In the movie, WALL•E, we see that he has compacted the trash, then he builds a "building" out of the blocks.
Is that WALL•E's own doing, or is that part of his programming?
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Building towers of trash are part of WALL•E's core functionality. He and his fellows are dropped off at a location with significant amounts of loose rubbish, compress it into towers which are then fed (via cranes) into incinerators.
The history of "trash planet" is that the Buy n Large Corporation sort of took over everything in true big box style and slowly mismanaged the handling of trash and eventually it overwhelmed the planet to the point where the humans have to get off so that the Buy n Large Corporation can just clean it without humans getting in the way and so they had to design little robots [like WALL•E] that could maneuver their way all around this way which is a WALL•E, and they would cube the trash, set it aside and then they would build towers and it then allows these large city-block wide sized incinerators that are on big tank treads to sort of roll in and like a hay baler with a big crane that can slice the towers down into digestible sections and incinerate them
You can see the cranes, along with some half-eaten towers, in the opening scenes as WALL•E returns to his mobile base.
The plan is clarified further by a bonus featurette on the home release called "Operation Cleanup":
Back on Earth, an army of BnL "super-automatons" take charge of the cleanup. The WALL•Es will gather, cube, and vertically stratify waste into orderly towers. Mobile BnL incinerator units will then take over, reducing each tower to a combustion stream while harmful vapors are simultaneously pumped out of the atmosphere.