LR Parsing: A Bottom-Up Parsing Technique for Compilers

Learn about LR parsing, a powerful bottom-up parsing technique used in compilers. This guide explains LR parsing's functionality, its deterministic nature, different LR variations (LALR, SLR), and the requirements for implementing an LR parser.

LR Parsing: A Bottom-Up Parsing Technique

Understanding LR Parsing

LR parsing is a powerful bottom-up parsing technique used in compilers to analyze source code and check if it conforms to the rules of a programming language’s grammar. It's called LR parsing because:

• L: The input string is scanned from left to right.
• R: It constructs a rightmost derivation in reverse.
• k: It uses a k-symbol lookahead to make parsing decisions (LR(k) parsing; k is often 0 or 1).

LR parsing is deterministic; for every input symbol and state, there's only one action the parser can take. This makes it efficient compared to other parsing techniques that might involve backtracking. The algorithm attempts to reduce the input string to the start symbol by applying grammar rules.

Types of LR Parsing

Several variations of LR parsing exist, each with its own characteristics and complexities:

• LR(0)
• SLR(1) (Simple LR)
• CLR(1) (Canonical LR)
• LALR(1) (Look-Ahead LR)

The LR Parsing Algorithm

The LR parsing algorithm requires:

• A stack: Stores grammar symbols ($ at the bottom).
• An input buffer: Contains the input string ($ at the end).
• A parsing table: A two-dimensional table guiding parsing actions (actions and go-to transitions).

The algorithm uses the parsing table to determine the next action based on the current stack state and input symbol. The parsing table will differ depending on the type of LR parsing being used.

LR(1) Parsing: Steps and Augmented Grammars

LR(1) parsing involves these steps:

1. Define the Context-Free Grammar: Specify the grammar rules for the language.
2. Check for Ambiguity: Ensure the grammar is unambiguous (only one parse tree exists for each valid input).
3. Augment the Grammar: Add a new start symbol to help the parser determine when parsing is complete.
4. Construct LR(0) Items: Create the canonical collection of LR(0) items. These items represent possible states in the DFA.
5. Create the DFA: Construct a Deterministic Finite Automaton (DFA) from the LR(0) items.
6. Create the LR(1) Parsing Table: Generate the parsing table based on the DFA.

Augmenting Grammars

Augmenting a grammar involves adding a new production rule with a new start symbol. The purpose is to provide a clear indication when the parse is complete. For example, given this grammar:

S → AA
A → aA | b

The augmented grammar would be:

S' → S
S → AA
A → aA | b