deretypes

Deretypes is a term used in theoretical and applied contexts to denote derivative type constructs obtained by applying a fixed set of transformation rules to a base type. The concept is intended to generalize ideas from subtyping and type derivation, and it appears in discussions of programming languages, data modeling, and knowledge representation.

Formally, let B be a base type and R a defined collection of derivation rules. A deretype d is any type obtainable from B by zero or more applications of rules in R, under the language’s typing semantics. The collection of all such deretypes derived from B under R is denoted D(B, R). Deretypes thus describe how a single base type can evolve into related types through systematic transformations.

Classification of deretypes can be helpful for analysis. Intrinsic deretypes arise from the internal structure of the base type, while extrinsic deretypes depend on external annotations or context. Static deretypes are determined at compile time or during schema design, whereas dynamic deretypes may change with runtime conditions. Structural deretypes emphasize changes in shape or fields, while nominal deretypes rely on name-based distinctions.

Examples are found across domains. In a programming language with generics and constraints, a deretype might be a specialized version of a generic type with certain constraints applied. In schema languages, a deretype could be a variant of a data record with a modified field set. In knowledge graphs, a deretype may represent a derived concept produced by a transformation rule from a base concept.

Related concepts include subtyping, type derivation, and type refinement. Deretypes offer a unified lens for describing how types evolve under transformations, informing type inference, API design, and data modeling.