1. Translator Architecture Code Generator ParserTokenizer string of characters (source code) string of tokens abstract program string of integers (object code) ? Parser

2. Here’s the Plan Design a context-free grammar to specify (syntactically) valid BL programs Use the grammar to implement a recursive descent parser (i.e., an algorithm to parse BL programs and construct the corresponding Program object)

3. Specifying Syntax with CFGs Context-free grammars (cfg) Some syntactically valid real constants: 37.044 615.22E16 99241. 18.E-93

4. Rewrite Rules for Real Constants . |. |.  E | E + | E -  |  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 can be rewritten as or

5. Four Components of a CFG Nonterminal symbols,,, Terminal symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, E, +, -,. Start symbol Rewrite rules on previous slide

6. A Derivation of 5.6E10 We begin with the start symbol… … and choose one of its rewrite rules: . |. |.

7. A Derivation of 5.6E10 . Now we choose one of the nonterminal symbols… … and choose one of its rewrite rules:  |

8. A Derivation of 5.6E10 . Again we choose one of the nonterminal symbols… … and choose one of its rewrite rules:  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

9. A Derivation of 5.6E10 .  5.  5. 6  5. 6 E  5. 6 E 1  5. 6 E 1 0 If it’s possible to find such a derivation, we write:  5.6E10 *

10. A Derivation Tree for 5.6E10. E 56 1 0

11. Find a Derivation Tree for 5.E3 The derivation tree: Can you find a derivation tree for.6E10?. E 35 Why not?

12. Language Generated by a CFG Definition: Let G = (Nonterminals, Terminals,, Rewrite Rules) be a context-free grammar. The language generated (or specified) by G is denoted L(G) and is defined as: * L(G) = {x: string of Terminals (  x)}

13. Another Example: A CFG for Boolean Expressions  T | F | NOT ( ) | ( AND ) | ( OR )

14. CFG for Boolean Expressions What are the nonterminal symbols? What are the terminal symbols? What is the start symbol? How many rewrite rules? T, F, AND, OR, NOT, (, ) 5

15. A Derivation Tree for NOT((T OR F)) NOT() OR() T F

16. Find a Derivation Tree for ((T OR NOT (F)) AND T) AND() T OR() TNOT() F

17. A Famous Context-free Grammar  |  |  ( ) |  + | -  * | DIV | MOD  |  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

18. What’s So Special About This CFG? Find a derivation tree for 4 + 6 * 2 4+ 6 * 2

19. What’s So Special Continued… Find the derivation tree for (4 + 6) * 2 4 * 2 () 6 +

20. How About These Rewrite Rules?  | ( ) |  + | - | * | DIV | MOD  |  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

21. New Rules Continued… Find a derivation tree for 4 + 6 * 2 4 + 6 * 2

22. New Rules Continued… How about this tree for 4 + 6 * 2? 2 * 4 + 6