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.
Best Answer
You can't be certain, but you just assume they are, until you discover they are not. There have been plenty of bugs in compilers and hardware over the years.
The way these are tested, for example a compiler, is that they are very narrowly and rigidly defined, carefully written, then tested with an enormous test suite to verify correctness. Add to that the wide user base of a compiler, and more bugs will be detected and reported. A dentist appointment scheduling app, comparatively, has many fewer users, and fewer still that are capable of detecting defects.
SQLite consists of about 73k lines of code, while its test suite consists of about 91378k lines of code, more than 1250x times that of SQLite itself. I expect compilers and other core tools have similar ratios. Processors today are designed essentially with software, using hardware description languages like Verilog or VHDL, and those have software tests run on them as well, as well as specialized IO pins for running self tests at the point of manufacture.
Ultimately it's a probability game, and repeated and broadly covering testing allows you to push the probability of defects down to an acceptably low level, the same as an other software project.