Syntax tree representation in Compiler Design - Step-by-Step Execution

Concept Flow - Syntax tree representation

Start: Source Code

↓

Lexical Analysis

↓

Tokens Stream

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Parsing

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Build Syntax Tree

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Syntax Tree Ready for Analysis

The source code is first broken into tokens, then parsed to build a tree structure representing the code's syntax.

Execution Sample

Compiler Design

Expression: 3 + 4 * 5
Tokens: [3, +, 4, *, 5]
Parse: Build tree with '*' as child of '+'

This example shows how an expression is tokenized and then parsed into a syntax tree reflecting operator precedence.

Analysis Table

Step	Action	Input	Output	Notes
1	Read source code	3 + 4 * 5	Source code string	Starting point
2	Lexical analysis	3 + 4 * 5	[3, +, 4, *, 5]	Split into tokens
3	Parsing - read token '3'	[3, +, 4, *, 5]	Node: 3	Create leaf node
4	Parsing - read token '+'	[+, 4, *, 5]	Operator node: +	Prepare to combine nodes
5	Parsing - read token '4'	[4, *, 5]	Node: 4	Create leaf node
6	Parsing - read token '*'	[*, 5]	Operator node: *	Higher precedence than '+'
7	Parsing - read token '5'	[5]	Node: 5	Create leaf node
8	Build subtree for '*'	4 * 5	Node '*' / \ 4 5	Multiply subtree created
9	Build root '+' node	3 + (4 * 5)	Node '+' / \ 3 '*' / \ 4 5	Final syntax tree
10	Parsing complete	All tokens processed	Syntax tree ready	Tree represents expression structure

💡 All tokens processed and syntax tree constructed representing the expression

State Tracker

Variable	Start	After Step 3	After Step 5	After Step 7	After Step 8	After Step 9	Final
Tokens	[3, +, 4, *, 5]	[+, 4, *, 5]	[*, 5]	[5]	[]	[]	[]
Current Node	null	3	4	5	'*' (4 * 5)	'+' (3 + (4 * 5))	'+' (3 + (4 * 5))
Syntax Tree	Empty	3	3 + 4	3 + 4 * 5 (partial)	Subtree '*'	Full tree '+'	Full tree '+'

Key Insights - 3 Insights

Why is '*' grouped before '+' in the syntax tree?

Because '*' has higher precedence than '+', the parser builds the '*' subtree first (see steps 6-8 in execution_table).

What happens to tokens as parsing progresses?

Tokens are consumed one by one from the list (see Tokens variable in variable_tracker), reducing until none remain.

Why do we create nodes for numbers and operators separately?

Numbers become leaf nodes, operators become internal nodes connecting operands, reflecting the expression structure (see steps 3,4,5,6).

Visual Quiz - 3 Questions

Look at the execution_table at step 8, what does the subtree '*' represent?

A The addition of 3 and 4

B The multiplication of 4 and 5

C A single number 5

D The entire expression 3 + 4 * 5

💡 Hint

Refer to step 8 in execution_table where '*' subtree is built from 4 and 5

At which step does the parser finish processing all tokens?

A Step 7

B Step 9

C Step 10

D Step 8

💡 Hint

Check the exit_note and step 10 in execution_table for completion

If the expression was '3 * 4 + 5', how would the syntax tree change?

A '+' would be the root with '*' as left child

B '*' would be the root with '+' as right child

C The tree would be flat with no precedence

D The tree would be the same as '3 + 4 * 5'

💡 Hint

Operator precedence means '*' binds before '+', so '*' subtree is built first as left child

Concept Snapshot

Syntax Tree Representation:
- Source code is tokenized into tokens.
- Parser reads tokens and builds a tree.
- Leaf nodes are operands (numbers).
- Internal nodes are operators.
- Tree structure shows operation order and precedence.
- Used in compilers to understand code structure.

Full Transcript

Syntax tree representation starts with source code which is split into tokens by lexical analysis. Then the parser reads tokens one by one, creating nodes for numbers and operators. Operators with higher precedence form subtrees first. For example, in '3 + 4 * 5', multiplication is grouped before addition. Tokens are consumed until none remain, resulting in a tree that shows the expression's structure clearly. This tree helps compilers understand and process code correctly.

Practice

1. What is the main purpose of a syntax tree in compiler design?

easy

A. To manage memory allocation during runtime

B. To execute the program directly

C. To represent the structure of source code clearly

D. To store compiled machine code

Solution

1. Step 1: Understand the role of syntax trees

   Syntax trees break down source code into parts showing its structure clearly.

2. Step 2: Compare with other compiler tasks

   Execution, machine code storage, and memory management are handled by other compiler stages, not syntax trees.

3. Final Answer:

   To represent the structure of source code clearly -> Option C

4. Quick Check:

   Syntax tree = code structure [OK]

Hint: Syntax trees show code parts and structure clearly [OK]

Common Mistakes:

• Confusing syntax tree with execution or memory management
• Thinking syntax trees store machine code
• Assuming syntax trees run the program

2. Which of the following is the correct way to represent the expression a + b * c in a syntax tree?

easy

A. Root node '+' with left child 'a' and right child '*' having children 'b' and 'c'

B. Root node '*' with left child '+' and right child 'c', '+' having children 'a' and 'b'

C. Root node '+' with children 'a', 'b', and 'c' directly

D. Root node 'a' with children '+' and '*'

Solution

1. Step 1: Recall operator precedence

   Multiplication (*) has higher precedence than addition (+), so '*' is evaluated before '+'.

2. Step 2: Build the tree respecting precedence

   The root is '+', left child is 'a', right child is '*', which has 'b' and 'c' as children.

3. Final Answer:

   Root node '+' with left child 'a' and right child '*' having children 'b' and 'c' -> Option A

4. Quick Check:

   Operator precedence guides tree structure [OK]

Hint: Remember operator precedence to build syntax trees [OK]

Common Mistakes:

• Ignoring operator precedence and ordering nodes incorrectly
• Placing all operands as direct children of root
• Confusing node roles and children

3. Given the syntax tree for the expression (x - y) / z, what is the correct preorder traversal output?

medium

A. - / x y z

B. / - x y z

C. / x - y z

D. - x y / z

Solution

1. Step 1: Understand preorder traversal

   Preorder visits root first, then left subtree, then right subtree.

2. Step 2: Apply preorder to the tree

   Root is '/', left child is '-', with children 'x' and 'y', right child is 'z'. So traversal is '/ - x y z'.

3. Final Answer:

   / - x y z -> Option B

4. Quick Check:

   Preorder = root-left-right [OK]

Hint: Preorder = root, left, right traversal order [OK]

Common Mistakes:

• Mixing traversal orders (inorder, postorder)
• Visiting children before root in preorder
• Confusing node positions in tree

4. Identify the error in this syntax tree representation of the expression a + (b * c: The tree has '+' as root, 'a' as left child, and '*' as right child with children 'b' and 'c'.

medium

A. Operator '*' should be root instead of '+'

B. The tree correctly represents the expression

C. Operands 'b' and 'c' should be swapped

D. Missing closing parenthesis causes incomplete tree

Solution

1. Step 1: Check expression syntax

   The expression has an opening parenthesis '(' but no closing ')', making it incomplete.

2. Step 2: Analyze tree correctness

   The tree structure matches the intended expression but the missing ')' means the expression is invalid, so the tree is incomplete.

3. Final Answer:

   Missing closing parenthesis causes incomplete tree -> Option D

4. Quick Check:

   Unmatched parentheses cause syntax tree errors [OK]

Hint: Check parentheses balance before building syntax tree [OK]

Common Mistakes:

• Assuming tree is correct despite syntax errors
• Confusing operator precedence with syntax errors
• Ignoring unmatched parentheses

5. How would you represent the nested expression (a + b) * (c - d) as a syntax tree to correctly reflect operator precedence and grouping?

hard

A. Root '*' with left child '+' (children 'a', 'b') and right child '-' (children 'c', 'd')

B. Root '+' with children 'a', 'b', '*', 'c', 'd'

C. Root '-' with left child '*' and right child '+'

D. Root '*' with children 'a', 'b', 'c', 'd' directly

Solution

1. Step 1: Identify operator precedence and grouping

   Parentheses force addition and subtraction to happen before multiplication.

2. Step 2: Build tree respecting groups

   Root is '*', left subtree is '+' with 'a' and 'b', right subtree is '-' with 'c' and 'd'.

3. Final Answer:

   Root '*' with left child '+' (children 'a', 'b') and right child '-' (children 'c', 'd') -> Option A

4. Quick Check:

   Parentheses define subtree grouping in syntax tree [OK]

Hint: Use parentheses to group subtrees in syntax tree [OK]

Common Mistakes:

• Ignoring parentheses and operator precedence
• Placing all operands as direct children of root
• Mixing operator positions in tree