1. LANGUAGE TRANSLATORS: WEEK 3 LECTURE: Grammar Theory Introduction to Parsing Parser - Generators TUTORIAL: Questions on grammar theory WEEKLY WORK: Read Chapter 1 of Appel’s Book, read the JavaCup manual, read an introduction to parsing (all online) School of Computing and Engineering, University of Huddersfield

2. GRAMMARS Theoretical properties and results about the nature of GRAMMARS have been used for 40 years to influence the design of PARSERS. A CONTEXT FREE (BNF) GRAMMAR contains a vocabulary = {terminals, non-terminals} and “production rules”/”re-write rules” of the form: non-terminal ::= v1 v2.........vn where the vi are members of the vocabulary. One non-terminal is called the SPECIAL SYMBOL School of Computing and Engineering, University of Huddersfield

3. PROPERTIES OF GRAMMARS -1 A syntax tree (parse tree) of a BNF Grammar G is a tree where - the root is the special symbol of G, - the leaves are terminals of G, - the nodes are non-terminals of G, - each node is the LHS of some rule P of G; the node’s children are connected to the node by arcs, and form the RHS of P - the leaves are all connected up to the root via arcs School of Computing and Engineering, University of Huddersfield

4. PROPERTIES OF GRAMMARS -2 A string of token is member of the language generated by a BNF grammar G IFF it forms the leaves (in the correct order) of some syntax tree generated by G G is AMBIGUOUS IFF at least one of the strings in its language has more than one distinct syntax tree School of Computing and Engineering, University of Huddersfield

5. PROPERTIES OF GRAMMARS -3 A BNF grammar G is LEFT-RECURSIVE if has at least one production of the form: X ::= X w where X is a non-terminal and w is a string of symbols in G’s vocabulary School of Computing and Engineering, University of Huddersfield

6. PROPERTIES OF GRAMMARS -4 If w is a list of symbols in the vocabulary of BNF grammar G then First(w) = set of TERMINAL symbols that may be at the front of ANY string derived from w using G’s productions School of Computing and Engineering, University of Huddersfield

7. PROPERTIES OF GRAMMARS -5 If X is a non-terminal of BNF grammar G then Follow(X) = set of TERMINAL symbols that can follow X in a derivation from G’s special symbol using G’s productions. Nullable(X) is true IFF the empty word can be derived from X School of Computing and Engineering, University of Huddersfield

8. PARSING A PARSER (or ‘PARSING ALGORITHM’) derives SYNTAX/PARSE TREES from a sequence of TOKENS Some well-known tools are little more than PARSERS e.g. Syntax Directed Editors - those that colour different syntax classes or point out syntax errors as you make them PARSING ALGORITHMS invariably are based on the CONTEXT FREE GRAMMAR that defines the language being parsed. School of Computing and Engineering, University of Huddersfield

9. Example Input String: b = 5; a = 5 * b; PRINT(b * a) Ouput PARSE TREE (as a Java data structure) new CompoundStm( new AssignStm("b",new NumExp(5)), new CompoundStm( new AssignStm("a", new OpExp(new NumExp(5), OpExp.Times, new IdExp("b"))), new PrintStm(new LastExpList(new OpExp(new IdExp("b"), OpExp.Times, new IdExp("a")))) ) ); School of Computing and Engineering, University of Huddersfield

10. PARSING ALGORITHMS Parsers that follow the language’s grammar can be TOP DOWN: - starting with the grammar’s special symbol, try to find a derivation of the string of tokens being parsed, consuming one token at a time BOTTOM UP: - start with the string viewed as a stack. Match the top ‘n’ tokens of the stack with the RHS of a grammar rule P and replace those tokens with the LHS of P School of Computing and Engineering, University of Huddersfield

11. PRACTICAL EXAMPLE OF THEORY An grammar G is LL(1) if and only if (i) G is NOT ambiguous (ii) G is NOT left recursive (iii) for EVERY two of G’s productions of the form X ::= W1, X ::= W2, it is the case that First(W1) and First(W2) have no common element LL(1) grammars are nice grammars, they can be translated into a very efficient LL(1) PARSING TABLE. School of Computing and Engineering, University of Huddersfield

12. Practical: JavaCup JavaCup is a tool that inputs a GRAMMAR in BNF form (+ other stuff..) and outputs a PARSE TREE (in the form of Java Constructors). Parsers created using JavaCup accept a sequence of TOKENS as input from a SCANNER such as last week’s. An easy way to show JavaCup’s use is to implement a simple interpreter with it: (i) JavaCup inputs a grammar and creates a corresponding parser P in java. (ii) P accepts tokens from the scanned input and generates and passes the parse tree to some Java code which then EVALUATES it. School of Computing and Engineering, University of Huddersfield

13. SUMMARY Parsers check strings are legal according to grammatical definitions, and build up a structure representing legal strings (parse trees) Parsers can sometimes be auto-generated from the defining grammar Theory of grammars helps us in the auto-generation of parsers School of Computing and Engineering, University of Huddersfield