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I don't think so. It seems to me that they did a good job on the interface between Objective-C and Swift, so one could perfectly live without the other. Objective-C constructs are exposed as native Swift constructs.

If they open sourced the compiler then maybe you could link against GNUstep on other platforms.

You're thinking of the Objective-C runtime, which in fact is opensource: http://www.opensource.apple.com/source/objc4/objc4-551.1

C# is "open source", but the CLR is not.