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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?
A parser checks the syntax of code to make sure it's correct.
Exactly! And Shift-Reduce parsing does it by using a stack to manage symbols. How do you think this could be useful?
It helps organize the code structure by breaking it down into manageable pieces.
Correct! Remember this acronym: 'S-R' for Shift-Reduce parsing. Let's begin with how the Shift action works.
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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?
It replaces symbols on the stack with a non-terminal?
Correct! It condenses multiple symbols into one non-terminal, simplifying the stack. Now, letβs go through a practical example with the expression 'a + b'. What would we do first?
We would Shift 'a' onto the stack.
Excellent! And when we see the '+'?
We would Shift it onto the stack too after processing 'a'!
Great! Remember, as you Shift and Reduce, you're building towards the final parse tree.
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Let's analyze how we can parse 'a + b'. Beginning with an empty stack and full input: '$ a + b $'. Whatβs our first move?
Shift 'a' onto the stack!
Correct! So now our stack has '$ a'. Next?
We can reduce 'a' to 'E' since 'a' is an ID.
Exactly! Now our stack is '$ E'. Whatβs next?
Shift '+' onto the stack.
Right! Now, if we continue with 'b', we can apply the same steps. Who can summarize the process so far?
We shifted 'a', reduced it to 'E', shifted '+' and then shifted 'b' onto the stack as well.
Wonderful! Now we know how to construct and interpret every step in Shift-Reduce Parsing.
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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.
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).
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.
Given a simplified grammar: E -> E + E | ID
$
a + b $
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.
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Assume simplified grammar: E -> E + E | ID
Initial state: Stack: $ | Input: a + b $ (where $ marks end of input)
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.
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.
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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! |
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.
Imagine you're assembling a sandwich. Each stepβadding the ingredients (tokens) like lettuce, tomatoes, and cucumbers (letters)βrepresents 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!
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Final state: Stack contains start symbol, and input is empty.
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.
Think of finishing a puzzle: youβve 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.
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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.
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Parsing the expression 'a + b' where 'a' and 'b' are variables and '+' is an operator.
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
Shift the floor, Reduce the core, Stack it right, Parse in sight.
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).
S-R: Shift first, then Reduce, to make parsing a breeze.
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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.