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 Int
contains 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.