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Yes, you can. In fact, there is even a book called "Write Your Own Lisp" which takes you through how to create your own programming language. You need to think how to do it. You will write the compiler, the syntax, the functions, etc. It is difficult, but possible. I know someone who wrote there own programming language in C called Flamingo. I suggest you first try to write a compiler (in C preferably) for a language that exists before making your own. Good Luck!