

C4type is a theoretical construct in type theory used to describe a class of types formed from four primitive components and governed by a fixed set of composition rules.

The name combines C for constraint or classification and 4 for the four parts.

In the most common formalization, a C4type is a quadruple (K, S, C, R) where K is a core type expression, S is a set of constraints parametrizing K, C is a context that provides ambient assumptions, and R is a resolution rule that derives a concrete type from K, S, and C.

The semantics of a C4type is given by an interpretation that assigns to each quadruple a type in the host language, ensuring closure under a composition operator and invariance under renaming.

C4types are primarily studied in theoretical contexts to explore how multi-component type information interacts and propagates through code modules.

Examples include a C4type representing an optional value with a constraint on its payload and a context-dependent unit type, or a four-ary function type where the result constraint depends on the three inputs.

Applications of the concept are mainly in research on type systems, modular verification, and formalizing multi-parameter type constructors.

While some programming languages incorporate ideas related to multi-parameter or constrained types, C4type itself is not a widely implemented feature; it serves as a formal tool for analysis and comparison of type-system design.

See also type theory, dependent types, generics, multi-parameter type classes, constrained types.