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Why doesn't Python spot errors before execution?

Suppose I have the following code in Python:
a = "WelcomeToTheMachine"
if a == "DarkSideOfTheMoon":
awersdfvsdvdcvd
print "done!"
Why doesn't this error? How does it even compile? In Java or C#, this would get spotted during compilation.

Python isn't a compiled language, that's why your code doesn't throw compilation errors.
Python is a byte code interpreted language. Technically the source code gets "compiled" to byte code, but then the byte code is just in time (JIT) compiled if using PyPy or Pyston otherwise it's line by line interpreted.
The workflow is as follows :
Your Python Code -> Compiler -> .pyc file -> Interpreter -> Your Output
Using the standard python runtime What does all this mean? Essentially all the heavy work happens during runtime, unlike with C or C++ where the source code in it's entirety is analyzed and translated to binary at compile time.

During "compiling", python pretty much only checks your syntax. Since awersdfvsdvdcvd is a valid identifier, no error is raised until that line actually gets executed. Just because you use a name which wasn't defined doesn't mean that it couldn't have been defined elsewhere... e.g.:
globals()['awersdfvsdvdcvd'] = 1
earlier in the file would be enough to suppress the NameError that would occur if the line with the misspelled name was executed.
Ok, so can't python just look for globals statements as well? The answer to that is again "no" -- From module "foo", I can add to the globals of module "bar" in similar ways. And python has no way of knowing what modules are or will be imported until it's actually running (I can dynamically import modules at runtime too).
Note that most of the reasons that I'm mentioning for why Python as a language can't give you a warning about these things involve people doing crazy messed up things. There are a number of tools which will warn you about these things (making the assumption that you aren't going to do stupid stuff like that). My favorite is pylint, but just about any python linter should be able to warn you about undefined variables. If you hook a linter up to your editor, most of the time you can catch these bugs before you ever actually run the code.

Because Python is an interpreted language. This means that if Python's interpreter doesn't arrive to that line, it won't produce any error.

There's nothing to spot: It's not an "error" as far as Python-the-language is concerned. You have a perfectly valid Python program. Python is a dynamic language, and the identifiers you're using get resolved at runtime.
An equivalent program written in C#, Java or C++ would be invalid, and thus the compilation would fail, since in all those languages the use of an undefined identifier is required to produce a diagnostic to the user (i.e. a compile-time error). In Python, it's simply not known whether that identifier is known or not at compile time. So the code is valid. Think of it this way: in Python, having the address of a construction site (a name) doesn't require the construction to have even started yet. What's important is that by the time you use the address (name) as if there was a building there, there better be a building or else an exception is raised :)
In Python, the following happens:
a = "WelcomeToTheMachine" looks up the enclosing context (here: the module context) for the attribute a, and sets the attribute 'a' to the given string object stored in a pool of constants. It also caches the attribute reference so the subsequent accesses to a will be quicker.
if a == "DarkSideOfTheMoon": finds the a in the cache, and executes a binary comparison operator on object a. This ends up in builtins.str.__eq__. The value returned from this operator is used to control the program flow.
awersdfvsdvdcvd is an expression, whose value is the result of a lookup of the name 'awersdfvsdvdcvd'. This expression is evaluted. In your case, the name is not found in the enclosing contexts, and the lookup raises the NameError exception.
This exception propagates to the matching exception handler. Since the handler is outside of all the nested code blocks in the current module, the print function never gets a chance of being called. The Python's built-in exception handler signals the error to the user. The interpreter (a misnomer!) instance has nothing more to do. Since the Python process doesn't try to do anything else after the interpreter instance is done, it terminates.
There's absolutely nothing that says that the program will cause a runtime error. For example, awersdfvsdvdcvd could be set in an enclosing scope before the module is executed, and then no runtime error would be raised. Python allows fine control over the lifetime of a module, and your code could inject the value for awersdfvsdvdcvd after the module has been compiled, but before it got executed. It takes just a few lines of fairly straightforward code to do that.
This is, in fact, one of the many dynamic programming techniques that get used in Python programs. Their judicious use makes possible the kinds of functionality that C++ will not natively get in decades or ever, and that are very cumbersome in both C# and Java. Of course, Python has a performance cost - nothing is free.
If you like to get such problems highlighted at compilation time, there are tools you can easily integrate in an IDE that would spot this problem. E.g. PyCharm has a built-in static checker, and this error would be highlighted with the red squiggly line as expected.

Tracking changes in python source files?

I'm learning python and came into a situation where I need to change the behvaviour of a function. I'm initially a java programmer so in the Java world a change in a function would let Eclipse shows that a lot of source files in Java has errors. That way I can know which files need to get modified. But how would one do such a thing in python considering there are no types?! I'm using TextMate2 for python coding.
Currently I'm doing the brute-force way. Opening every python script file and check where I'm using that function and then modify. But I'm sure this is not the way to deal with large projects!!!
Edit: as an example I define a class called Graph in a python script file. Graph has two objects variables. I created many objects (each with different name!!!) of this class in many script files and then decided that I want to change the name of the object variables! Now I'm going through each file and reading my code again in order to change the names again :(. PLEASE help!
Example: File A has objects x,y,z of class C. File B has objects xx,yy,zz of class C. Class C has two instance variables names that should be changed Foo to Poo and Foo1 to Poo1. Also consider many files like A and B. What would you do to solve this? Are you serisouly going to open each file and search for x,y,z,xx,yy,zz and then change the names individually?!!!

Sounds like you can only code inside an IDE!
Two steps to free yourself from your IDE and become a better programmer.
Write unit tests for your code.
Learn how to use grep
Unit tests will exercise your code and provide reassurance that it is always doing what you wanted it to do. They make refactoring MUCH easier.
grep, what a wonderful tool grep -R 'my_function_name' src will find every reference to your function in files under the directory src.
Also, see this rather wonderful blog post: Unix as an IDE.

Whoa, slow down. The coding process you described is not scalable.
How exactly did you change the behavior of the function? Give specifics, please.
UPDATE: This all sounds like you're trying to implement a class and its methods by cobbling together a motley patchwork of functions and local variables - like I wrongly did when I first learned OO coding in Python. The code smell is that when the type/class of some class internal changes, it should generally not affect the class methods. If you're refactoring all your code every 10 mins, you're doing something seriously wrong. Step back and think about clean decomposition into objects, methods and data members.
(Please give more specifics if you want a more useful answer.)
If you were only changing input types, there might be no need to change the calling code.
(Unless the new fn does something very different to the old one, in which case what was the argument against calling it a different name?)
If you changed the return type, and you can't find a common ancestor type or container (tuple, sequence etc.) to put the return values in, then yes you need to change its caller code. However...
...however if the function should really be a method of a class, declare that class and the method already. The previous paragraph was a code smell that your function really should have been a method, specifically a polymorphic method.
Read about code smells, anti-patterns and When do you know you're dealing with an anti-pattern?. There e.g. you will find a recommendation for the video "Recovery from Addiction - A taste of the Python programming language's concision and elegance from someone who once suffered an addiction to the Java programming language." - Sean Kelly
Also, sounds like you want to use Test-Driven Design and add some unittests.
If you give us the specifics we can critique it better.

You won't get this functionality in a text editor. I use sublime text 3, and I love it, but it doesn't have this functionality. It does however jump to files and functions via its 'Goto Anything' (Ctrl+P) functionality, and its Multiple Selections / Multi Edit is great for small refactoring tasks.
However, when it comes to IDEs, JetBrains pycharm has some of the amazing re-factoring tools that you might be looking for.
The also free Python Tools for Visual Studio (see free install options here which can use the free VS shell) has some excellent Refactoring capabilities and a superb REPL to boot.
I use all three. I spend most of my time in sublime text, I like pycharm for refactoring, and I find PT4VS excellent for very involved prototyping.
Despite python being a dynamically typed language, IDEs can still introspect to a reasonable degree. But, of course, it won't approach the level of Java or C# IDEs. Incidentally, if you are coming over from Java, you may have come across JetBrains IntelliJ, which PyCharm will feel almost identical to.
One's programming style is certainly different between a statically typed language like C# and a dynamic language like python. I find myself doing things in smaller, testable modules. The iteration speed is faster. And in a dynamic language one relies less on IDE tools and more on unit tests that cover the key functionality. If you don't have these you will break things when you refactor.

One answer only specific to your edit:
if your old code was working and does not need to be modified, you could just keep old names as alias of the new ones, resulting in your old code not to be broken. Example:
class MyClass(object):
def __init__(self):
self.t = time.time()
# creating new names
def new_foo(self, arg):
return 'new_foo', arg
def new_bar(self, arg):
return 'new_bar', arg
# now creating functions aliases
foo = new_foo
bar = new_bar
if your code need rework, rewrite your common code, execute everything, and correct any failure. You could also look for any import/instantiation of your class.

One of the tradeoffs between statically and dynamically typed languages is that the latter require less scaffolding in the form of type declarations, but also provide less help with refactoring tools and compile-time error detection. Some Python IDEs do offer a certain level of type inference and help with refactoring, but even the best of them will not be able to match the tools developed for statically typed languages.
Dynamic language programmers typically ensure correctness while refactoring in one or more of the following ways:
Use grep to look for function invocation sites, and fix them. (You would have to do that in languages like Java as well if you wanted to handle reflection.)
Start the application and see what goes wrong.
Write unit tests, if you don't already have them, use a coverage tool to make sure that they cover your whole program, and run the test suite after each change to check that everything still works.

Python Module Initialization Order?

I am a Python newbie coming from a C++ background. While I know it's not Pythonic to try to find a matching concept using my old C++ knowledge, I think this question is still a general question to ask:
Under C++, there is a well known problem called global/static variable initialization order fiasco, due to C++'s inability to decide which global/static variable would be initialized first across compilation units, thus a global/static variable depending on another one in different compilation units might be initialized earlier than its dependency counterparts, and when dependant started to use the services provided by the dependency object, we would have undefined behavior. Here I don't want to go too deep on how C++ solves this problem. :)
On the Python world, I do see uses of global variables, even across different .py files, and one typycal usage case I saw was: initialize one global object in one .py file, and on other .py files, the code just fearlessly start using the global object, assuming that it must have been initialized somewhere else, which under C++ is definitely unaccept by myself, due to the problem I specified above.
I am not sure if the above use case is common practice in Python (Pythonic), and how does Python solve this kind of global variable initialization order problem in general?

Under C++, there is a well known problem called global/static variable initialization order fiasco, due to C++'s inability to decide which global/static variable would be initialized first across compilation units,
I think that statement highlights a key difference between Python and C++: in Python, there is no such thing as different compilation units. What I mean by that is, in C++ (as you know), two different source files might be compiled completely independently from each other, and thus if you compare a line in file A and a line in file B, there is nothing to tell you which will get placed first in the program. It's kind of like the situation with multiple threads: you cannot say whether a particular statement in thread 1 will be executed before or after a particular statement in thread 2. You could say C++ programs are compiled in parallel.
In contrast, in Python, execution begins at the top of one file and proceeds in a well-defined order through each statement in the file, branching out to other files at the points where they are imported. In fact, you could almost think of the import directive as an #include, and in that way you could identify the order of execution of all the lines of code in all the source files in the program. (Well, it's a little more complicated than that, since a module only really gets executed the first time it's imported, and for other reasons.) If C++ programs are compiled in parallel, Python programs are interpreted serially.
Your question also touches on the deeper meaning of modules in Python. A Python module - which is everything that is in a single .py file - is an actual object. Everything declared at "global" scope in a single source file is actually an attribute of that module object. There is no true global scope in Python. (Python programmers often say "global" and in fact there is a global keyword in the language, but it always really refers to the top level of the current module.) I could see that being a bit of a strange concept to get used to coming from a C++ background. It took some getting used to for me, coming from Java, and in this respect Java is a lot more similar to Python than C++ is. (There is also no global scope in Java)
I will mention that in Python it is perfectly normal to use a variable without having any idea whether it has been initialized/defined or not. Well, maybe not normal, but at least acceptable under appropriate circumstances. In Python, trying to use an undefined variable raises a NameError; you don't get arbitrary behavior as you might in C or C++, so you can easily handle the situation. You may see this pattern:
try:
duck.quack()
except NameError:
pass
which does nothing if duck does not exist. Actually, what you'll more commonly see is
try:
duck.quack()
except AttributeError:
pass
which does nothing if duck does not have a method named quack. (AttributeError is the kind of error you get when you try to access an attribute of an object, but the object does not have any attribute by that name.) This is what passes for a type check in Python: we figure that if all we need the duck to do is quack, we can just ask it to quack, and if it does, we don't care whether it's really a duck or not. (It's called duck typing ;-)

Python import executes new Python modules from beginning to end. Subsequent imports only result in a copy of the existing reference in sys.modules, even if still in the middle of importing the module due to a circular import. Module attributes ("global variables" are actually at the module scope) that have been initialized before the circular import will exist.
main.py:
import a
a.py:
var1 = 'foo'
import b
var2 = 'bar'
b.py:
import a
print a.var1 # works
print a.var2 # fails

What's the best way to record the type of every variable assignment in a Python program?

Python is so dynamic that it's not always clear what's going on in a large program, and looking at a tiny bit of source code does not always help. To make matters worse, editors tend to have poor support for navigating to the definitions of tokens or import statements in a Python file.
One way to compensate might be to write a special profiler that, instead of timing the program, would record the runtime types and paths of objects of the program and expose this data to the editor.
This might be implemented with sys.settrace() which sets a callback for each line of code and is how pdb is implemented, or by using the ast module and an import hook to instrument the code, or is there a better strategy? How would you write something like this without making it impossibly slow, and without runnning afoul of extreme dynamism e.g side affects on property access?

I don't think you can help making it slow, but it should be possible to detect the address of each variable when you encounter a STORE_FAST STORE_NAME STORE_* opcode.
Whether or not this has been done before, I do not know.
If you need debugging, look at PDB, this will allow you to step through your code and access any variables.
import pdb
def test():
print 1
pdb.set_trace() # you will enter an interpreter here
print 2

What if you monkey-patched object's class or another prototypical object?
This might not be the easiest if you're not using new-style classes.

You might want to check out PyChecker's code - it does (i think) what you are looking to do.

Pythoscope does something very similar to what you describe and it uses a combination of static information in a form of AST and dynamic information through sys.settrace.
BTW, if you have problems refactoring your project, give Pythoscope a try.

python coding speed and cleanest

Python is pretty clean, and I can code neat apps quickly.
But I notice I have some minor error someplace and I dont find the error at compile but at run time. Then I need to change and run the script again. Is there a way to have it break and let me modify and run?
Also, I dislike how python has no enums. If I were to write code that needs a lot of enums and types, should I be doing it in C++? It feels like I can do it quicker in C++.

"I don't find the error at compile but at run time"
Correct. True for all non-compiled interpreted languages.
"I need to change and run the script again"
Also correct. True for all non-compiled interpreted languages.
"Is there a way to have it break and let me modify and run?"
What?
If it's a run-time error, the script breaks, you fix it and run again.
If it's not a proper error, but a logic problem of some kind, then the program finishes, but doesn't work correctly. No language can anticipate what you hoped for and break for you.
Or perhaps you mean something else.
"...code that needs a lot of enums"
You'll need to provide examples of code that needs a lot of enums. I've been writing Python for years, and have no use for enums. Indeed, I've been writing C++ with no use for enums either.
You'll have to provide code that needs a lot of enums as a specific example. Perhaps in another question along the lines of "What's a Pythonic replacement for all these enums."
It's usually polymorphic class definitions, but without an example, it's hard to be sure.

With interpreted languages you have a lot of freedom. Freedom isn't free here either. While the interpreter won't torture you into dotting every i and crossing every T before it deems your code worthy of a run, it also won't try to statically analyze your code for all those problems. So you have a few choices.
1) {Pyflakes, pychecker, pylint} will do static analysis on your code. That settles the syntax issue mostly.
2) Test-driven development with nosetests or the like will help you. If you make a code change that breaks your existing code, the tests will fail and you will know about it. This is actually better than static analysis and can be as fast. If you test-first, then you will have all your code checked at test runtime instead of program runtime.
Note that with 1 & 2 in place you are a bit better off than if you had just a static-typing compiler on your side. Even so, it will not create a proof of correctness.
It is possible that your tests may miss some plumbing you need for the app to actually run. If that happens, you fix it by writing more tests usually. But you still need to fire up the app and bang on it to see what tests you should have written and didn't.

You might want to look into something like nosey, which runs your unit tests periodically when you've saved changes to a file. You could also set up a save-event trigger to run your unit tests in the background whenever you save a file (possible e.g. with Komodo Edit).
That said, what I do is bind the F7 key to run unit tests in the current directory and subdirectories, and the F6 key to run pylint on the current file. Frequent use of these allows me to spot errors pretty quickly.

Python is an interpreted language, there is no compile stage, at least not that is visible to the user. If you get an error, go back, modify the script, and try again. If your script has long execution time, and you don't want to stop-restart, you can try a debugger like pdb, using which you can fix some of your errors during runtime.
There are a large number of ways in which you can implement enums, a quick google search for "python enums" gives everything you're likely to need. However, you should look into whether or not you really need them, and if there's a better, more 'pythonic' way of doing the same thing.