Constructing SLR Parsing Tables (Simple LR)
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Introduction to SLR Parsing Tables
π Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Today we're diving into SLR parsing tables. Can anyone tell me what an SLR parsing table is designed to accomplish?
I think it's used in parsers to guide how the input is processed, right?
Exactly! The SLR parsing table helps the parser decide whether to shift or reduce based on the current input. The structure comprises both an ACTION and a GOTO table. Let's break those down.
What's in the ACTION table?
Great question! The ACTION table contains instructions to 'shift', 'reduce', 'accept', or 'error'. These instructions guide the parser's operations as it processes tokens.
So how does the GOTO table fit into this?
"The GOTO table helps when we handle non-terminals. It tells the parser where to go after a reduction. Letβs note that!
Constructing SLR Parsing Tables
π Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Now that we have the basics down, letβs look at how to construct an SLR parsing table from a grammar. Whatβs the first step?
Is it to define our grammar with the necessary components?
Correct! First, we define the grammar components: productions, terminals, and non-terminals. Then we create the LR(0) items for the grammar. Can anyone tell me what that means?
It's about placing a dot in our production rules to show the parser's current position?
Exactly! That's the heart of our parser's state. Next, we apply the CLOSURE operation for these items to expand our state effectively until there are no new items to add. Who remembers how that works?
We repeatedly add items based on the non-terminals we encounter, right?
Thatβs right! Finally, we build the canonical collection of items, extracting unique states in our parser. This process sets the stage for creating our ACTION and GOTO tables. Who can briefly summarize how to fill them out?
We fill ACTION based on shift and reduce actions tied to the state and input. GOTO captures transitions to the next state for non-terminals.
Spot on! Hence, the construction process aligns the grammar process into a structured format where our parser can efficiently operate.
Handling Conflicts in SLR Parsing Tables
π Unlock Audio Lesson
Sign up and enroll to listen to this audio lesson
Conflicts can arise while constructing our parsing tables. Can anyone name the two types we typically deal with?
Shift/Reduce conflicts and Reduce/Reduce conflicts?
Correct! Shift/Reduce conflicts occur when a parser has to choose between shifting a terminal or reducing a non-terminal. How do we mitigate these?
I think we need to carefully manage the FOLLOW set for our productions.
Precisely! Adjusting the FOLLOW set helps ascertain clear reduction opportunities. What about Reduce/Reduce conflicts?
Those happen because multiple reductions can apply at once?
That's correct! We resolve these by ensuring that each reduction rule is uniquely applied based on the FOLLOW context. Summarizing today: understanding and carefully structuring both tables eliminates ambiguities during parsing.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
In this section, students learn how to construct SLR parsing tables, which include an ACTION table for shift and reduce operations and a GOTO table for non-terminals. By utilizing the FOLLOW set, students will understand how to avoid parsing conflicts, ensuring efficient and accurate syntax analysis for compilers.
Detailed
Detailed Summary
This section delves into the construction of SLR (Simple LR) parsing tables, a crucial component in the bottom-up parsing approach used in modern compilers. The main components of an SLR parsing table include:
SLR Parsing Table Structure
- ACTION Table: This table outlines the actions to be performed based on the current parser state and the lookahead symbol from the input. The possible actions include:
- shift j: Move to a new state upon reading a terminal.
- reduce A β Ξ²: Replace a matched sequence on the stack with a non-terminal.
- accept: Indicate successful parsing.
- error: Report an invalid syntax.
- GOTO Table: Defines transitions between states for non-terminals.
Rules for Constructing SLR Table Entries
- Shift Actions: Defined when a production ruleβs right side is about to be processed.
- Reduce Actions: Implement reductions based on the FOLLOW set, which helps determine valid opportunities for reductions.
- Accept Action: Complete parsing successfully if the start symbol is reached.
- GOTO Actions: Used to transition based on grammar structures.
SLR Conflicts
An SLR grammar is conflict-free, meaning the ACTION table must not have multiple entries for any given state and terminal. Two primary conflicts are:
- Shift/Reduce Conflict: Indicates ambiguity in whether to shift or reduce based on the current state and input.
- Reduce/Reduce Conflict: Occurs when multiple reductions are possible for the same terminal.
By understanding these fundamental concepts, students will appreciate how SLR parsing optimizes grammatical analysis and resolves potential ambiguities.
Audio Book
Dive deep into the subject with an immersive audiobook experience.
SLR Parsing Table Structure
Chapter 1 of 3
π Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
SLR (Simple LR) parsing leverages the LR(0) sets of items but adds the FOLLOW set to make reduce decisions.
SLR Parsing Table Structure:
- ACTION Table: ACTION[State_i, Terminal_a] can be:
- shift j: Push a and transition to state j.
- reduce A -> Ξ²: Pop |Ξ²| symbols, push A, and use the GOTO table.
- accept: Input successfully parsed.
- error: Syntax error.
- GOTO Table: GOTO[State_i, NonTerminal_A] = State_j: The state to transition to after reducing to NonTerminal_A from State_i.
Detailed Explanation
The SLR parsing table is made up of two parts: the ACTION table and the GOTO table. The ACTION table tells the parser what to do based on the current state and the next input token. For example, if the current state suggests 'shift', it moves to another state by pushing the current token. The GOTO table indicates what state to transition to next after completing a reduction involving a non-terminal. This structure is essential for guiding the parserβs decisions as it attempts to analyze the input based on grammar rules.
Examples & Analogies
Think of the ACTION and GOTO tables like a road map for a journey. The ACTION table is like a set of instructions that tells you when to turn, and the GOTO table shows which road to take next, depending on where you are currently. Just as following a road map helps you reach your destination without getting lost, these tables help the parser successfully process code according to the rules of the language.
Rules for Constructing SLR Parsing Table Entries
Chapter 2 of 3
π Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
Rules for Constructing SLR Parsing Table Entries:
- Shift Actions: For Atoalpha.abeta in state I_i where a is a terminal, and GOTO(I_i,a) is I_j, set ACTION[i, a] = shift j.
- Reduce Actions: For Atoalpha. in state I_i (entire right-hand side matched), then for every terminal b in FOLLOW(A), set ACTION[i, b] = reduce A -> Ξ±. The FOLLOW(A) set is crucial, ensuring a reduction is performed only if b can legally follow A.
- Accept Action: If Sβ²toS. is in state I_i, set ACTION[i, $] = accept.
- GOTO Actions: If GOTO(I_i,A) is I_j (where A is a non-terminal), set GOTO[i, A] = j.
Detailed Explanation
Rules for constructing entries in SLR parsing tables guide how the parser makes decisions while reading input. For shift actions, if a terminal is recognized, the parser shifts to a new state. When it recognizes an entire production (right-hand side), it performs a reduce action, which means replacing the recognized symbols with a non-terminal. The accept action indicates successful parsing when the start symbol is alone on the stack. The GOTO entries indicate what state to transition to after a reduction completes.
Examples & Analogies
Imagine you are following a recipe while cooking. The 'shift' action is like adding an ingredient to your bowl. The 'reduce' action is like combining multiple ingredients into a single dish; once you combine them, you replace the ingredients on your counter with the new dish. The 'accept' action means youβve finished cooking and can serve your dish. The 'GOTO' here is like checking your recipe to see what the next step is after combining specific ingredients.
SLR Conflicts
Chapter 3 of 3
π Unlock Audio Chapter
Sign up and enroll to access the full audio experience
Chapter Content
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:
- Shift/Reduce Conflict: A state implies both a shift on a terminal a and a reduce action.
- Reduce/Reduce Conflict: A state implies reductions by two different rules for the same lookahead terminal.
Detailed Explanation
SLR conflicts indicate that the grammar being processed may not be suitable for SLR parsing. A conflict occurs when the ACTION table has more than one possible action for the same state and terminal. For example, if the table suggests both a shift and a reduce for the same input, the parser cannot decide which action to take, leading to ambiguity. The presence of multiple rules for a single terminal in a reduce context creates conflicting interpretations, preventing successful parsing.
Examples & Analogies
Consider a situation where a guest arrives at a restaurant and the hostess is unsure whether to seat them at a table or ask them to wait because two reservations overlap for similar times. Just like the hostess faced with conflicting decisions, the parser encounters a problem when its table prompts it to take two different actions for one input. This conflict hampers the ability to follow a clear path for processing the input, leading to confusion.
Key Concepts
-
SLR Parsing: A bottom-up parsing strategy that utilizes LR(0) items and FOLLOW sets to construct parsing tables.
-
ACTION Table: A component of the SLR table that describes the operations to perform on terminal symbols.
-
GOTO Table: A component of the SLR table that guides transitions between states involving non-terminals.
-
FOLLOW Set: A critical tool that helps manage reduction decisions in the parsing process.
Examples & Applications
Example of an ACTION Table for a grammar where actions specify shifts upon specific tokens.
Illustration of a GOTO Table highlighting moves for non-terminal reductions.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
SHIFT to bring tokens near, REDUCE when structures appear!
Stories
Imagine a parser as an explorer navigating a maze. The ACTION table gives directions on whether to move forward into the maze or retreat back to gather more clues, ensuring no dead ends occur.
Memory Tools
Remember 'SAG' for SLR: 'Shift', 'Accept', 'Goto!'
Acronyms
S-L-R
'Simple'
'Logic'
'Rules' - a systematic way to organize parsing actions and transitions.
Flash Cards
Glossary
- SLR Parsing Table
A table that directs the actions of a parser based on its state and lookahead terminal, maximized for efficiency in parsing.
- ACTION Table
A table entry that indicates the action a parser should take, such as shift, reduce, accept, or error.
- GOTO Table
A table that specifies the next state transition for a non-terminal during parsing.
- FOLLOW Set
A collection of terminals that can appear immediately after a non-terminal in some sentential form.
- Shift/Reduce Conflict
An ambiguous situation where a parser must decide whether to shift a terminal or reduce it to a non-terminal.
- Reduce/Reduce Conflict
A situation in a parser where multiple reduction rules can apply to the same lookahead terminal.
Reference links
Supplementary resources to enhance your learning experience.