Cool concept, got a bit of a laugh out of the "tadaa" effect.
I was having issues with the command inputs though. For example, when I do <- 0 and ^ 5, it seems to do both at once, causing a diagonal direction.
Also you should limit the number of moves the player can make, either on a level-by-level basis or a hard cap. I was able to stack so many ^ 0s that I broke out of the level bounds. It only shows 14 arrows on the display, but it seems like you can add an infinite number.
Also the grid is ever so slightly off center so there's a little white space on the side. Super minor nitpick.
Didn't have time to go through a lot of levels, but what you had as far as level design seemed interesting!