  We propose a new extension of higher-order pushdown automata, which allows to
use an infinite alphabet. The new automata recognize languages of data words
(instead of normal words), which beside each its letter from a finite alphabet
have a data value from an infinite alphabet. Those data values can be loaded to
the stack of the automaton, and later compared with some farther data values on
the input. Our main purpose for introducing these automata is that they may
help in analyzing normal automata (without data). As an example, we give a
proof that deterministic automata with collapse can recognize more languages
than deterministic automata without collapse. This proof is simpler than in the
no-data case. We also state a hypothesis how the new automaton model can be
related to the original model of higher-order pushdown automata.
