q1. pypy is the interpreter, a RPython program which can interpret Python code, there is no output language, so we can't consider it as a compiler, right?
PyPy is similar to CPython, both has a compiler+interpreter. CPython has a compiler written in C that compiles Python to Python VM bytecode then executes the bytecode in an interpreter written in C. PyPy has a compiler written in RPython that compiles Python to Python VM bytecode, then executes it in PyPy Interpreter written in RPython.
q2. Can compiler py2rpy exist, transforming all Python programs to RPython? In which language it's written is irrelevant. If yes, we get another compiler py2c. What's the difference between pypy and py2rpy in nature? Is py2rpy much harder to write than pypy?
Can a compiler py2rpy exists? Theoretically yes. Turing completeness guarantees so.
One method to construct py2rpy is to simply include the source code of a Python interpreter written in RPython in the generated source code. An example of py2rpy compiler, written in Bash:
// suppose that /pypy/source/ contains the source code for pypy (i.e. Python -> Nothing RPython)
cp /pypy/source/ /tmp/py2rpy/pypy/
// suppose $inputfile contains an arbitrary Python source code
cp $inputfile /tmp/py2rpy/prog.py
// generate the main.rpy
echo "import pypy; pypy.execfile('prog.py')" > /tmp/py2rpy/main.rpy
cp /tmp/py2rpy/ $outputdir
now whenever you need to translate a Python code to RPython code, you call this script, which produces -- in the $outputdir -- an RPython main.rpy, the RPython's Python Interpreter source code, and a binary blob prog.py. And then you can execute the generated RPython script by calling rpython main.rpy.
(note: since I'm not familiar with rpython project, the syntax for calling the rpython interpreter, the ability to import pypy and do pypy.execfile, and the .rpy extension is purely made up, but I think you get the point)
q3. Is there some general rules or theory available about this?
Yes, any Turing Complete language can theoretically be translated to any Turing Complete language. Some languages may be much more difficult to translate than other languages, but if the question is "is it possible?", the answer is "yes"
q4. ...
There is no question here.
I say you have to sharpen your Clojure experience first, Google Closure after all is a JavaScript library and some other tools.
However, you need you check ClojureScript One:
ClojureScript One will show you how ClojureScript reduces the complexity of web development by allowing you to write applications using one language to unify development across the client and the server
Best Answer
The Closure Compiler is a minifier, an optimiser and a validator all-in-one. That kind of puts it in its own category, because you're correct that a compiler should at least take something that won't run in its current form and turn it into something that will (take TypeScript for an ECMAScript-based example).
But do you blame Google for stretching the terminology? What else were they going to call it? Google Minifier? No, it's more than that, and there are hundreds of those out there. Google Optimiser? It's way more than that. Google Validator? No, it's way more than that too.
So the choice is
It does everything you would expect a compiler to do, with only a semantic difference. And, in the end, all words are defined by their usage, to some extent. So if Google can convince people to call this a compiler, the definition of compiler changes slightly. Certainly not in any way that will cause a problem.
Or, to come back to the earlier example, can you find anything significant about TypeScript that allows it to be called a "true compiler", while Google Closure Compiler should be restricted to "almost a compiler"?