lifted domain

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 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.