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jgs Compilers Lecture 09: Precedence of Operators I Dr. Javier Gonzalez-Sanchez [email protected]

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jgs Previously …

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Dr. Javier Gonzalez-Sanchez | Compilers | 3 jgs Do not Forget ▪ Terminals: Represented in lowercase, enclosed in single or double quotes, or depicted as ovals in diagrams. ▪ Non-Terminals: Represented with an uppercase initial letter, enclosed in angle brackets (< >), or depicted as rectangles in diagrams.

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Dr. Javier Gonzalez-Sanchez | Compilers | 4 jgs Test Yourselves Syntax Diagrams for Java: - Class - Attributes - Methods - Parameters - Instruction (stop here) Do not forget static, final, public, private, data-types, abstract, extends, implements …

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Dr. Javier Gonzalez-Sanchez | Compilers | 5 jgs Handwritten Notes

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Dr. Javier Gonzalez-Sanchez | Compilers | 6 jgs Rule 1. Create New Rules to Facilitate Understanding Divide-and-Conquer Approach

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jgs Test Yourselves

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Dr. Javier Gonzalez-Sanchez | Compilers | 8 jgs

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jgs Problem Precedence of Operators

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Dr. Javier Gonzalez-Sanchez | Compilers | 10 jgs Grammar | Derivation 5 integer / operator 5 integer x ID = operator

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Dr. Javier Gonzalez-Sanchez | Compilers | 11 jgs Grammar | Derivation 5 integer / operator 5 integer x ID = operator Expression: Operator: Assignment:

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Dr. Javier Gonzalez-Sanchez | Compilers | 12 jgs Grammar | Derivation 5 integer / operator 20 integer x ID = operator Expression: Operator: Assignment:

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Dr. Javier Gonzalez-Sanchez | Compilers | 13 jgs Grammar | Derivation 1 integer + operator 2 integer x ID = operator / operator 3 integer 1 integer / operator 2 integer x ID = operator + operator 3 integer

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Dr. Javier Gonzalez-Sanchez | Compilers | 14 jgs Grammar | Derivation 1 integer + operator 2 integer x ID = operator / operator 3 integer 1 integer / operator 2 integer x ID = operator + operator 3 integer

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Dr. Javier Gonzalez-Sanchez | Compilers | 15 jgs Layering 2 3 1

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Dr. Javier Gonzalez-Sanchez | Compilers | 16 jgs Layering Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 . . . . . Leaf (Terminals, i.e., Tokens) Root Start symbol Layers

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Dr. Javier Gonzalez-Sanchez | Compilers | 17 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

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Dr. Javier Gonzalez-Sanchez | Compilers | 18 jgs Rule 2. Create New Rules to Establish Levels of Precedence for Operators

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jgs Step 1 Arithmetic Operators

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Dr. Javier Gonzalez-Sanchez | Compilers | 20 jgs Exercise 1 | Precedence New Grammar: → <__> + <__> | <__> < > → <__> - <__> | <__> < > → - __ | __ Original Grammar: E → E OP E | E E → integer OP→ + | - | * | /

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Dr. Javier Gonzalez-Sanchez | Compilers | 21 jgs Precedence Precedence of operators + - * / -

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Dr. Javier Gonzalez-Sanchez | Compilers | 22 jgs Exercise 1 | Handwritten notes

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Dr. Javier Gonzalez-Sanchez | Compilers | 23 jgs Exercise | Precedence → | {'+' } | {'-' } → | {'*' } | {'/' } → '-' | → integer

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Dr. Javier Gonzalez-Sanchez | Compilers | 24 jgs Exercise 1 | Precedence → {(’+'|'-’) } → {('*'|'/') } → ['-'] → integer

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Dr. Javier Gonzalez-Sanchez | Compilers | 25 jgs Syntax Diagrams E A B C

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Dr. Javier Gonzalez-Sanchez | Compilers | 26 jgs Exercise 1 | Handwritten notes

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jgs To be continued…

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Dr. Javier Gonzalez-Sanchez | Compilers | 28 jgs Questions

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jgs Compilers Javier Gonzalez-Sanchez, Ph.D. [email protected] Spring 2026 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.