singletype

Singletype, commonly referred to as a singleton type, is a type that has exactly one possible value or inhabitant. In type theory and programming language design, singleton types are used to encode information that is guaranteed to be unique by the type system. They provide a way to represent a quantity with no variable data and can support type-level programming and formal reasoning within dependently typed languages.

In practice, the unit type is the most familiar example of a singleton type. For instance, in Haskell the unit type is (), which has exactly one value, (). Other languages may call this the unit type or, in some contexts, the void type. A boolean can be viewed as a sum of two singleton types, since Bool is isomorphic to 1 + 1, where 1 denotes a singleton type.

Dependent type systems may parameterize singleton types by values, creating types that are inhabited only by terms equal to that value. This allows precise constraints to be expressed at the type level, enabling proofs of correctness, safer APIs, and optimizations driven by compile-time information. Singleton types are thus a tool for encoding invariants and guiding program construction through types rather than runtime checks.

Related concepts include the unit type, the bottom (empty) type, and broader notions of refinement or dependent types that allow types to depend on values. While the exact terminology varies by language and paradigm, singletype generally denotes the idea of a type with a single, uniquely determined inhabitant.