Sure! Here's a **full solution** for your question based on the grammar of arithmetic expressions with addition and multiplication. --- ### 📘 **Given Grammar:** ``` E → E + T E → T T → T * F T → F F → digit ``` --- ## ✅ (a) Synthesized Attributes and Semantic Rules We define a **synthesized attribute** `val` to represent the **numeric value** of each non-terminal. The `digit.lexval` holds the integer value of the digit token. ### 🎯 Semantic Rules: ``` E → E1 + T { E.val = E1.val + T.val } E → T { E.val = T.val } T → T1 * F { T.val = T1.val * F.val } T → F { T.val = F.val } F → digit { F.val = digit.lexval } ``` --- ## ✅ (b) Evaluate Expression: `2 + 3 * 4` ### 🔹 Operator Precedence - According to grammar: - `*` has **higher precedence** than `+` - So: `2 + (3 * 4) = 2 + 12 = 14` --- ### 🔢 Step-by-step Attribute Evaluation: 1. `digit(2)` → `F.val = 2` → `T.val = 2` → `E1.val = 2` 2. `digit(3)` → `F.val = 3` 3. `digit(4)` → `F.val = 4` → `T1.val = 3`, `F.val = 4` → `T.val = 3 * 4 = 12` 4. `E.val = E1.val + T.val = 2 + 12 = 14` ✅ Final Result: `E.val = 14` --- ## ✅ (c) Annotated Parse Tree (with Synthesized Attributes) ``` E (14) / | \ E(2) + T(12) | | T(2) T(12) | | F(2) T(3) * F(4) | | F(3) F(4) ``` ### 🔹 Attribute Flow: | Symbol | Value | |------------|--------| | F(2) | 2 | | T(2) | 2 | | E1 | 2 | | F(3) | 3 | | F(4) | 4 | | T(3 * 4) | 12 | | E(2 + 12) | 14 | --- Let me know if you’d like this in **PowerPoint** or **PDF** format or want a **tree diagram image** of the parse tree!

1. Syntax Directed Definition (SDD)
Technical and Numerical View

2. What is SDD?
• A Syntax Directed Definition (SDD) is a
context-free grammar combined with
attributes and semantic rules.
• Attributes carry values or information.
• Two types of attributes:
• - Synthesized (bottom-up)
• - Inherited (top-down)

3. Attribute Types
• Attribute Type | Flow Direction | Example
Use
• -------------------|----------------|-------------
• Synthesized | Bottom-up | Compute
expression values
• Inherited | Top-down | Pass type
information

4. Example Rule with Attributes
• Grammar:
• E → E1 + T
• Attributes:
• E.val = E1.val + T.val
• If:
• E1.val = 5, T.val = 7
• Then:

5. Full Numerical Example
• Grammar:
• E → E1 + T
• E → T
• T → num
• Input: 3 + 4
• Attribute Values:
• Node | Attribute | Value

6. Syntax Tree with Attributes
• Draw this tree:
• E
• /|
• E1 + T
• | |
• T num(4)
• |
• num(3)

7. Summary
• Syntax Directed Definition helps in annotating
parse trees.
• Synthesized attributes are most common in
bottom-up parsing.
• Numerical evaluations (like calculator apps)
use SDD heavily.