Bottom-Up Parsing (Shift-Reduce Parsing)
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Overview of Bottom-Up Parsing
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Welcome, everyone! Today weβre starting with Bottom-Up Parsing. Can anyone explain what paradigm it represents?
Isnβt it where the parser starts from the input tokens and works its way up to construct a tree?
Exactly! We begin by using the input tokens. What do we do with these tokens?
We shift them onto a stack until we can reduce them?
Correct! When we can reduce, it means we can replace some symbols on the stack with a non-terminal representing those symbols. This is a key action in our Parsing strategies.
So, shifting and reducing helps in forming the parse tree from bottom to top?
Exactly! Keep that in mind as we move forward. Remember the acronym SR for Shift and Reduce, which captures our main actions.
To conclude this session, whatβs the overall goal of Bottom-Up Parsing?
To successfully parse the entire input, building up to the start symbol!
Components of Shift-Reduce Parsing
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Letβs dive into the components of Shift-Reduce Parsing. What are the primary tools used by the parser?
The input buffer and the stack!
Great! And what does each component hold?
The input buffer holds the stream of tokens, while the stack holds symbols that are either terminals or non-terminals.
Exactly! Now, can you explain how the parsing table fits into this process?
It guides the parser's decisions on whether to shift or reduce based on the current state and the lookahead token.
Spot on! And we need to remember that both decisions depend on the symbols seen in the stack. Can anyone recall what happens if a valid action cannot be performed?
A syntax error is reported!
Exactly! Always useful to keep error handling in mind. So, what are the four main actions performed during parsing?
Shift, reduce, accept, and error!
Absolutely! Great retention. Letβs summarize: the input buffer and stack are crucial tools, and the parsing table drives our actions.
Understanding Viable Prefixes and Items
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Now, letβs talk about viable prefixes in parsing. Who can define what a viable prefix is?
A viable prefix is any prefix of a rightmost sentential form that can exist on the stack while parsing.
Good! And how does understanding these prefixes help us as parsers?
If we know the prefixes that are viable, we can make better decisions about what to shift and when to reduce.
Precisely! Now, what about items? How do they function in Shift-Reduce Parsing?
Items represent a production rule with a dot indicating how much of the right-hand side has been recognized so far.
Exactly! They are critical for building states in our parser. Remember the format A -> Ξ± . Ξ². Can anyone give an example?
Sure! E -> .E + E means we expect more input to be E + E.
Perfect! That clarity will help in parsing decisions.
To summarize this session, viable prefixes and items are crucial in guiding parsing actions and decisions.
Constructing LR Parsing Tables
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Letβs move on to constructing LR parsing tables. Whatβs the first step in this process?
We need to create an augmented grammar by adding a new start production.
Correct! Why do we do that?
To ensure a clear indication when the parsing is successful!
Exactly! After that, what is the next important operation we perform?
The CLOSURE operation, right?
Yes! It expands a set of items based on the items collected thus far. What happens after we perform the CLOSURE?
Then we apply the GOTO operation!
Correct! GOTO determines the next state after recognizing a grammar symbol. How do we build the canonical collection of LR(0) items?
We start with initial state I_0 and use CLOSURE repeatedly to build our states.
Excellent work! This process is essential in ensuring parser efficiency. Letβs conclude this session with a summary of constructing LR tables: start with an augmented grammar, perform CLOSURE and GOTO, and build unique states.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
Shift-Reduce parsing, a key technique in bottom-up parsing, proceeds by reading input tokens and building a parse tree upwards. The parser uses a stack to manage symbols and applies production rules iteratively to match and reduce sequences into higher-level constructs before accepting or reporting errors.
Detailed
Bottom-Up Parsing (Shift-Reduce Parsing)
In this section, we delve into Shift-Reduce Parsing, a fundamental strategy of bottom-up parsing where the process begins with the input tokens and builds a parse tree incrementally upwards. The parser utilizes two main data structures: a stack which holds the symbols currently in scope and an input buffer containing the stream of tokens produced by the lexical analyzer. The Shift-Reduce Parsing process entails the following core actions:
- Shift: Move the next token from the input buffer to the stack.
- Reduce: If the top symbols on the stack match the right-hand side of a production rule, pop them off the stack and push the corresponding non-terminal.
- Accept: If the stack contains only the start symbol and the input buffer is empty, the parse is successful.
- Error: If no valid action can be carried out, a syntax error is raised.
Viable Prefixes and Items are essential concepts in guiding parser decisions. The parser tracks viable prefixes of valid sentential forms and utilizes items to represent the state of the parsing process. Constructing LR(0) sets of items leads to creating parsing tables that orchestrate the parsing actions based on the current parser state and next token. By employing the SLR (Simple LR) strategy, a parser can effectively resolve shift/reduce conflicts and reduce/reduce conflicts to ensure efficient processing of inputs with a formal grammar.
This section provides insight into not only how to implement Shift-Reduce Parsing but also its significance in modern compiler design, emphasizing automated parsing techniques and their importance in compiler construction.
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Constructing LR(0) Sets of Items
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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.
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.
4. Building the Canonical Collection of LR(0) Items: This algorithm generates all unique states. It starts with an initial state I_0=CLOSURE(Sβ²to.S). Then, for each state I and every grammar symbol X that appears after a dot in I, it computes J=GOTO(I,X). If J is new, it's added to the collection and processed. The resulting collection of states forms the basis for constructing the LR parsing tables.
Detailed Explanation
Building an LR parser involves defining a set of potential parsing states that can occur during the parsing process. The first step in this procedure is to augment the grammar by introducing a new start symbol, which provides clarity on successful parsing. The next step is the CLOSURE operation, which examines each item and identifies all possible productions that could expand from a given non-terminal. By doing so, it enhances the existing set of items with new potential productions until no more can be added. The GOTO operation then predicts what state the parser will transition into when it recognizes a particular grammar symbol. Following this, the entire process can be repeated to gather a comprehensive collection of all unique parsing states, which then form the foundation for constructing parsing tables required for the parser's decision-making.
Examples & Analogies
Imagine you're organizing a room (the grammar) for an event. When you first enter, you might add placeholders (the augmented grammar) for everything you need to set up (make it clear what the end goal is). As you determine what each area requires (the CLOSURE operation), you take stock of everything essential and possible adjustments you might need (every production that could occur). Next, you figure out how to rearrange what's already present once adjustments are made (the GOTO operation). Finally, by constantly reassessing your layout and gathering various configurations (the collection of LR(0) items), you ensure the best setup for the event, making it accessible and efficient for everyone attending.
Key Concepts
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Bottom-Up Parsing: A strategy beginning with input tokens to build parse trees upwards.
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Shift-Reduce Parsing: A specific method within bottom-up parsing involving shifting and reducing actions.
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Viable Prefixes: Prefixes of valid sentential forms that guide parser actions.
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Items: Representations of production rules in parsing indicating recognized input.
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CLOSURE Operation: Expands items in the state set to include derivations.
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GOTO Operation: Determines the parsing state after recognizing symbols.
Examples & Applications
In parsing the expression a + b, the parser begins with shifting 'a' and 'b' onto the stack and reducing when the stack matches the right-hand side of a production rule.
An example of a viable prefix is '$E+' where the parser has recognized that 'E' can lead to a valid reduction.
Memory Aids
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Rhymes
In parsing, first we Shift with glee, then Reduce to see, our grammarβs structure clear as can be.
Stories
Imagine building a tower with blocks (tokens). First, you stack the blocks up (Shift), and when they match a pre-defined design (Reduce), you replace them with a label (non-terminal). Then you check if what's left is stable (Accept) or if it toppled (Error).
Memory Tools
Remember the acronym S.R.A.E for Shift, Reduce, Accept, Error in parsing actions.
Acronyms
SRAE for Shift, Reduce, Accept, Error helps us recall the actions in parsing!
Flash Cards
Glossary
- BottomUp Parsing
A parsing strategy that begins with input tokens and works upward to construct a parse tree.
- ShiftReduce Parsing
A technique within bottom-up parsing that involves shifting input tokens onto a stack and reducing sequences into non-terminals based on grammar.
- Viable Prefix
A prefix of a rightmost sentential form that can exist on the stack during Shift-Reduce parsing.
- Item (LR(0) Item)
A production rule with a 'dot' indicating how much of the right-hand side has been recognized.
- Action Table
A table that directs the parser on whether to shift, reduce, accept, or report an error based on current state and input.
- CLOSURE Operation
An operation that expands a set of LR(0) items to include all items that can be derived from the current state.
- GOTO Operation
An operation that finds the next state of the parser after recognizing a grammar symbol.
- LR Parsing
A family of bottom-up parsing strategies that process symbols from left to right and attempt to reduce them to a start symbol.
- SLR Parsing
Simple LR parsing, which builds on LR(0) parsing but incorporates FOLLOW sets to make reduce decisions.
Reference links
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