UP Lecture 08

Compilers
Grammar II
(202402)

Transcript

1. jgs Compilers Lecture 08: Grammars II Dr. Javier Gonzalez-Sanchez jgonzalezs@up.edu.mx
2. jgs Previously …
3. jgs Dr. Javier Gonzalez-Sanchez | Compilers | 3 5 / 20 integer operator integer E ⇒ E OP E ⇒ integer OP E ⇒ integer / E ⇒ integer / integer Grammar | Derivation Derivation Tree Grammar 01
4. jgs Test Yourselves
5. jgs Dr. Javier Gonzalez-Sanchez | Compilers | 5 Grammar | Derivation Derivation Tree Grammar 01 5 * ( 7 + 20 ) Integer operator delimiter integer operator integer delimiter E ⇒ E OP E ⇒ integer OP E ⇒ integer * E ⇒ integer * (E) ⇒ integer * (E OP E) ⇒ integer * (integer OP E) ⇒ integer * (integer + E) ⇒ integer * (integer + integer)
6. Dr. Javier Gonzalez-Sanchez | Compilers | 6 jgs Parse Tree
7. jgs Definitions
8. Dr. Javier Gonzalez-Sanchez | Compilers | 8 jgs Grammar | Definition A Grammar is a collection of four elements: 1. Set of nonterminal symbols (uppercase) 2. Set of terminal symbols (lowercase). Terminals can be tokens or specific words. 1. Set of production rules saying how each nonterminal can be converted by a string of terminals and nonterminals, 2. A start symbol
9. jgs Dr. Javier Gonzalez-Sanchez | Compilers | 9 E à ( E ) E à E OP E E à integer OP à + | - | * | / Grammar | Definition
10. Dr. Javier Gonzalez-Sanchez | Compilers | 10 jgs Parse Tree § A parse tree is a tree encoding the steps in a derivation. § Internal nodes represent nonterminal symbols used in the production. § Inorder walk of the leaves contains the generated string. § Encodes what productions are used, not the order in which those productions are applied.
11. Dr. Javier Gonzalez-Sanchez | Compilers | 11 jgs Goal The g oal of syntax analysis: § Recover a parse tree for the given input (a series of tokens).
12. jgs Next Problem
13. Dr. Javier Gonzalez-Sanchez | Compilers | 13 jgs The problem 5 * ( 7 + 20 ) Integer operator delimiter integer operator integer delimiter
14. Dr. Javier Gonzalez-Sanchez | Compilers | 14 jgs The problem 5 * 7 + 20 Integer operator integer operator integer
15. Dr. Javier Gonzalez-Sanchez | Compilers | 15 jgs A serious problem
16. Dr. Javier Gonzalez-Sanchez | Compilers | 16 jgs Ambiguity § A grammar is said to be ambiguous if there is at least one string with two or more parse trees. § Note that ambiguity is a property of grammars, not languages. We will review this topic in the next lecture
17. Dr. Javier Gonzalez-Sanchez | Compilers | 17 jgs Solution § If a grammar can be made unambiguous at all, it is usually made unambiguous through layering. § Have exactly one way to build each piece of the string. § Have exactly one way of combining pieces back together. § Recursive constructions
18. Dr. Javier Gonzalez-Sanchez | Compilers | 18 jgs Layering Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 . . . . . Leaf (Terminals, i.e., Tokens) Root Start symbol Layers
19. Dr. Javier Gonzalez-Sanchez | Compilers | 19 jgs Layering 1 2 4 5 3 inputs: § 1 + 2 + 3 < 4 * 5 § 1 * 2 + 3 + 4 < 5 § 1 < 2 + 3 + 4 * 5 § 1 + 2 < 3 * 4 + 5 § 1 + 2 * 3 < 4 + 5
20. Dr. Javier Gonzalez-Sanchez | Compilers | 20 jgs Exercise Provide a Grammar that is Not ambiguous for arithmetic expressions 10 * 20 + 15 Precedence of operators and Associativity þ (10 * 20) + 15 ý 10 * (20 + 15)
21. Dr. Javier Gonzalez-Sanchez | Compilers | 21 jgs Syntax Diagrams E A B C
22. Dr. Javier Gonzalez-Sanchez | Compilers | 22 jgs Exercise 1 Include rules for handling parenthesis into the previous grammar. The grammar should accept as correct the following expressions: 10 * 20 + 15 (10 * 20) + 15 10 * (20 + 15) (10) * (20) + (15) (10 * 20 + 15) 10 * (20) + 15
23. Dr. Javier Gonzalez-Sanchez | Compilers | 23 jgs Syntax Diagrams E A B C
24. Dr. Javier Gonzalez-Sanchez | Compilers | 24 jgs Exercise 2 Include rules to accept variables names (identifiers) in expressions. The grammar should accept as correct the following expressions: A * 20 + time (x * y) + 15 10 * (ASU + cse340) (10) * (20) + (15) (hello * world + Arizona) 10 * (counter) + 15
25. Dr. Javier Gonzalez-Sanchez | Compilers | 25 jgs Syntax Diagrams E A B C
26. Dr. Javier Gonzalez-Sanchez | Compilers | 26 jgs Exercise 3 Provide a Grammar that is Not ambiguous with Precedence of operators and Associativity for this: 10 + 20 > 15 & -10 != 1 | 20 / ( 10 + 1) < 5
27. Dr. Javier Gonzalez-Sanchez | Compilers | 27 jgs Exercise 3 | Note Precedence of operators | & ! < > == != <= >= + - * / - ( )
28. Dr. Javier Gonzalez-Sanchez | Compilers | 28 jgs Exercise 3 R EXPRESSION X Y
29. Dr. Javier Gonzalez-Sanchez | Compilers | 29 jgs Exercise 3 E A B C
30. Dr. Javier Gonzalez-Sanchez | Compilers | 30 jgs Questions
31. Dr. Javier Gonzalez-Sanchez | Compilers | 31 jgs Homework Review Recursion
32. Dr. Javier Gonzalez-Sanchez | Compilers | 32 jgs Homework Finish Your Lexer (Try the new test cases)
33. jgs Compilers Javier Gonzalez-Sanchez, Ph.D. jgonzalezs@up.edu.mx Spring 2024 Copyright. These slides can only be used as study material for the Compilers course at Universidad Panamericana. They cannot be distributed or used for another purpose.