Source : Free On-Line Dictionary of Computing

lifted domain
     
         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 language}s, 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}.