I\'m somewhat moderate in my C++ knowledge but know next to nothing regarding Objective-C. I am planning (and even starting to) learn Objective-C so I can attempt to write a
Changes required in build settings to use C++ files in iOS project under "Apple LLVM compiler 4.2 - Language" Option
C++ Language Dialect: Compiler Default C++ Standard Library: Compiler Default
You could use Cocos2d-x engine and write pure C++ for your iOS app, including UI (cocos has basic ui classes like buttons, scroll views, table views, etc - but you need to develop your own Controllers, and Models using various C++ libraries like Hiberlite, or raw SQLite etc)
Cocos has its own interface with iOS/MacOS (a few basic .mm objective-c classes to setup Application run cycle - like app delegate, or runloop and drawing cycle)
So you just write your user code with C++
Is it possible to write an iOS and / or a Mac OS X application entirely with C++ including the UI components? If it isn't possible to do it entirely in C++ then to what degree is it possible to use mostly C++?
I think it is possible to use pure c++ if you want to depend on some 3rd part lib, then yes.
Without that 3rd part lib you have to write all the UI using objective-c the rest you can use c++ as much as you like.
Short answer, yes.
For pure C++, you should take a look at the QT framework.
Otherwise, you'll have hard time for the UI part.
But also remember that Objective-C can be mixed with C++.
That's called Objective-C++ (.mm files).
You can then write code that mix C++ and Objective-C code. With this, you can have the UI parts in Objective-C (may be better, as it will use the native frameworks for the UI components), and the other things in C++.
If you've decided to learn Objective-C, but still want to code in C++ for some parts, I would recommend this approach, instead of pure C++.
On iOS, this is also the only way. While you can code in C++, you have to use Objective-C for the UI part.
EDIT
Here are a few links to get started with Objective-C++:
Look this question
I don't know about Mac OS, but in IOS applications you can use C++ in logic but you have to write user interface on Objective-C.