Why can't the compiler just compile my code as I type it?
From the user's point of view, it could work as smoothly as syntax colouring does today. If you stop typing for long enough (maybe a couple of seconds) the compilation (not linking) would finish, and code errors would be identified using something like syntax colouring.
It's not like my 3GHz quad core monster computer was really busy doing something else. Why not let it compile all the time?
Some IDEs do compile (or at least check syntax and some semantics) code as it is typed. For example, I think Eclipse does it. I think Visual Basic 6 (and maybe earlier versions) did this.
It can. Or, to be more useful, the answer to this question depends on
Some really strong optimizations would be very messy to mess with on the fly. On the other hand, a basic compilation, if there's no need to worry about assigning offsets for X86 instructions? Sure.
That's exactly what the VB.NET code editor in Visual Studio does.
The advantage is much more accurate IntelliSense than C#. The disadvantage is that it wastes truly vast amounts of processor time and memory. :-(
I'm not well-versed in compilers or the methods by which code is converted to IL and machine language, etc. But even so I can see how altering my program by one flow control statement can completely invalidate the work a compiler has done up to that point. By adding or changing a single line of code, entire portions of a program may become obsolete, unused, or in some other way require re-evaluation.
I think I'd rather save those CPU cycles for distributed.net or SETI @ Home instead of constantly recompiling my code as I alter it.
That totally depend on the language.
Languages that have context-independent syntaxes "could" pre-compile expressions once typed. However, compilation of such languages project is always fast, so why use the cpu when you can batch quickly the work when the code is ready?
Other languages, like infamously C++, are context-dependent. In most cases, the compiler can't understand an expression without having already read the whole code before the expression. It's really really hard to parse and that's why we have error checking before compilation only now (in VS2010 and other recent ide). In this case it looks like impossible to implement the feature you're asking for.
That said, I'm not a specialist at all. That's all I know about it.
Resharper Plug-in from JetBrains does a minimal syntax check with your code while you are typing. You should try it.
Even interpreted languages like PHP have support for this in the Komodo editor. I'm sure there's many more editors out there that support this for almost any language.