Objective-C compiler on iPhone

You didn't mention whether you were talking about using the official SDK or jailbreaking.

Either way, AFAIK right now you pretty much have to do your compiling on a full computer, and transfer the compiled output over to the iPhone.

That's probably for the best, for a couple of reasons.

For one thing, with programs of a substantial size, the system's 128 MB of RAM, with no swap memory, is potentially insufficient as compilers tend to be memory hogs. Less than that would actually be accessible to the compiler after the OS and always-on applications have taken their share.

As well, compiling applications can result in quite a few temporary files being created on the filesystem, which are subsequently thrown away once the build is complete. These files being created and destroyed would have an unwelcome effect on the useful life of your Flash storage.