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Concept
Empty type
Summary
In type theory, an empty type or absurd type, typically denoted is a type with no terms. Such a type may be defined as the nullary coproduct (i.e. disjoint sum of no types). It may also be defined as the polymorphic type
For any type , the type is defined as . As the notation suggests, by the Curry–Howard correspondence, a term of type is a false proposition, and a term of type is a disproof of proposition P.
A type theory need not contain an empty type. Where it exists, an empty type is not generally unique. For instance, is also uninhabited for any inhabited type .
If a type system contains an empty type, the bottom type must be uninhabited too, so no distinction is drawn between them and both are denoted .
Official source
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