Example Walkthrough: Parsing a + b with Shift-Reduce - 6.2.1.1 | Module 3: Syntax Analysis (Parsing) | Compiler Design /Construction
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6.2.1.1 - Example Walkthrough: Parsing a + b with Shift-Reduce

Practice

Interactive Audio Lesson

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Introduction to Shift-Reduce Parsing

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Teacher
Teacher

Today, we'll learn about Shift-Reduce parsing! This is a fundamental technique used by parsers to interpret programming languages. Who can tell me what a parser does?

Student 1
Student 1

A parser checks the syntax of code to make sure it's correct.

Teacher
Teacher

Exactly! And Shift-Reduce parsing does it by using a stack to manage symbols. How do you think this could be useful?

Student 2
Student 2

It helps organize the code structure by breaking it down into manageable pieces.

Teacher
Teacher

Correct! Remember this acronym: 'S-R' for Shift-Reduce parsing. Let's begin with how the Shift action works.

Understanding the Shift and Reduce Actions

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Teacher
Teacher

In Shift-Reduce parsing, the 'Shift' action takes a token from the input and puts it on the stack. What do you think 'Reduce' does?

Student 3
Student 3

It replaces symbols on the stack with a non-terminal?

Teacher
Teacher

Correct! It condenses multiple symbols into one non-terminal, simplifying the stack. Now, let’s go through a practical example with the expression 'a + b'. What would we do first?

Student 4
Student 4

We would Shift 'a' onto the stack.

Teacher
Teacher

Excellent! And when we see the '+'?

Student 2
Student 2

We would Shift it onto the stack too after processing 'a'!

Teacher
Teacher

Great! Remember, as you Shift and Reduce, you're building towards the final parse tree.

Example Walkthrough of Parsing 'a + b'

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0:00
Teacher
Teacher

Let's analyze how we can parse 'a + b'. Beginning with an empty stack and full input: '$ a + b $'. What’s our first move?

Student 1
Student 1

Shift 'a' onto the stack!

Teacher
Teacher

Correct! So now our stack has '$ a'. Next?

Student 3
Student 3

We can reduce 'a' to 'E' since 'a' is an ID.

Teacher
Teacher

Exactly! Now our stack is '$ E'. What’s next?

Student 4
Student 4

Shift '+' onto the stack.

Teacher
Teacher

Right! Now, if we continue with 'b', we can apply the same steps. Who can summarize the process so far?

Student 2
Student 2

We shifted 'a', reduced it to 'E', shifted '+' and then shifted 'b' onto the stack as well.

Teacher
Teacher

Wonderful! Now we know how to construct and interpret every step in Shift-Reduce Parsing.

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

This section delves into Shift-Reduce parsing, explaining how parsers use this strategy to interpret and validate expressions in programming languages.

Standard

In this section, we explore the fundamentals of Shift-Reduce parsing, a bottom-up method that allows parsers to construct parse trees by shifting tokens onto a stack and reducing them based on grammar rules. An example illustrates how an expression like 'a + b' is processed step by step to achieve valid parsing.

Detailed

Example Walkthrough: Parsing a + b with Shift-Reduce

Shift-Reduce parsing is an essential concept in compiler design, specifically in the context of bottom-up parsing. This technique operates by attempting to construct a parse tree from the leaves (input tokens) upwards to the root (start symbol).

Core Components

  • Input Buffer: Contains the stream of tokens generated by the lexical analyzer, waiting to be processed.
  • Stack: The working area of the parser that holds a sequence of symbols (both terminals and non-terminals) during parsing.
  • Parsing Table: Pre-computed table guiding the parser on when to shift, reduce, accept, or report errors.

Parsing Process

The process involves two main actions: Shift and Reduce.
- Shift: The parser pulls the next token from the input buffer and adds it to the top of the stack.
- Reduce: If the top of the stack matches the right-hand side of one of the production rules, those symbols are replaced with the corresponding non-terminal.

Example Walkthrough: Parsing 'a + b'

Given a simplified grammar: E -> E + E | ID

Steps: 1. Initialize Stack and Input

  • Stack: $
  • Input: a + b $

Steps of Parsing:

  1. Shift 'a' onto the stack.
  2. Reduce ID to E for 'a'.
  3. Shift '+' onto the stack.
  4. Shift 'b' onto the stack.
  5. Reduce ID to E for 'b'.
  6. Reduce E + E to E for the complete expression.
  7. Accept the parsing as successful because the stack contains only the start symbol and the input is empty.

Significance

Understanding Shift-Reduce parsing is crucial as it lays the groundwork for how modern compilers analyze code structures and enforce grammatical correctness, ensuring effective program execution.

Audio Book

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Introduction to Shift-Reduce Parsing

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Assume simplified grammar: E -> E + E | ID
Initial state: Stack: $ | Input: a + b $ (where $ marks end of input)

Detailed Explanation

In this section, we introduce shift-reduce parsing with a simplified grammar for expressions. The grammar defines an expression (E) that can either be the sum of two expressions (E + E) or a single identifier (ID). The initial state of the parser includes a stack that contains a special symbol ($) indicating the start of parsing and the input buffer which has the tokens 'a', '+', and 'b', followed by a '$' indicating the end of the input.

Examples & Analogies

Think of the stack as a container where you start building a LEGO structure (the parse tree). Initially, the container is empty except for a base marker ($) that shows where your structure begins. The tokens 'a', '+', and 'b' are like LEGO pieces laid out flat, ready to be added to the structure.

Parser Actions Explained

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Stack Input Action (determined by Parsing Table) Explanation
$ a + b $ Shift Push 'a' onto stack.
$ a + b $ Reduce E -> ID 'a' is an ID. Reduce 'ID' to 'E'. Pop 'a', push 'E'.
$ E + b $ Shift Push '+' onto stack.
$ E + b $ Shift Push 'b' onto stack.
$ E + E $ Reduce E -> ID 'b' is an ID. Reduce 'ID' to 'E'. Pop 'b', push 'E'.
$ E + E $ Reduce E -> E + E 'E + E' is on top of stack. Reduce to 'E'. Pop 'E', '+', 'E', push 'E'.
$ E $ Accept Stack has start symbol, input empty. Success!

Detailed Explanation

This table outlines the series of actions the parser takes as it processes the input tokens using the shift-reduce strategy. During 'Shift' actions, the parser moves tokens from the input to the stack. For instance, when it encounters 'a', it shifts 'a' onto the stack. The 'Reduce' action occurs when the parser identifies that a valid production rule matches the sequence currently on the stack, allowing it to replace part of the stack with the corresponding non-terminal. For example, when 'ID' is reduced to 'E', it signifies that 'a' is part of a valid expression. The process continues until only the start symbol ($) remains in the stack, signifying successful parsing of the entire input.

Examples & Analogies

Imagine you're assembling a sandwich. Each stepβ€”adding the ingredients (tokens) like lettuce, tomatoes, and cucumbers (letters)β€”represents a shift. When you finally have a full layer of ingredients (recognizing a grammar production), you compress them into a sandwich (reduce). Completing the sandwich means you can enjoy it, just like reaching the final parse with all input consumed signals success!

Final State and Acceptance

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Final state: Stack contains start symbol, and input is empty.

Detailed Explanation

In the final state of our shift-reduce parsing example, the stack contains only the start symbol which indicates the parse is complete, and there are no remaining tokens in the input buffer. This means the parsing has been successful, and the input string 'a + b' has been correctly interpreted according to our grammar rules.

Examples & Analogies

Think of finishing a puzzle: you’ve placed all the pieces (tokens) together to form a complete picture (the parse tree). Once you have the last piece in place (the start symbol at the top of the stack), you step back and see that the entire puzzle is assembled. Completing your parsing puzzle means you can move on to the next phase of processing the code.

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Shift: The action of moving a token onto the stack.

  • Reduce: The action of replacing symbols on the stack with a non-terminal.

  • Parse Tree: Visual representation of the syntactic structure of an expression.

  • Handle: Any substring on the stack matching the right-hand side of a production.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Parsing the expression 'a + b' where 'a' and 'b' are variables and '+' is an operator.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎡 Rhymes Time

  • Shift the floor, Reduce the core, Stack it right, Parse in sight.

πŸ“– Fascinating Stories

  • Imagine a builder (parser) who first lays down bricks (tokens) one by one. Each brick fits into the wall (stack) until it forms a window (non-terminal) that can be 'reduced' into a beautiful house (parse tree).

🧠 Other Memory Gems

  • S-R: Shift first, then Reduce, to make parsing a breeze.

🎯 Super Acronyms

S for Stack, R for Reduce β€” it’s how we build a valid produce!

Flash Cards

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Glossary of Terms

Review the Definitions for terms.

  • Term: Shift

    Definition:

    An action in parsing that moves the next input token onto the top of the stack.

  • Term: Reduce

    Definition:

    An action in parsing that replaces a series of grammar symbols on the stack with a single non-terminal.

  • Term: Parser

    Definition:

    A program that analyzes code for correct syntax according to predefined grammar.

  • Term: Parse Tree

    Definition:

    A tree structure that represents the syntactic structure of a string according to a grammar.

  • Term: Handle

    Definition:

    A part of the stack that matches the right-hand side of a production rule and is eligible for reduction.