Bottom-Up Parsing in Detail: Shift-Reduce and SLR
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Introduction to Shift-Reduce Parsing
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Today, we'll delve into Shift-Reduce parsing, a crucial bottom-up parsing strategy. What do you think Shift-Reduce parsing means, Student_1?
I think it involves shifting tokens and then reducing them, but I'm not sure how.
Exactly! The parser shifts tokens from the input onto a stack. It then looks for 'handles'βsubstrings on the stack that can be reduced. Can anyone tell me what a handle is?
Is it a part of the stack that matches a production rule?
Yes, fantastic! The handle corresponds to the right-hand side of a grammar rule. This allows the parser to effectively organize the tokens. Let's remember that: **H** for handle! Now, Student_3, could you explain what happens if we canβt find a handle?
I think it means thereβs a syntax error, right?
Precisely! If the parser doesn't find a handle, an error is reported. So far, we've learned about shifting, reducing, and error-checking. Can anyone summarize the key actions in Shift-Reduce parsing?
Shift, reduce, and report error if nothing matches!
Great summary! Remember, the key actions are the backbone of Shift-Reduce parsing.
Parsing Table and Example
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Now, let's discuss the parsing table. It tells the parser whether to shift, reduce, accept or report an error based on the current state and next token. Can anyone give me an example of when we would shift?
When we're trying to add new tokens to the stack, right?
Correct! If the next token in the input is not part of a recognized handle, we perform a shift. Let's do a quick example. What happens if our input is 'a + b' under the production rule E -> E + E | ID?
We start with an empty stack and shift 'a' onto it.
Exactly! Then what?
Then we try to reduce ID to E, right?
Yes! After reducing 'a' to E, we push '+', then shift 'b', and finally reduce again to finish parsing. This illustrates how using a parsing table guides our actions step by step.
Viable Prefixes and LR(0) Items
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Next, letβs discuss 'viable prefixes.' A viable prefix is any prefix of a rightmost sentential form that can exist on the stack. Can anyone recall what that means?
Itβs the valid sequences that can be in the parserβs stack while processing the input.
Exactly! Now, moving on to LR(0) items. What is an LR(0) item?
Itβs a production rule with a dot showing how much has been recognized so far.
That's correct! The dot helps us determine whatβs been matched and what is still expected. Can anyone give me an example of an LR(0) item?
For 'E -> E + E', it could be 'E -> E . + E' if weβve matched E.
Beautifully done! The dot is crucial for understanding parser states.
Constructing SLR Parsing Tables
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Letβs now construct SLR parsing tables. These tables use the FOLLOW set to make reduction decisions. What does the FOLLOW set represent?
It tells us which terminals can follow a non-terminal in some sentential form.
Exactly right! Itβs crucial for ensuring valid reductions. The ACTION table will help us decide what action to take depending on the current state. What are the possible actions in the ACTION table?
Shift, reduce, accept, and error!
Great! When we have a state with multiple possible actions, what happens? Can it be problematic?
Yes, we could have conflicts, like a shift/reduce or reduce/reduce conflict.
Exactly! Such conflicts mean the grammar is not suitable for SLR parsing. Understanding these conflicts is key. Letβs summarize: SLR parsing tables use FOLLOW sets and must avoid conflicts to be effective.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
The section focuses on Shift-Reduce parsing, explaining critical concepts such as handles, viable prefixes, and LR(0) items. It delves into constructing SLR parsing tables, helping students understand how these tools aid in syntactic analysis of programming languages through bottom-up parsing techniques.
Detailed
Detailed Summary
Shift-Reduce Parsing: Shift-Reduce parsing is a fundamental bottom-up approach in parsing, where the parser attempts to identify 'handles' within its stack to recognize sequences that can be reduced to non-terminals. It operates using an input buffer, stack, and a parsing table, which guides actions like shift, reduce, accept, or error based on the parser's state and the next token.
The parser continuously modifies the stack through actions:
- Shift pushes the next token onto the stack.
- Reduce recognizes a sequence (handle) that matches the right-hand side of a production rule and replaces it with the corresponding non-terminal.
- Accept indicates successful parsing when only the start symbol remains on the stack and the input buffer is empty.
Example Walkthrough: An example is provided, showing how a Shift-Reduce parser would process the input 'a + b' under a simplified grammar. Each step illustrates the actions taken until acceptance.
Viable Prefixes and Items: The concept of 'viable prefixes'βvalid prefixes of a rightmost sentential form that can occur on the stackβis vital. The section introduces LR(0) items that represent the parser's progress, using a dot to indicate recognized symbols.
Constructing LR(0) Sets: Steps to create an LR parser from augmented grammar, the closure operation, and the GOTO operation display how states are defined in the parserβs development.
SLR Parsing Tables: The creation of SLR parsing tables adds the FOLLOW set to distinguish valid reduce actions. The structure of ACTION and GOTO tables is defined, along with the rules for populating the tables, ensuring each parsing action is clearly determined. Challenges such as conflicts in SLR parsing indicate when the grammar is unsuitable for this method.
This section equips learners with essential understanding and practical skills in implementing bottom-up parsing techniques pivotal for syntax analysis in compilers.
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Introduction to Shift-Reduce Parsing
Chapter 1 of 8
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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 fundamental approach used in bottom-up parsers. In this method, the parser looks for a specific part of its stack, called the 'handle,' which is a sequence of symbols that correlates with the right-hand side of a grammar rule. When the parser finds this handle, it can then reduce it to a non-terminal's name, effectively productively reconstructing a larger portion of the input according to the grammar's production rules.
Examples & Analogies
Imagine that you're building a model from blocks. Each block represents a piece of code, and certain arrangements of blocks represent valid structures. When you identify a specific arrangement of blocks (the handle), you can replace that arrangement with a single, larger block that represents that valid structure. This is similar to how a parser recognizes a handle and reduces it to a non-terminal.
The Parser's Tools
Chapter 2 of 8
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β’ Input Buffer: Where the raw stream of tokens from the lexical analyzer waits.
β’ Stack: The parser's primary working area, storing a sequence of grammar symbols.
β’ 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
Performing effective parsing involves several key components. First, the input buffer holds the tokens, which are the basic elements extracted from the source code. The stack serves as the workspace for the parser, allowing it to manipulate these symbols as it works through potential grammar productions. Finally, the parsing table is a critical tool that acts like a guidebook. It specifies actions based on the current state of the stack and the next token, ensuring the parser follows the right process to either shift (add more information), reduce (simplify information), or report errors.
Examples & Analogies
Think of it like a chef (the parser) preparing a dish (the code) using ingredients (tokens) from a pantry (the input buffer). The counter (the stack) allows the chef to organize the ingredients they are currently using. The recipe book (the parsing table) tells the chef what actions to take next, based on the ingredients they already have prepared.
Core Actions of the Parser
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The core actions: The parser continuously performs one of these actions:
β’ Shift: Takes the next incoming token from the input buffer and pushes it onto the stack.
β’ Reduce: When symbols on the top of the stack match the entire right-hand side (beta) of a production rule (Atobeta), the parser pops these matched symbols and pushes the non-terminal A onto the stack.
β’ Accept: If the stack contains only the start symbol (Sβ²) and the input buffer is empty, the entire program has been successfully parsed.
β’ Error: If the parser cannot perform a valid action, a syntax error is reported.
Detailed Explanation
The parser operates predominantly through four actions: 'Shift', 'Reduce', 'Accept', and 'Error'. The 'Shift' action enables the parser to add the next token to the stack, progressively building the structure. The 'Reduce' action allows the parser to replace a sequence of symbols that matches a production rule with a non-terminal, simplifying the structure. Successful parsing concludes with the 'Accept' action when the start symbol is the only item left in the stack and there are no remaining tokens to process. If ever the parser finds itself without a valid action to take, it triggers an 'Error', indicating a syntax issue in the input.
Examples & Analogies
Imagine a puzzle (the program) that you are solving (parsing). Each piece you pick up is an action. When you place a piece (Shift), you're adding to your puzzle. When you find that a group of pieces fits perfectly together (Reduce), you replace them with a single larger piece in the completed puzzle. If you finish the puzzle (Accept) and every piece fits perfectly, you're done. But if you ever can't find a piece that fits (Error), something has gone wrong, and you need to reassess.
Example Walkthrough: Parsing with Shift-Reduce
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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
This walkthrough demonstrates how the parser processes a simple expression 'a + b'. At the initial state, the parser starts with an empty stack and the input 'a + b'. As a first action, it shifts the first token 'a' onto the stack. Recognizing 'a' as an identifier, it then reduces it to 'E'. Next, the parser shifts the next token, '+', and after that, it shifts 'b'. After reducing 'b' to 'E', it sees the combination 'E + E' on the stack and reduces it to a single 'E'. Finally, if only the start symbol remains on the stack with no input left, it successfully accepts the input as valid.
Examples & Analogies
Ultimately, this is like laying tiles in a pattern. You start by placing a few tiles down (shifting), realizing a group fits well together (reducing), eventually forming a complete section of your design. Once the entire area is filled correctly, you can step back and say, 'It's done!' (accept). If you suddenly find that a tile simply won't fit (error), you must reassess where you went wrong.
Viable Prefixes and Valid Items
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To build robust bottom-up parsers, we use "items" to describe the parser's progress.
β’ Viable Prefix: Any prefix of a rightmost sentential form that can exist on the stack during a shift-reduce parse. The parser's stack always holds a viable prefix.
β’ Item (LR(0) Item): A production rule with a "dot" (.) placed somewhere in its right-hand side. The dot indicates how much of the right-hand side has been recognized so far.
Detailed Explanation
In bottom-up parsing, two important concepts help guide the parser's decisions: viable prefixes and items. A 'viable prefix' is a sequence of symbols that can potentially be on the stack at any given point in the parsing process. This sequence must represent the beginning of a derivation leading to a valid string from the grammar. An 'item' is a production rule that contains a dot, which indicates how much of the right-hand side of the production has been matched so far. This dot helps the parser keep track of its progress in recognizing the structure of the input.
Examples & Analogies
Consider viable prefixes like pieces of a puzzle that may already be fitted togetherβa person assembling a puzzle can only actually place sections that fit in limited ways (the prefixes) at any moment. The items, with their dots, represent guiding instructions on where the individual pieces are in terms of completion. This is akin to tracking how far along you are in completing your puzzle section.
Constructing LR(0) Sets of Items
Chapter 6 of 8
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Chapter Content
To create an LR parser, we define all its possible "states" using "sets of LR(0) items." 1. Augmented Grammar: Add a new start production Sβ²toS to the original grammar. This ensures a single, clear reduction (Sβ²toS.) signals successful parsing. 2. CLOSURE Operation: Expands a set of items. If an item Atoalpha.Bbeta (expecting non-terminal B) is in a set, then for every production Btogamma, add Bto.gamma to the set. Repeat until no new items can be added. 3. GOTO Operation: Determines the next state after recognizing a grammar symbol X. For a set of items I and symbol X, it finds all items in I where the dot is before X (Atoalpha.Xbeta), moves the dot past X (AtoalphaX.beta), and then takes the CLOSURE of this new set of items.
Detailed Explanation
When constructing LR parsers, we create states that represent all potential configurations of the parser, utilizing sets of LR(0) items. The first step is to augment the grammar by adding a new start production to clearly identify when parsing is successful. The CLOSURE operation expands these sets when they encounter a non-terminal, adding any productions that apply and repeating this process until no new items can be added. The GOTO operation assists in transitioning between states as symbols are recognized, using the dot to track progress through the production rules.
Examples & Analogies
This process can be likened to organizing a team for a project. Each team state might represent a different phase in a project where tasks (items) exist. When a new task is added (CLOSURE), it might create more tasks (productions) that need to be tackled together. Transitioning between phases (GOTO) allows the team to tackle tasks effectively, keeping track of where they are in the project.
Constructing SLR Parsing Tables
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SLR (Simple LR) parsing leverages the LR(0) sets of items but adds the FOLLOW set to make reduce decisions. SLR Parsing Table Structure: β’ ACTION Table: ACTION[State_i, Terminal_a] can be:
β shift j: Push a and transition to state j.
β reduce A -> Ξ²: Pop |Ξ²| symbols, push A, and use the GOTO table.
β accept: Input successfully parsed.
β error: Syntax error.
Detailed Explanation
SLR parsing simplifies the construction of parsing tables by utilizing both sets of LR(0) items and the FOLLOW set, which defines what terminals may legally follow a given non-terminal. Parsing tables consist of an ACTION table that determines immediate actions to be taken (shift, reduce, accept, error) based on the current parser state and token. Reductions only occur when the FOLLOW condition is met, ensuring no ambiguity arises during parsing.
Examples & Analogies
Consider the SLR parsing table like a decision-making chart for navigating a maze. Each path taken (shift) leads you to a new point (state), while certain decisions (reduce) can only be made if you are in a specific area of the maze (according to the FOLLOW set). Successfully navigating the maze (accept) means you reached your destination smoothly. If you arrive at a place where no exits exist (error), it suggests the path taken was incorrect.
SLR Conflicts
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SLR Conflicts: A grammar is SLR(1) if its SLR parsing table contains no conflicts. Conflicts arise if a cell in the ACTION table has multiple entries: β’ Shift/Reduce Conflict: A state implies both a shift on a terminal a and a reduce action. β’ Reduce/Reduce Conflict: A state implies reductions by two different rules for the same lookahead terminal.
Detailed Explanation
For a grammar to be labeled as SLR(1), its parsing table must be conflict-free. Conflicts occur when a single entry in the ACTION table has more than one applicable action, which complicates the parsing process. Shift/reduce conflicts occur when there are both a shift and a reduce action available for the same symbol, while reduce/reduce conflicts arise when different reductions are suggested for the same terminal. The presence of conflicts suggests that the grammar cannot be parsed using the SLR method effectively.
Examples & Analogies
Imagine playing a board game where you have to make a decision, but the game rules arenβt clear. If you reach a point where you can either advance your piece (shift) or claim a bonus (reduce) with the same token piece, you face a conflict about what to do next. This uncertainty can lead to confusionβeven resulting in errors in the game, just as it does in the parsing process.
Key Concepts
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Shift-Reduce Parsing: A fundamental technique in bottom-up parsing that focuses on shifting tokens and reducing them to grammar rules.
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Handle: A substring on the stack that matches a grammar rule's right-hand side and can be reduced.
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Parsing Table: A table guiding the parser to take actions based on the current state and the next input.
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Viable Prefix: Valid prefixes of a sentential form representing potential stack states during parsing.
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LR(0) Item: A production rule representation indicating recognized symbols for parsing progress.
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SLR Parsing: A method using FOLLOW sets in parsing tables to clarify reduction actions and avoid conflicts.
Examples & Applications
An example of Shift-Reduce Parsing: For the input 'a + b' under the rule E -> E + E | ID, the stack transitions through shifts and reductions until the input is parsed successfully.
Viable prefixes example: During the parsing of an input, if the stack holds '$E+' or '$E+b', these are viable prefixes that indicate valid progress towards deriving a complete sentence.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
When you're parsing, shift it right; reduce with a handle, that's your might.
Stories
Imagine a construction worker building from ground up (shift tokens) and replacing blocks with pillars (reduce to non-terminals), finally reaching the roof (accept completed parse).
Memory Tools
Remember S for Shift and R for Reduce β this keeps your parsing in good use!
Acronyms
H.A.S.S
Handle
Action
Shift
Stack β the four essentials for a quick parsing hack.
Flash Cards
Glossary
- ShiftReduce Parsing
A bottom-up parsing strategy that builds the parse tree by shifting tokens onto a stack and reducing them to non-terminals when possible.
- Handle
A substring on the stack that matches the right-hand side of a grammar production and can be reduced to a non-terminal.
- Parsing Table
A pre-computed table used by the parser to decide actions like shift, reduce, accept, or error based on the current state and next input token.
- 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 so far.
- SLR Parsing
Simple LR parsing, which adds the FOLLOW set to LR(0) items to resolve reduce actions in parsing tables.
- ACTION Table
A component of the parsing table that defines the parser's actions based on the current state and input token.
- GOTO Table
A component of the parsing table that indicates the next state after recognizing a grammar symbol.
- FOLLOW Set
A set of terminals that can appear immediately to the right of a non-terminal in some sentential form.
- Conflict
A situation where a parsing table entry indicates multiple actions (e.g., shift/reduce conflict), which can disrupt parsing accuracy.
Reference links
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