Thanks everyone...this is all really neat. I like the idea of the shadows staying the same and getting greater contrast between the shadows and higher midtones and highlights, if I understand correctly.
Before I was unclear why use 400 ASA at 800 instead of just using 800. But, this is exactly what I always did with digital files...clipping the highlights, pushing up the mid-tones and losing some details in the shadows. With film, the additional benefit would be more grain...and I can't tell you how much I love film grain (in moderation, of course!)
I'm not sure taking 400 ASA up to 1600 would be good...too much and the image starts to become more like a cutout graphic and less like a photo. But 400 to 800 or 800 to 1600 sounds like a nice way to add some character to the film.
Careful!
To be pedantic, "pushing" film really only refers to the development stage - it means increasing development, and therefore contrast.
People often erroneously refer to "pushing" film, when they really mean a combination of two things: under-exposing the film, and then trying to compensate by increasing development.
If you under-expose the film, you lose shadow detail, which you (mostly) cannot retrieve by increasing development. All you can achieve by increasing the time is to make the contrast of the near shadows appear more attractive.
If you expose the film by metering at the ISO speed (i.e. you do
not under-expose it), and then push the development, you will retain the shadow detail, and increase the contrast of everything. Your shadows will become more differentiated from the mid-tones, although you may very well lose highlight detail. With modern films though, much of the highlight detail may be retrievable with printing manipulations. And if you want the shadows to be dark enough to hide the details that are there, you can achieve that through printing controls.
In Zone System speak, increasing the development when shadows are correctly exposed results in expansion. That is a tool used to convert a low contrast scene into a regular contrast print, by way of adjusting the negative to match the characteristics of the printing paper.
You need to be particularly careful about analogizing digital with negative film behavior. Poorly exposed digital files tend to lose data in the highlights, while poorly exposed film negatives tend to lose image detail in the shadows.