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What is bottom-up parsing in compiler design?

Published in Compiler Design 3 mins read

Bottom-up parsing is a method used in compiler design to analyze a sequence of input tokens (like words or symbols) and build a parse tree representing the grammatical structure of the input. It works by starting with the individual tokens and progressively combining them into larger structures until the entire input is represented as a single parse tree.

Here's how it works:

  • Starts from the bottom: It begins with the individual tokens of the input string.
  • Builds upwards: It gradually combines these tokens into larger structures based on the grammar rules.
  • Uses a stack: A stack data structure is used to store the intermediate parse tree nodes as they are constructed.
  • Applies grammar rules: It repeatedly applies the grammar rules to the stack until a single tree representing the entire input is formed.
  • Goal: The goal is to reduce the input string to the start symbol of the grammar, indicating a successful parse.

Types of Bottom-Up Parsing:

There are two main types of bottom-up parsing:

  1. Shift-Reduce Parsing: This is the most common type of bottom-up parsing. It alternates between two actions:
    • Shift: Moves the next input token onto the stack.
    • Reduce: Applies a grammar rule to replace a sequence of symbols on the stack with a non-terminal symbol.
  2. LR Parsing: This is a more powerful and efficient type of bottom-up parsing. It uses a deterministic finite automaton (DFA) to determine the appropriate action (shift or reduce) based on the current state and the input token. LR parsers are generally faster and more efficient than shift-reduce parsers.

Example:

Let's consider a simple grammar for arithmetic expressions:

E -> E + T
E -> T
T -> T * F
T -> F
F -> ( E )
F -> id

Suppose we want to parse the expression id + id * id.

A bottom-up parser would start with the individual tokens: id, +, id, *, id. It would then combine these tokens based on the grammar rules, eventually building the parse tree representing the entire expression.

Advantages of Bottom-Up Parsing:

  • Handles left recursion: It can handle left-recursive grammars, which are difficult for top-down parsers.
  • More efficient: It can be more efficient than top-down parsing for some grammars.
  • Can detect errors early: It can detect syntax errors early in the parsing process.

Disadvantages of Bottom-Up Parsing:

  • More complex: It can be more complex to implement than top-down parsing.
  • Can be inefficient for some grammars: It can be inefficient for some grammars, especially those with many ambiguous rules.

Conclusion:

Bottom-up parsing is an essential technique in compiler design for analyzing input code and building a parse tree representing its grammatical structure. It starts from the individual tokens and progressively combines them into larger structures, using grammar rules to guide the process. This method is efficient for handling left-recursive grammars and can detect syntax errors early.

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