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Compiler Design CLR(1) Parsing

Compiler Design: CLR(1) Parsing

In the field of compiler design, CLR(1) parsing is an important concept. It is a bottom-up parsing technique that is used to analyze and understand the structure of a given source code. CLR(1) parsing is based on a parsing table called the Canonical LR(1) Parsing Table, which is constructed from the given grammar. In this article, we will explore the concept of CLR(1) parsing and provide examples to illustrate its usage.

Understanding Parsing

Parsing is the process of analyzing a sequence of tokens (lexical units) based on a given grammar. It involves determining the syntactic structure of the input and creating a parse tree that represents the hierarchical relationship between the tokens. There are different parsing techniques, such as top-down parsing and bottom-up parsing, each with its own advantages and limitations.

Bottom-Up Parsing

Bottom-up parsing is a technique where the parser starts with the input tokens and tries to reduce them to the start symbol of the grammar. It is also known as shift-reduce parsing because it involves shifting tokens onto a stack and then reducing them based on the grammar rules. Bottom-up parsing is more powerful than top-down parsing as it can handle a wider range of grammars.

CLR(1) Parsing

CLR(1) parsing is a specific type of bottom-up parsing that is based on the Canonical LR(1) Parsing Table. CLR stands for “Canonical LR” and (1) refers to the number of tokens of lookahead used by the parser. The CLR(1) parsing algorithm is efficient and can handle a large class of grammars, including left-recursive and ambiguous grammars.

Canonical LR(1) Parsing Table

The Canonical LR(1) Parsing Table is a table that guides the CLR(1) parser in making decisions on how to shift or reduce the input tokens. It is constructed from the given grammar and contains the following information:

  • State numbers: Each row of the table represents a state of the parser.
  • Actions: The actions column specifies whether to shift a token onto the stack or reduce the stack based on the current state and input token.
  • Next state: The next state column indicates the state to transition to after performing a shift operation.
  • Reduce rule: The reduce rule column specifies the grammar rule to be applied when a reduction operation is performed.

Example of CLR(1) Parsing

Let’s consider an example to illustrate the concept of CLR(1) parsing. Suppose we have the following grammar:

S -> EE -> E + T | TT -> T * F | FF -> ( E ) | id

We can construct the Canonical LR(1) Parsing Table for this grammar. The table will have rows representing the states and columns representing the input symbols. Here is a simplified version of the table:

State+*()id$ETF-----------------------------------------0s4s5s1231r2s6r2r22r4r4r4r43r6r6r6r64s4s5s785r8r8r8r86s4s597s4s5108s4s5119r1s6r1r110r3r3r3r311r5r5r5r5

Now, let’s say we have the input string “id + id * id”. We can use the CLR(1) parsing algorithm and the parsing table to parse this input string.

Initially, the parser is in state 0 and the input symbol is “id”. The action in state 0 for “id” is to shift and go to state 5. The parser shifts “id” onto the stack and transitions to state 5.

In state 5, the input symbol is “+”. The action in state 5 for “+” is to shift and go to state 7. The parser shifts “+” onto the stack and transitions to state 7.

In state 7, the input symbol is “id”. The action in state 7 for “id” is to shift and go to state 8. The parser shifts “id” onto the stack and transitions to state 8.

In state 8, the input symbol is “*”. The action in state 8 for “*” is to shift and go to state 11. The parser shifts “*” onto the stack and transitions to state 11.

In state 11, the input symbol is “id”. The action in state 11 for “id” is to shift and go to state 8. The parser shifts “id” onto the stack and transitions to state 8.

Now, the input symbol is “$” (end of input). The action in state 8 for “$” is to reduce by the rule “T -> T * F”. The parser reduces the stack by applying this rule and transitions to state 4.

In state 4, the input symbol is “+”. The action in state 4 for “+” is to shift and go to state 5. The parser shifts “+” onto the stack and transitions to state 5.

In state 5, the input symbol is “id”. The action in state 5 for “id” is to shift and go to state 7. The parser shifts “id” onto the stack and transitions to state 7.

In state 7, the input symbol is “$” (end of input). The action in state 7 for “$” is to reduce by the rule “E -> E + T”. The parser reduces the stack by applying this rule and transitions to state 1.

In state 1, the input symbol is “$” (end of input). The action in state 1 for “$” is to accept. The parser accepts the input string as valid.

This example demonstrates the step-by-step process of CLR(1) parsing using the parsing table. It shows how the parser shifts and reduces the input symbols based on the grammar rules and the current state of the parser.

Conclusion

CLR(1) parsing is a powerful bottom-up parsing technique used in compiler design. It allows for efficient and accurate parsing of a wide range of grammars. By constructing the Canonical LR(1) Parsing Table from the given grammar, the CLR(1) parser can analyze and understand the structure of the input source code. Understanding CLR(1) parsing is essential for anyone involved in compiler design and implementation.

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