RealsBooleans

RealsBooleans is a term used in theoretical computer science and language design to describe a composite data type that unifies real numbers and boolean values into a single value domain. Formally, it can be modeled as a tagged union of the real numbers R and the boolean set {true, false}, sometimes written as R ⊎ {true, false}. A value of this type is either a real number or a boolean, and the two kinds of values carry distinct tags to allow runtime or compile-time distinction.

Semantics and operations are typically defined to respect the separation between the two branches. Arithmetic and most numeric operations are defined only when both operands are real numbers, yielding real results. Boolean operations are defined when operands are booleans, yielding booleans. In mixed contexts, languages may coerce booleans to numbers (for example, false = 0, true = 1) or raise a type error, depending on the design. Some approaches also provide explicit conversion functions, such as toReal and toBool, to manage these transitions.

Programming language implementations may use realsBooleans as a variant or sum type, enabling pattern matching to handle the two cases safely. This can support DSLs, templating systems, or domain-specific workflows where numerical data and truth values must be carried in a common channel.

Relation to other concepts includes sum types and variant types, option types, and dynamic typing systems that permit mixed-value containers. RealsBooleans is not a standard primitive in mainstream languages, but it conceptually illustrates how a single type can accommodate distinct data facets while preserving type distinctions through tagging and explicit conversions.