Shift-reduce parsing in Compiler Design - Full Explanation

Introduction

Imagine trying to understand a sentence by reading it word by word and deciding when to group words together to form meaningful parts. Shift-reduce parsing solves the problem of analyzing sentences or code by deciding when to read more input and when to combine parts into larger structures.

Explanation

Shift operation

The parser reads the next input symbol and pushes it onto a stack. This means it delays making decisions and gathers more information before combining parts. Shifting helps the parser collect pieces of the sentence or code step by step.

Shift means reading the next input and storing it for later processing.

Reduce operation

When the top elements on the stack match the right side of a grammar rule, the parser replaces them with the rule's left side. This combines smaller parts into a bigger, meaningful unit. Reduction simplifies the structure by grouping related symbols.

Reduce means combining stack elements into a higher-level structure based on grammar rules.

Parsing stack

The stack holds symbols and partial results during parsing. It helps keep track of what has been read and what can be combined. The stack grows with shifts and shrinks with reductions, guiding the parser's decisions.

The stack stores symbols and partial groups to manage parsing progress.

Parsing decisions

The parser must decide whether to shift or reduce at each step. This decision depends on the grammar and the current stack content. Correct decisions lead to successful parsing, while wrong ones cause errors or confusion.

Choosing when to shift or reduce is crucial for correct parsing.

Real World Analogy

Imagine building a puzzle by picking up pieces one by one (shift) and then connecting pieces that fit together to form a bigger part of the picture (reduce). You keep doing this until the whole puzzle is complete.

Shift operation → Picking up a new puzzle piece and holding it before connecting

Reduce operation → Connecting puzzle pieces that fit to form a bigger section

Parsing stack → The pile of puzzle pieces you are currently holding and working with

Parsing decisions → Deciding whether to pick another piece or connect pieces you have

Diagram

Diagram

Input: a b c d

Stack: [ ]

Step 1: Shift 'a'
Stack: [a]

Step 2: Shift 'b'
Stack: [a b]

Step 3: Reduce 'a b' to X
Stack: [X]

Step 4: Shift 'c'
Stack: [X c]

Step 5: Reduce 'X c' to Y
Stack: [Y]

Step 6: Shift 'd'
Stack: [Y d]

Step 7: Reduce 'Y d' to Z
Stack: [Z]

Parsing complete.

This diagram shows how the parser shifts input symbols onto the stack and reduces them step by step to parse the input.

Key Facts

Shift → Reading the next input symbol and pushing it onto the stack.

Reduce → Replacing stack symbols matching a grammar rule's right side with the rule's left side.

Parsing stack → A data structure that holds symbols and partial results during parsing.

Shift-reduce conflict → A situation where the parser cannot decide whether to shift or reduce next.

Bottom-up parsing → Parsing approach that builds parse trees from input symbols up to the start symbol.

Common Confusions

Believing shift-reduce parsing only shifts or only reduces at fixed times.

Believing shift-reduce parsing only shifts or only reduces at fixed times. Shift-reduce parsing dynamically chooses to shift or reduce based on the current stack and input, not in a fixed order.

Thinking the stack holds only input symbols.

Thinking the stack holds only input symbols. The stack holds both input symbols and intermediate results after reductions.

Assuming reduce always happens after all input is read.

Assuming reduce always happens after all input is read. Reductions can happen anytime when the top stack symbols match a grammar rule, even before all input is consumed.

Summary

Shift-reduce parsing reads input symbols and decides when to combine them into larger structures using a stack.

The parser shifts symbols onto the stack and reduces them based on grammar rules to build the parse tree from bottom up.

Correctly choosing when to shift or reduce is key to successfully understanding the input.

Practice

1. What is the main purpose of shift in shift-reduce parsing?

easy

A. To move the next input symbol onto the stack

B. To remove symbols from the stack

C. To check the grammar rules

D. To accept the input string

Solution

1. Step 1: Understand the role of shift

   In shift-reduce parsing, shifting means taking the next input symbol and placing it on the stack.

2. Step 2: Differentiate shift from reduce

   Reduce means replacing symbols on the stack using grammar rules, while shift just moves input symbols onto the stack.

3. Final Answer:

   To move the next input symbol onto the stack -> Option A

4. Quick Check:

   Shift = move input symbol to stack [OK]

Hint: Shift means push next input symbol onto stack [OK]

Common Mistakes:

• Confusing shift with reduce
• Thinking shift removes symbols
• Assuming shift checks grammar

2. Which of the following is the correct sequence of actions in shift-reduce parsing?

easy

A. Accept, Shift, Reduce

B. Reduce, Shift, Accept

C. Shift, Reduce, Accept

D. Shift, Accept, Reduce

Solution

1. Step 1: Recall the parsing process order

   Shift-reduce parsing first shifts symbols onto the stack, then reduces them using grammar rules, and finally accepts if input is valid.

2. Step 2: Match the correct sequence

   The correct order is Shift, then Reduce, then Accept.

3. Final Answer:

   Shift, Reduce, Accept -> Option C

4. Quick Check:

   Shift -> Reduce -> Accept [OK]

Hint: Remember parsing order: shift first, then reduce [OK]

Common Mistakes:

• Mixing up reduce and shift order
• Thinking accept happens before reduce
• Assuming reduce happens before any shift

3. Given the grammar rules:
S -> aA
A -> b
And input string ab, what is the correct sequence of stack contents during shift-reduce parsing?

medium

A. [ ] -> [a] -> [b] -> [S]

B. [ ] -> [a] -> [S] -> [S, b]

C. [ ] -> [b] -> [a, b] -> [S]

D. [ ] -> [a] -> [a, b] -> [S]

Solution

1. Step 1: Shift input symbols onto stack

   First, shift 'a' onto the stack: stack = [a]. Then shift 'b': stack = [a, b].

2. Step 2: Apply reductions using grammar rules

   Reduce 'b' to 'A' using A -> b, then reduce 'aA' to 'S' using S -> aA. Final stack is [S].

3. Final Answer:

   [ ] -> [a] -> [a, b] -> [S] -> Option D

4. Quick Check:

   Shift a, shift b, reduce to S [OK]

Hint: Shift all input, then reduce using grammar rules [OK]

Common Mistakes:

• Reducing too early before all symbols shifted
• Mixing order of symbols on stack
• Skipping reduction steps

4. In a shift-reduce parser, if the parser tries to reduce a symbol that does not match any grammar rule, what is the likely problem?

medium

A. The parser is shifting symbols incorrectly

B. The input string is invalid or contains errors

C. The parser is correctly accepting the input

D. The grammar rules are too simple

Solution

1. Step 1: Understand reduction failure

   If no grammar rule matches the symbols on the stack, the parser cannot reduce, indicating a problem with the input.

2. Step 2: Interpret the failure meaning

   This usually means the input string does not follow the grammar rules and is invalid or contains errors.

3. Final Answer:

   The input string is invalid or contains errors -> Option B

4. Quick Check:

   Failed reduce = invalid input [OK]

Hint: No matching reduce means input error [OK]

Common Mistakes:

• Assuming parser is always correct
• Thinking reduce failure means grammar is simple
• Confusing shift errors with reduce errors

5. Consider the grammar:
E -> E + T | T
T -> int
For the input string int + int + int, which sequence of actions correctly shows the shift-reduce parsing steps to fully reduce the input?

hard

A. Shift int, reduce T, reduce E, shift +, shift int, reduce T, reduce E, shift +, shift int, reduce T, reduce E

B. Shift int, shift +, reduce T, reduce E, shift int, shift +, reduce T, reduce E, shift int, reduce E

C. Shift int, reduce T, shift +, reduce E, shift int, reduce T, shift +, reduce E, shift int, reduce T

D. Shift int, reduce E, shift +, shift int, reduce T, reduce E, shift +, shift int, reduce T, reduce E

Solution

1. Step 1: Shift and reduce first int

   Shift 'int', reduce to T, then reduce T to E (since E -> T).

2. Step 2: Process first plus and second int

   Shift '+', shift 'int', reduce 'int' to T, then reduce 'E + T' to E.

3. Step 3: Process second plus and third int

   Shift '+', shift 'int', reduce 'int' to T, then reduce 'E + T' to E again, fully reducing input.

4. Final Answer:

   Shift int, reduce T, reduce E, shift +, shift int, reduce T, reduce E, shift +, shift int, reduce T, reduce E -> Option A

5. Quick Check:

   Shift and reduce each int, then reduce E + T repeatedly [OK]

Hint: Shift int, reduce T, reduce E, repeat for each + int [OK]

Common Mistakes:

• Reducing E too early or too late
• Skipping shifts of '+' symbols
• Confusing order of reduce steps