bottom up and lr parsing notes

Chapter Roadmap: Bottom-Up and LR Parsing

Chapter Roadmap: Bottom-Up and LR Parsing Building the parse tree from leaves to root: rightmost derivation in reverse. Your Learning Journey 1. Bottom-Up Parser Types and LR Grammar Classes The foundation. Understanding handle pruning, rightmost derivations in reverse, and the strict hierarchy of LR(0), SLR(1), LALR(1), and CLR(1) parsers. 2. Operator Precedence and Shift-Reduce Parsing The mechanics. How shift-reduce parsing works in practice, identifying handles, and the specialized rules of operator precedence grammars. 3. LR Item Closure and GOTO Computation The engine. Step-by-step construction of canonical collections of LR items, the CLOSURE operation, and the GOTO function that builds the parsing DFA. 4. LR Parsing Conflicts and Grammar Ambiguity The resolution. Identifying shift-reduce and reduce-reduce conflicts, understanding why they occur, and techniques to resolve them or prove a grammar is not LR. Chapter Weightage: High. Expect 1 to 2 questions directly testing LR item construction, conflict identification, or grammar class hierarchy.

Bottom-Up Parser Types and LR Grammar Classes

Bottom-Up Parser Types and LR Grammar Classes Why this matters: Bottom-up parsing is the most powerful class of deterministic parsing. It forms the basis of almost all automatic parser generators (like YACC and Bison) used in real-world compilers. What you will learn here The core concept of "handle pruning" and rightmost derivation in reverse The meaning of the L, R, and k in LR(k) parsing The strict hierarchy of LR grammar classes: LR(0), SLR(1), LALR(1), and CLR(1) How lookahead power trades off with the number of parser states Chapter context: Parser Types and LR Classes \to Shift-Reduce Mechanics \to Item Closure and GOTO \to Conflict Resolution

The Bottom-Up Parsing Strategy

The Bottom-Up Parsing Strategy Bottom-up parsing builds a parse tree from the leaves (input tokens) up to the root (start symbol). Core Mechanism: Handle Pruning Start with the input string of terminals. Identify a handle: A substring that matches the right-hand side of some production A \to β, such that reducing β to A represents one step along the reverse of a rightmost derivation. Reduce: Replace the handle β with the non-terminal A . Repeat until the string is reduced to the start symbol S . Rightmost Derivation in Reverse If a grammar generates a string via a rightmost derivation: S \Rightarrow_{r m}^{*} α A w \Rightarrow_{r m} α β w \Rightarrow_{r m}^{*} input string Then the bottom-up parser reverses this: input string \Rightarrow_{r m}^{*} α β w \Rightarrow_{r m} α A w \Rightarrow_{r m}^{*} S The substring β in the right-sentential form α β w is the handle .

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Bottom-Up and LR Parsing Notes for GATE CS

Bottom-Up and LR Parsing notes for GATE CS: 34 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Chapter Roadmap: Bottom-Up and LR Parsing

Building the parse tree from leaves to root: rightmost derivation in reverse.

Your Learning Journey

1. Bottom-Up Parser Types and LR Grammar Classes

The foundation. Understanding handle pruning, rightmost derivations in reverse, and the strict hierarchy of LR(0), SLR(1), LALR(1), and CLR(1) parsers.

2. Operator Precedence and Shift-Reduce Parsing

The mechanics. How shift-reduce parsing works in practice, identifying handles, and the specialized rules of operator precedence grammars.

3. LR Item Closure and GOTO Computation

The engine. Step-by-step construction of canonical collections of LR items, the CLOSURE operation, and the GOTO function that builds the parsing DFA.

4. LR Parsing Conflicts and Grammar Ambiguity

The resolution. Identifying shift-reduce and reduce-reduce conflicts, understanding why they occur, and techniques to resolve them or prove a grammar is not LR.

Chapter Weightage: High. Expect 1 to 2 questions directly testing LR item construction, conflict identification, or grammar class hierarchy.

Bottom-Up Parser Types and LR Grammar Classes

Why this matters: Bottom-up parsing is the most powerful class of deterministic parsing. It forms the basis of almost all automatic parser generators (like YACC and Bison) used in real-world compilers.

What you will learn here

The core concept of "handle pruning" and rightmost derivation in reverse
The meaning of the L, R, and k in LR(k) parsing
The strict hierarchy of LR grammar classes: LR(0), SLR(1), LALR(1), and CLR(1)
How lookahead power trades off with the number of parser states

Chapter context: Parser Types and LR Classes → Shift-Reduce Mechanics → Item Closure and GOTO → Conflict Resolution

The Bottom-Up Parsing Strategy

Bottom-up parsing builds a parse tree from the leaves (input tokens) up to the root (start symbol).

Core Mechanism: Handle Pruning

Start with the input string of terminals.
Identify a handle: A substring that matches the right-hand side of some production $A \to β$ , such that reducing $β$ to $A$ represents one step along the reverse of a rightmost derivation.
Reduce: Replace the handle $β$ with the non-terminal $A$ .
Repeat until the string is reduced to the start symbol $S$ .

Rightmost Derivation in Reverse

If a grammar generates a string via a rightmost derivation:

S \Rightarrow_{r m}^{*} α A w \Rightarrow_{r m} α β w \Rightarrow_{r m}^{*} input string

Then the bottom-up parser reverses this:

input string \Rightarrow_{r m}^{*} α β w \Rightarrow_{r m} α A w \Rightarrow_{r m}^{*} S

The substring $β$ in the right-sentential form $α β w$ is the handle.

Understanding LR(k) Notation

The notation $L R (k)$ precisely defines the capabilities of a bottom-up parser:

L: Left-to-right scanning of the input string.

R: Constructing a Rightmost derivation in reverse.

k: The number of lookahead input symbols used to make parsing decisions.

Why $k = 1$ is Standard

While $L R (k)$ parsers exist for $k > 1$ , they are rarely used in practice because:

Most programming language constructs can be parsed deterministically with just one symbol of lookahead.
Increasing $k$ exponentially increases the size of the parsing table, making it impractical.
Any $L R (k)$ grammar can be transformed into an equivalent $L R (1)$ grammar (though this may increase the number of states).