Empty type
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In type theory, an empty type or absurd type, typically denoted \mathbb 0 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 \forall t.t For any type P , the type \neg P is defined as P\to \mathbb 0 . As the notation suggests, by the Curry–Howard correspondence, a term of type \mathbb 0 is a false proposition, and a term of type \neg P 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, T \to \mathbb 0 is also uninhabited for any inhabited type T . 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 \bot .
In type theory, an empty type or absurd type, typically denoted \mathbb 0 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 \forall t.t For any type P , the type \neg P is defined as P\to \mathbb 0 . As the notation suggests, by the Curry–Howard correspondence, a term of type \mathbb 0 is a false proposition, and a term of type \neg P 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, T \to \mathbb 0 is also uninhabited for any inhabited type T . 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 \bot . ==References==
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