1. Recursive descent parsing 12-Nov-15

2. Abstract Syntax Trees (ASTs) An AST is a way of representing a computer program It is abstract because it throws away unnecessary information (comments, whitespace, punctuation used only for disambiguation, etc.) It represents syntax, not semantics However, well-written syntax can sometimes help with the semantics For example, ::= | + | * is technically correct, but gives us no help in recognizing that multiplication has precedence over addition The program is represented as a tree 2

3. The Stack One easy way to do recursive descent parsing is to have each parse method take the tokens it needs, build a parse tree, and put the parse tree on a global stack Write a parse method for each nonterminal in the grammar Each parse method should get the tokens it needs, and only those tokens Those tokens (usually) go on the stack Each parse method may call other parse methods, and expect those methods to leave their results on the stack Each (successful) parse method should leave one result on the stack

4. From Recognizer to Parser First, make a Recognizer The Recognizer code will form the “skeleton” of your Parser Create a Stack > as a globally available instance variable You will use this to hold the trees as you build them The methods from the Recognizer all return a boolean ; do not change this Your new results will go onto the Stack Each time you recognize something, also build a Tree to represent it, and put this Tree onto the Stack Most of the time, you will assemble the new Tree from the two Tree s you most recently put onto the Stack

5. Example: Unary minus A simple example of an is -5 As the program steps through the code for, it puts – (minus) on the stack, then it puts 5 on the stack Each of these is in the form of a Tree consisting of a single node with a Token as its value Note that the most recently parsed item, 5, is on the top of the stack These can be combined into a new Tree, with the minus as the root and the 5 as its child

6. makeTree /** * Removes two Trees from the stack, makes a new Tree and * puts it on the stack. The element on the top of the stack * (the most recently seen element) is made the child of the * element beneath it (which was seen earlier). */ private void makeTree() { Tree child = stack.pop(); Tree parent = stack.pop(); parent.addChild(child); stack.push(parent); }

7. Example: while statement ::= “while” The parse method for a does this: Calls the Tokenizer, which returns a “while” token Makes the “while” into a Tree, which it puts on the stack Calls the parser for, which parses a condition and puts a Tree representation of that condition on the stack Stack now contains: “while” (stack “top” is on the right), where stands for some created Tree Calls the parser for, which parses a block and puts a Tree representation of that block on the stack Stack now contains: “while” Pops the top three things from the stack, assembles them into a Tree representing a while statement, and pushes this Tree onto the stack

8. Sample Java code public boolean whileCommand() { if (keyword("while")) { if (condition()) { if (block()) { makeTree(3, 2, 1); return true; } } error("Error in \"while\" statement"); } return false; } while conditionblock

9. makeTree private void makeTree(int rootIndex, int... childIndices) { // Get root from stack Tree root = getStackItem(rootIndex); // Get other trees from stack and add them as children of root for (int i = 0; i getStackItem(int n) { return stack.get(stack.size() - n); }

10. Fancier error messages public boolean whileCommand() { if (keyword("while")) { if (condition()) { if (block()) { makeTree(3, 2, 1); // or some such return true; } error("Error in \"while\" block"); } error("Error in \"while\" condition"); } return false; }

11. Alternative code public boolean whileCommand() { if (keyword("while") && condition() && block()) { makeTree(3, 2, 1); // or some such return true; } return false; } No room for an error condition in this code

12. Alternative code with one message public boolean whileCommand() { if (keyword("while")) { if (condition()) && (block()) { makeTree(3, 2, 1); // or some such return true; } error("Error in \"while\" statement"); } return false; }

13. Tricky problem: Defining ::= “*” | (For simplicity, I’m ignoring the “/” and “%” operators) This is logically correct, but it defines the wrong tree for expressions such as x * y * z -- treats it as x * (y * z) ::= “*” | This is equally correct, and correctly defines x * y * z as meaning (x * y) * z However, the left recursion can’t be programmed: “To recognize a term, first recognize a term” Solution: ::= { “*” } This turns the recursion into an iteration The result is easy to program correctly

14. Code for term() public boolean term() { if (!factor()) return false; while (multiplyOperator()) { if (!factor()) { error("No term after '*' or '/'"); } makeTree(2, 3, 1); // *, first factor, second factor } return true; } Here’s a snippet of code from my JUnit test methods: use("x * y * z"); assertTrue(parser.term()); assertTree("*(*(x, y), z)"); use(String) and assertTree(String) are helper methods that I’ve written; you should be able to figure out what they do

15. An isCommand() method public boolean command() { if (action()) return true; if (thought()) return true; }

16. My helper methods I wrote a number of helper methods for the Parser and for the ParserTest classes One very useful method is tree, in the ParserTest class tree just takes Objects and builds a tree from them This method lets me build parse trees for use in assertEquals tests Another is assertStackTop, which is just private void assertStackTop(Tree bt) { assertEquals(bt, parser.stack.peek()); } Examples: Tree condition = tree("=", "2", "2"); assertStackTop(tree("if", condition, "list"));

17. 17 The End