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Can we write a program which is capable of writing further program for itself?
I am talking about a computer program which is able to write(and compile too) its further codes made on its experience with environment.. Sounds like machine learning..
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That's not machine learning, but machine learning can be used to teach it to write effective code. As for compiling, you can use your program to start other programs (like a compiler). How you do that depends on your OS.
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It can be a good application of machine learning
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https://research.googleblog.com/2017/05/using-machine-learning-to-explore.html?m=1
Auto-ML doesn't write code like you asked, but is capable of creating new neural networks