Bottom-up parsing techniques (LR parsing)

Bottom-up parsing is a vital concept in the field of compiler design. It is the process of analyzing and parsing a string of tokens to recognize the underlying grammar rules and structure of a programming language from the bottom (input) to the top (output). LR parsing, which stands for Left-to-right, Rightmost derivation, is one of the most commonly used bottom-up parsing techniques.

Introduction to LR parsing

LR parsing utilizes a parsing technique based on a bottom-up approach where it builds the parse tree from leaf nodes up to the root. It starts with the input tokens and applies a set of production rules until it successfully identifies the root of the parse tree. LR parsing is an efficient and robust parsing technique widely used in modern compiler design.

LR Parsing Algorithm

The LR parsing algorithm involves several key components:

  1. LR(0) items: LR(0) items represent a configuration of the parser's state. Each item contains a production rule with a dot representing the current position in the rule. The parser uses these items to explore different possibilities during the parsing process.

  2. LR(0) Automaton: The LR(0) automaton is a directed graph that represents the states and transitions in the parsing process. Each state represents a set of items, and the transitions between states occur as the parser consumes tokens.

  3. Parsing Table: The parsing table is a crucial data structure that guides the parser's actions during the parsing process. It consists of two types of entries: Action entries and Goto entries. The action entries dictate the parser's shifts and reductions, while the Goto entries represent state transitions.

  4. Shift-Reduce Parsing: During the shift-reduce parsing, the parser shifts the input token onto the stack, or it reduces a set of tokens on the stack to a non-terminal symbol using a production rule. This process continues until it reaches the accept state or encounters an error.

LR parsing types

There are several variants of LR parsing algorithms, namely LR(0), SLR(1), LALR(1), and LR(1), which differ in terms of their lookahead and conflict resolution abilities. These variants provide different levels of parsing power and parsing table sizes.

  1. LR(0): The LR(0) parser has no lookahead, and it uses the dot notation to indicate the current position within a production rule. It has a small parsing table but can suffer from shift-reduce and reduce-reduce conflicts.

  2. SLR(1): The SLR(1) parser improves upon the LR(0) parser by utilizing a simple and static lookahead for conflict resolution. It resolves shift-reduce conflicts by looking at the Follow set of the non-terminal symbols.

  3. LALR(1): The LALR(1) parser further enhances the SLR(1) parser by using a more compact state representation. It reduces the parsing table's size and retains the same parsing power as the SLR(1) parser.

  4. LR(1): The LR(1) parser has a greater lookahead capability as compared to the previous parsers. It considers the immediate terminal symbol as well as the immediate context to resolve conflicts.

Advantages and disadvantages of LR parsing

LR parsing offers several advantages in compiler design:

  • It can handle a wide range of programming languages efficiently.
  • LR parsing supports left-recursive grammar rules.
  • It provides a systematic approach for error recovery.

However, LR parsing also has a few limitations:

  • Building LR parsing tables can be computationally expensive, especially for LR(1) parsers.
  • It may suffer from conflicts, such as shift-reduce or reduce-reduce conflicts, that require conflict resolution strategies.
  • Understanding and implementing LR parsing algorithms can be challenging for beginners.


Bottom-up parsing techniques, especially LR parsing, play a crucial role in compiler design. They provide efficient and powerful methods to analyze and parse the underlying grammar of a programming language. Various LR parsing variants, such as LR(0), SLR(1), LALR(1), and LR(1), offer different trade-offs in parsing power and table size. Despite some challenges, LR parsing remains a fundamental tool for designing robust compilers that can handle complex programming languages.

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