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.
It's important to remember that interpreting and compiling are not just alternatives to each other. In the end, any program that you write (including one compiled to machine code) gets interpreted. Interpreting code simply means taking a set of instructions and returning an answer.
Compiling, on the other hand, means converting a program in one language to another language. Usually it is assumed that when compilation takes place, the code is compiled to a "lower-level" language (eg. machine code, some kind of VM bytecode, etc.). This compiled code is still interpreted later on.
With regards to your question of whether there is a useful distinction between interpreted and compiled languages, my personal opinion is that everyone should have a basic understanding of what is happening to the code they write during interpretation. So, if their code is being JIT compiled, or bytecode-cached, etc., the programmer should at least have a basic understanding of what that means.
Best Answer
No. The reason why there are speed differences between languages like Python and C++ is because statically-typed languages give the compiler tons of information about the structure of the program and its data which allows it to optimize both computations and memory access. Because C++ knows that variable is of type int, it can determine the optimal way to manipulate that variable even before the program is run. In Python on the other hand, the runtime doesn't know what value is in a variable right until the line is reached by the interpreter. This is extremely important for structures, where in C++, the compiler can easily tell the size of the structure and every location of its fields within memory during compilation. This gives it huge power in predicting how the data might be used and lets it optimize according to those predictions. No such thing is possible for languages like Python.
To effectively compile languages like Python you would need to: