Save and run at the same time in Vim

Okay, the simplest form of what you're looking for is the pipe command. It allows you to run multiple cmdline commands on the same line. In your case, the two commands are write `w` and execute current file `! %:p`. If you have a specific command you run for you current file, the second command becomes, e.g. `!python %:p`. So, the simplest answer to you question becomes:

:w | ! %:p
 ^ ^ ^
 | | |--Execute current file
 | |--Chain two commands
 |--Save current file

One last thing to note is that not all commands can be chained. According to the Vim docs, certain commands accept a pipe as an argument, and thus break the chain...

Option 1:

Write a function similar to this and place it in your startup settings:

function myex()
   execute ':w'
   execute ':!!'
endfunction

You could even map a key combination to it -- look at the documentation.

Option 2 (better):

Look at the documentation for remapping keystrokes - you may be able to accomplish it through a simple key remap. The following works, but has "filename.py" hardcoded. Perhaps you can dig in and figure out how to replace that with the current file?

:map <F2> <Esc>:w<CR>:!filename.py<CR>

After mapping that, you can just press F2 in command mode.

imap, vmap, etc... are mappings in different modes. The above only applies to command mode. The following should work in insert mode also:

:imap <F2> <Esc>:w<CR>:!filename.py<CR>a

Section 40.1 of the Vim manual is very helpful.

Use the autowrite option:

:set autowrite

Write the contents of the file, if it has been modified, on each :next, :rewind, :last, :first, :previous, :stop, :suspend, :tag, :!, :make, CTRL-] and CTRL-^ command [...]