For some one how has only knowledge on tree data structure Is it evident for him to write an Arithmetic Expressions parser without the help of compilation techniques ?
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Without knowledge of compilation techniques it would be ugly. But there is no need to learn a ton of compilation for an introductory example like this.
Look at something like http://www.codeproject.com/Articles/345888/How-to-write-a-simple-interpreter-in-JavaScript and see if it makes sense to you.