I'm trying to write a simple interpreted programming language in C++. I've read that a lot of people use tools such Lex/Flex Bison to avoid "reinventing the wheel", but since my goal is to understand how these little beasts work improving my knowledge, i've decided to write the Lexer and the Parser from scratch. At the moment i'm working on the parser (the lexer is complete) and i was asking myself what should be its output. A tree? A linear vector of statements with a "depth" or "shift" parameter? How should i manage loops and if statements? Should i replace them with invisible goto statements?
A parser should almost always output an AST. An AST is simply, in the broadest sense, a tree representation of the syntactical structure of the program. A Function becomes an AST node containing the AST of the function body. An if becomes an AST node containing the AST of the condition and the body. A use of an operator becomes an AST node containing the AST of each operand. Integer literals, variable names, and so on become leaf AST nodes. Operator precedence and such is implicit in the relationship of the nodes: Both 1 * 2 + 3 and (1 * 2) + 3 are represented as Add(Mul(Int(1), Int(2)), Int(3)).
Many details of what's in the AST depend on your language (obviously) and what you want to do with the tree. If you want to analyze and transform the program (i.e. split out altered source code at the end), you might preserve comments. If you want detailed error messages, you might add source locations (as in, this integer literal was on line 5 column 12).
A compiler will proceed to turn the AST into a different format (e.g. a linear IR with gotos, or data flow graphs). Going through the AST is still a good idea, because a well-designed AST has a good balance of being syntax-oriented but only storing what's important for understanding the program. The parser can focus on parsing while the later transformations are protected from irrelevant details such as the amount of white space and operator precedence. Note that such a "compiler" might also output bytecode that's later interpreted (the reference implementation of Python does this).
A relatively pure interpreter might instead interpret the AST. Much has been written about this; it is about the easiest way to execute the parser's output. This strategy benefits from the AST in much the same way as a compiler; in particular most interpretation is simply top-down traversal of the AST.
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