ABtype

ABtype is a theoretical data construct used in programming language theory to represent a value that may be one of two distinct alternatives, A or B. It is a binary sum type, also known as a discriminated union, where exactly one variant is present at runtime.

Formal definition: ABtype<A, B> consists of two constructors, A(value: A) and B(value: B).

Semantics and usage: Values of ABtype are created by one of the two constructors. Pattern matching or case analysis is used to determine which variant is active, and code typically handles both possibilities. The type is parameterizable, so ABtype can carry any pair of types in A and B.

Relation to other types: ABtype is analogous to a sum type found in many languages, such as Haskell's Either a b or a TypeScript discriminated union. In languages without native sum types, ABtype can be simulated with tagged objects or class hierarchies with an explicit tag.

Use cases: ABtype is useful for modeling choices between two forms, such as a computation that may succeed with a value of type A or fail with a value of type B, or an input that is either provided (A) or missing (B). It supports exhaustive handling and precise type safety.

Examples: Haskell-like: data ABtype a b = A a | B b. TypeScript-like: type ABtype<a,b> = { tag: 'A', value: a } | { tag: 'B', value: b }.