Example Walkthrough: Parsing a + b with Shift-Reduce
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Introduction to Shift-Reduce Parsing
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Today, we are going to explore shift-reduce parsing. Can anyone tell me what a parser does in general?
It checks if the source code is structured correctly based on syntax rules.
Exactly! A parser takes tokens and organizes them into a valid syntax structure. Shift-reduce parsing specifically starts with the input tokens and works up to the start symbol. Let's remember this approach using the acronym SH-R, Shift-Reduce.
What does 'Shift' actually mean in this context?
Great question! 'Shift' means taking the next token from the input buffer and moving it onto the stack. This prepares the parser to recognize patterns.
What about 'Reduce'?
When the stack's top symbols match a production rule's right side, we can 'reduce' those symbols into the corresponding non-terminal, simplifying our structure. Remember - SH-R helps us keep track!
Can you show us a real example?
Certainly! We will break down the expression 'a + b' step-by-step after this. Overall, remember β we shift tokens onto the stack and reduce them to form higher-level structures.
Steps in Parsing `a + b`
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Let's dive into parsing the expression `a + b`. Initially, our stack is just `$`, and our input is `a + b $`. What do we do first?
We would shift the first token, which is `a`, onto the stack.
Correct! So now our stack is `$ a`. What comes next?
Now we can reduce because `a` is an ID, and it matches the production rule for E.
That's right! After reducing, we now have `$ E`. And then?
Next, we shift the `+` onto the stack, making it `$ E +`.
Exactly! This combines `E` with `+`, and what happens when we shift `b` onto the stack next?
We can then reduce again to get `$ E + E`!
Wonderful! Finally, since we can reduce the entire stack down to just `E`, we accept the parse. This process showcases how shift-reduce parsing captures structure step by step.
Understanding Viable Prefixes and Items
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Now, let's talk about viable prefixes. Who can explain what it means?
That's any prefix of a rightmost sentential form that could be present on the stack during our parsing.
Exactly! For example, in our parsing of `a + b`, some viable prefixes include `$`, `$ E`, and `$ E +`. Why do you think understanding these helps the parser?
Knowing the viable prefixes allows the parser to make correct decisions on what to shift or reduce next!
Correct! And we also have items or LR(0) items, which show how much of a right-hand side of a rule has been recognized. Can anyone give me an example of an item?
Like `E -> ID .`? That shows we matched an ID and are ready to reduce.
Right again! Items provide the current status of parsing and help guide the parser's actions effectively.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
In this section, we demonstrate the shift-reduce parsing technique with the example expression a + b. The operations involved, such as shifting, reducing, and accepting, are explained in detail. The importance of viable prefixes and items in guiding the parsing process is also highlighted.
Detailed
Detailed Summary
In this section, we delve into the mechanics of Shift-Reduce Parsing, a fundamental technique in bottom-up parsing. This technique systematically transforms a sequence of tokens into a syntactically correct structure based on predefined grammar rules.
The example provided, parsing the input string a + b, illustrates how the parser leverages an input buffer, a stack, and a precomputed parsing table to determine the appropriate actions:
- Initial Setup: The parsing begins with the input string, which includes tokens separated by an end marker symbol (
$). - Actions Explained: The parser can perform four core actions:
- Shift: This action transfers the next token from the input buffer to the stack.
- Reduce: This happens when the sequence at the top of the stack matches the right-hand side of a production rule, allowing it to replace that sequence with the corresponding non-terminal.
- Accept: This indicates the successful completion of parsing when the stack contains only the start symbol and the input buffer is empty.
- Error: If none of the valid actions can be performed, a syntax error is flagged.
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Example Walkthrough of Parsing
a + b: Utilizing the grammar: E -> E + EE -> ID
The step-by-step actions to parse the expressiona + bdemonstrate how the parser interacts with both the stack and input buffer until it either accepts or errors out. An example state is shown at each step, allowing students to visualize how parsing evolves through various stages:- Start: Stack contains only
$(indicating the start), and input isa + b $. - Shifting and reducing operations are explained alongside diagrams showing the stack's evolution.
- Viable Prefixes and LR(0) Items: The section concludes with definitions of viable prefixes and items, which are instrumental in guiding shift-reduce parses by indicating valid states of the parser during execution.
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Introduction to Shift-Reduce Parsing
Chapter 1 of 4
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Chapter Content
Shift-Reduce parsing is a strategy that operates by trying to find the "handle" in the parser's stack. A handle is a substring on the stack that matches the right-hand side of a grammar production and can be "reduced" to its corresponding non-terminal.
Detailed Explanation
Shift-Reduce parsing is a method used in bottom-up parsing where the parser takes actions based on the current content of its stack (which holds symbols) and the input (the remaining tokens to be processed). It specifically searches for a 'handle,' which is a sequence of symbols on the stack that matches the right-hand side of a grammar production rule. When it finds such a match, it performs a reduction, replacing that sequence with the corresponding non-terminal symbol from the left-hand side of the rule.
Examples & Analogies
Imagine you are a chef following a recipe. Each step corresponds to a grammar production. If you have a bowl of mixed ingredients (the stack) and you're trying to recognize certain combinations (handles), you combine them to make a dish (reduce). When you fully complete a dish (recognizing a non-terminal), you can serve it (accept).
The Parser's Tools
Chapter 2 of 4
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Chapter Content
The Parser's Tools:
- Input Buffer: Where the raw stream of tokens from the lexical analyzer waits.
- Stack: The parser's primary working area, storing a sequence of grammar symbols.
- Parsing Table: Pre-computed from the grammar, it tells the parser what to do (shift, reduce, accept, or error) based on the current state (top of stack) and the next input token (the "lookahead" symbol).
Detailed Explanation
In Shift-Reduce parsing, the parser relies on three primary tools. The Input Buffer holds the tokens generated by the lexical analyzer, which the parser processes sequentially. The Stack is where the parser builds potential structures by pushing symbols onto it and popping them off when certain rules apply. The Parsing Table is crucial; it predefines the parser's actionsβwhether to shift a token onto the stack, reduce a sequence of symbols to a non-terminal, or accept the completed parse. This table is determined based on the grammar's production rules.
Examples & Analogies
Think of this setup like a train station. The Input Buffer is like the train tracks where incoming trains (tokens) wait. The Stack represents the platforms where each train may stop (push and pop symbols). The Parsing Table acts as the station's schedule, indicating which train (action) goes where and when, directing operations.
The Core Actions
Chapter 3 of 4
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Chapter Content
The core actions: the parser continuously performs one of these actions:
- Shift: Takes the next incoming token from the input buffer and pushes it onto the stack.
- Reduce: When symbols on the top of the stack match the entire right-hand side (beta) of a production rule (A to beta), the parser pops these matched symbols and pushes the non-terminal A onto the stack. This signifies that a complete grammatical construct has been recognized.
- Accept: If the stack contains only the start symbol (Sβ²) and the input buffer is empty, the entire program has been successfully parsed.
- Error: If the parser cannot perform a valid action, a syntax error is reported.
Detailed Explanation
In Shift-Reduce parsing, the parser can perform four core actions:
1. Shift: This action takes the next token from the input buffer and adds it to the stack, increasing the amount of information available for matching production rules.
2. Reduce: When the top of the stack contains a sequence of symbols matching a production rule's right-hand side, the parser removes that sequence and adds back the corresponding non-terminal, indicating that it has successfully recognized a valid construct.
3. Accept: This action occurs when the stack has been reduced to only contain the start symbol and there are no more tokens left in the input buffer, indicating successful parsing.
4. Error: If the parser finds itself in a situation where none of its defined actions can be applied, it signals a syntax error, indicating that something went wrong with the input.
Examples & Analogies
Consider a puzzle where each piece corresponds to a token. Shifting is like adding a new piece to the puzzle (stack). Reducing is when you recognize a cluster of pieces that fit together to create a bigger picture (non-terminal). Accepting is when the whole puzzle is complete and all pieces fit (successful parse), and an error happens when you find a piece that doesnβt fit anywhere.
Example Walkthrough
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Chapter Content
Example Walkthrough: Parsing a + b with Shift-Reduce (Assume simplified grammar: E -> E + E | ID)
Initial state: Stack: $ | Input: a + b $ (where $ marks end of input)
Stack Input Action (determined by Parsing Table)
$ a + b $ Shift a
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 b
Push b onto stack.
$E+b $ 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
In this walkthrough, we apply Shift-Reduce parsing to the expression 'a + b' using a simplified grammar. We initialize the stack with a special end marker, and the input consists of tokens 'a', '+', and 'b'. Starting with the input 'a + b', we first 'shift' the token 'a' onto the stack. Next, since 'a' is recognized as an identifier (ID), we perform a 'reduce' action, replacing 'a' with a non-terminal 'E'. We continue by shifting the '+' token and then the 'b' token onto the stack. After recognizing 'b' as another ID and reducing it to 'E', we have 'E + E' on the stack. The final reduction combines this into a single 'E', and upon verifying that the stack's content equals the start symbol with an empty input, the parser accepts the input as successfully parsed.
Examples & Analogies
Think of parsing 'a + b' like building a bridge. Begin with small pieces (the tokens). First, place piece 'a' (shift). Recognize that 'a' fits into the structure (reduce). Next, add piece '+' and then 'b' in the same way. Each time you recognize the pieces fitting together (reducing), you're constructing something bigger until you finally see the whole bridge is built (accept).
Key Concepts
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Shift: The action of moving the next token onto the stack.
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Reduce: The process of replacing a series of symbols on the stack with a non-terminal.
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Accept: Indicates successful parsing when only the start symbol remains on the stack.
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Error: A state of syntax error when no further valid actions can be applied.
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Viable Prefix: Refers to all prefixes that can appear on the stack during the parsing.
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LR(0) Item: Shows the status of a production rule's recognition in parsing.
Examples & Applications
When parsing 'a + b', the sequence of actions starts with shifting 'a' onto the stack, followed by reducing it to E, and progressing through shifts and reduces until the input is fully accepted.
A viable prefix during the parsing process could be $a+$, which indicates that this sequence could be recognized at that state.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
Shift it left, reduce it tight, parsing code feels just right!
Stories
Imagine a train (the input) moving into a station (the stack), stopping to offload passengers (tokens) one by one, while the dispatcher (parser) decides whether to board them (reduce) into the final train (valid structure).
Memory Tools
The Actions of Parsing: 'S' for Shift, 'R' for Reduce, 'A' for Accept, 'E' for Error = 'SRAE'.
Acronyms
SH-R
Shift and Reduce; remember the flow of parsing actions!
Flash Cards
Glossary
- Shift
An action in parsing that moves the next token from the input buffer onto the stack.
- Reduce
An action that replaces a sequence of symbols on the stack with a corresponding non-terminal according to a production rule.
- Accept
The condition indicating successful parsing when the stack contains only the start symbol and the input buffer is empty.
- Error
A state reached when no valid actions can be performed, indicating a syntax error.
- Viable Prefix
Any prefix of a rightmost sentential form that can exist on the stack during a shift-reduce parse.
- LR(0) Item
A production rule with a dot (.) indicating how much of the right-hand side has been recognized.
Reference links
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