<*theory*> In domain theory, a domain with a new bottom
element added. Given a domain D, the lifted domain, lift D
contains an element lift d corresponding to each element d in
D with the same ordering as in D and a new element bottom
which is less than every other element in lift D.

In functional languages, a lifted domain can be used to model a constructed type, e.g. the type

data LiftedInt = K Intcontains the values K minint .. K maxint and K bottom, corresponding to the values in Int, and a new value bottom. This denotes the fact that when computing a value v = (K n) the computation of either n or v may fail to terminate yielding the values (K bottom) or bottom respectively.

(In LaTeX, a lifted domain or element is indicated by a subscript \perp).

See also tuple.

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**Nearby terms:**
Life is hard « LIFIA « LIFO « **lifted domain** » LIGHT » light client » light-emitting diode

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Copyright Denis Howe 1985