1. Recursive descent parsing
13-Nov-18

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, <expr> ::= <integer> | <expr> + <expr> | <expr> * <expr> is technically correct, but gives us no help in recognizing that multiplication has precedence over addition
The program is represented as a tree

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<Tree<Token>> 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 Trees you most recently put onto the Stack

5. Example: Unary minus A simple example of an <expression> is -5
As the program steps through the code for <expression>, 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<Token> child = stack.pop(); Tree<Token> parent = stack.pop(); parent.addChild(child); stack.push(parent); }

7. Example: while statement
<while statement> ::= “while” <condition> <block>
The parse method for a <while statement> 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 <condition>, which parses a condition and puts a Tree representation of that condition on the stack
Stack now contains: “while” <condition> (stack “top” is on the right), where <condition> stands for some created Tree
Calls the parser for <block>, which parses a block and puts a Tree representation of that block on the stack
Stack now contains: “while” <condition> <block>
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
<block>
<condition>
while
public boolean whileCommand() { if (keyword("while")) { if (condition()) { if (block()) { makeTree(3, 2, 1); return true; } } error("Error in \"while\" statement"); } return false; }
while
condition
block
<while stmt>

9. makeTree
private void makeTree(int rootIndex, int... childIndices) { // Get root from stack Tree<Token> root = getStackItem(rootIndex); // Get other trees from stack and add them as children of root for (int i = 0; i < childIndices.length; i++) { root.addChild(getStackItem(childIndices[i])); } // Pop root and all children from stack for (int i = 0; i <= childIndices.length; i++) { stack.pop(); } // Put the root back on the stack stack.push(root); } private Tree<Token> 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 No room for an error condition in this 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 <term>
<term> ::= <factor> “*” <term> | <factor>
(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)
<term> ::= <term> “*” <factor> | <factor>
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: <term> ::= <factor> { “*” <factor> }
This turns the recursion into an iteration
The result is easy to program correctly

14. Code for term() Here’s a snippet of code from my JUnit test methods:
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. The End